LifeWiki - User contributions [en]

Rule:Trine

2023-11-25T10:12:55Z

Freywa: Universal Triangle Rule update

@RULE Trine

A hybrid of Wireworld Modern (https://conwaylife.com/forums/viewtopic.php?f=11&t=3640)
and Wireworld5 (https://conwaylife.com/forums/viewtopic.php?f=11&t=5035)
with truly inline inverters and rephasers.

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@TABLE
neighborhood: Moore
symmetries: rotate4reflect
n_states: 7

var any.0 = {0,1,2,3,4,5,6}
var any.1 = any.0
var any.2 = any.0
var any.3 = any.0
var any.4 = any.0
var any.5 = any.0
var any.6 = any.0
var any.7 = any.0
var A.0 = {1,4}
var A.1 = A.0
var A.2 = A.0
var B.0 = {2,5}
var B.1 = B.0
var B.2 = B.0
var C.0 = {3,6}
var C.1 = C.0
var C.2 = C.0
var An.0 = {0,2,5}
var An.1 = An.0
var An.2 = An.0
var An.3 = An.0
var An.4 = An.0
var An.5 = An.0
var An.6 = An.0
var Bn.0 = {0,3,6}
var Bn.1 = Bn.0
var Bn.2 = Bn.0
var Bn.3 = Bn.0
var Bn.4 = Bn.0
var Bn.5 = Bn.0
var Bn.6 = Bn.0
var Cn.0 = {0,1,4}
var Cn.1 = Cn.0
var Cn.2 = Cn.0
var Cn.3 = Cn.0
var Cn.4 = Cn.0
var Cn.5 = Cn.0
var Cn.6 = Cn.0
var _a0.0 = {0,1,2,4,5}
var _a0.1 = _a0.0
var _a0.2 = _a0.0
var _a0.3 = _a0.0
var _a0.4 = _a0.0
var _a0.5 = _a0.0
var _a0.6 = _a0.0
var _b0.0 = {0,2,3,5,6}
var _b0.1 = _b0.0
var _b0.2 = _b0.0
var _b0.3 = _b0.0
var _b0.4 = _b0.0
var _b0.5 = _b0.0
var _b0.6 = _b0.0
var _c0.0 = {0,1,3,4,6}
var _c0.1 = _c0.0
var _c0.2 = _c0.0
var _c0.3 = _c0.0
var _c0.4 = _c0.0
var _c0.5 = _c0.0
var _c0.6 = _c0.0

A.0, B.0, any.0, B.1, any.1, Cn.0, 6, Cn.1, any.2, 4
B.0, An.0, 4, An.1, any.0, C.0, any.1, C.1, any.2, 5
C.0, A.0, any.0, A.1, any.1, Bn.0, 5, Bn.1, any.2, 6
A.0, B.0, any.0, Cn.0, 6, Cn.1, _a0.0, _a0.1, any.1, 4
B.0, An.0, 4, An.1, any.0, C.0, any.1, _b0.0, _b0.1, 5
C.0, A.0, any.0, Bn.0, 5, Bn.1, _c0.0, _c0.1, any.1, 6
A.0, Cn.0, 6, Cn.1, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, 4
B.0, An.0, 4, An.1, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, 5
C.0, Bn.0, 5, Bn.1, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, 6
A.0, 6, _a0.0, B.0, any.0, _a0.1, any.1, B.1, _a0.2, 4
B.0, 4, _b0.0, C.0, any.0, _b0.1, any.1, C.1, _b0.2, 5
C.0, 5, _c0.0, A.0, any.0, _c0.1, any.1, A.1, _c0.2, 6
A.0, 6, _a0.0, _a0.1, any.0, B.0, any.1, _a0.2, _a0.3, 4
B.0, 4, _b0.0, _b0.1, any.0, C.0, any.1, _b0.2, _b0.3, 5
C.0, 5, _c0.0, _c0.1, any.0, A.0, any.1, _c0.2, _c0.3, 6
A.0, 6, _a0.0, _a0.1, _a0.2, _a0.3, any.0, B.0, any.1, 4
B.0, 4, _b0.0, _b0.1, _b0.2, _b0.3, any.0, C.0, any.1, 5
C.0, 5, _c0.0, _c0.1, _c0.2, _c0.3, any.0, A.0, any.1, 6
A.0, 6, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, _a0.5, _a0.6, 4
B.0, 4, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, _b0.5, _b0.6, 5
C.0, 5, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, _c0.5, _c0.6, 6
A.0, 1, An.0, An.1, An.2, An.3, An.4, An.5, An.6, 4
A.0, An.0, 1, An.1, An.2, An.3, An.4, An.5, An.6, 4
A.0, 4, An.0, An.1, An.2, An.3, An.4, An.5, An.6, 1
A.0, An.0, 4, An.1, An.2, An.3, An.4, An.5, An.6, 1
B.0, 2, Bn.0, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, Bn.6, 5
B.0, Bn.0, 2, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, Bn.6, 5
B.0, 5, Bn.0, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, Bn.6, 2
B.0, Bn.0, 5, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, Bn.6, 2
C.0, 3, Cn.0, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, Cn.6, 6
C.0, Cn.0, 3, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, Cn.6, 6
C.0, 6, Cn.0, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, Cn.6, 3
C.0, Cn.0, 6, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, Cn.6, 3
A.0, 6, C.0, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, C.1, 4
B.0, 4, A.0, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, A.1, 5
C.0, 5, B.0, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, B.1, 6
A.0, 6, 6, A.1, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, 4
B.0, 4, 4, B.1, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, 5
C.0, 5, 5, C.1, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, 6
A.0, 3, 6, Cn.0, any.0, B.0, any.1, B.1, any.2, 4
B.0, 1, 4, An.0, any.0, C.0, any.1, C.1, any.2, 5
C.0, 2, 5, Bn.0, any.0, A.0, any.1, A.1, any.2, 6
A.0, 3, 6, Cn.0, any.0, B.0, any.1, _a0.0, _a0.1, 4
B.0, 1, 4, An.0, any.0, C.0, any.1, _b0.0, _b0.1, 5
C.0, 2, 5, Bn.0, any.0, A.0, any.1, _c0.0, _c0.1, 6
A.0, 3, 6, Cn.0, _a0.0, _a0.1, any.0, B.0, any.1, 4
B.0, 1, 4, An.0, _b0.0, _b0.1, any.0, C.0, any.1, 5
C.0, 2, 5, Bn.0, _c0.0, _c0.1, any.0, A.0, any.1, 6
A.0, 3, 6, Cn.0, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, 4
B.0, 1, 4, An.0, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, 5
C.0, 2, 5, Bn.0, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, 6
A.0, 1, 4, An.0, An.1, An.2, An.3, An.4, An.5, 1
A.0, A.1, A.2, An.0, An.1, An.2, An.3, An.4, An.5, 4
B.0, 2, 5, Bn.0, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, 2
B.0, B.1, B.2, Bn.0, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, 5
C.0, 3, 6, Cn.0, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, 3
C.0, C.1, C.2, Cn.0, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, 6
A.0, B.0, any.0, Cn.0, 6, Cn.1, C.0, Cn.2, any.1, 4
B.0, An.0, 4, An.1, A.0, An.2, any.0, C.0, any.1, 5
C.0, A.0, any.0, Bn.0, 5, Bn.1, B.0, Bn.2, any.1, 6
A.0, Cn.0, 6, Cn.1, C.0, Cn.2, _a0.0, _a0.1, _a0.2, 4
B.0, An.0, 4, An.1, A.0, An.2, _b0.0, _b0.1, _b0.2, 5
C.0, Bn.0, 5, Bn.1, B.0, Bn.2, _c0.0, _c0.1, _c0.2, 6
A.0, An.0, 1, An.1, 1, An.2, An.3, An.4, An.5, 4
B.0, Bn.0, 2, Bn.1, 2, Bn.2, Bn.3, Bn.4, Bn.5, 5
C.0, Cn.0, 3, Cn.1, 3, Cn.2, Cn.3, Cn.4, Cn.5, 6
A.0, 6, _a0.0, 6, any.0, B.0, any.1, B.1, any.2, 4
B.0, 4, _b0.0, 4, any.0, C.0, any.1, C.1, any.2, 5
C.0, 5, _c0.0, 5, any.0, A.0, any.1, A.1, any.2, 6
A.0, 6, _a0.0, 6, any.0, B.0, any.1, _a0.1, _a0.2, 4
B.0, 4, _b0.0, 4, any.0, C.0, any.1, _b0.1, _b0.2, 5
C.0, 5, _c0.0, 5, any.0, A.0, any.1, _c0.1, _c0.2, 6
A.0, 6, _a0.0, 6, _a0.1, _a0.2, _a0.3, _a0.4, _a0.5, 4
B.0, 4, _b0.0, 4, _b0.1, _b0.2, _b0.3, _b0.4, _b0.5, 5
C.0, 5, _c0.0, 5, _c0.1, _c0.2, _c0.3, _c0.4, _c0.5, 6
A.0, 1, An.0, A.1, An.1, An.2, An.3, An.4, An.5, 4
B.0, 2, Bn.0, B.1, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, 5
C.0, 3, Cn.0, C.1, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, 6
A.0, 3, _a0.0, Cn.0, 3, Cn.1, any.0, B.0, any.1, A.0
B.0, 1, _b0.0, An.0, 1, An.1, any.0, C.0, any.1, B.0
C.0, 2, _c0.0, Bn.0, 2, Bn.1, any.0, A.0, any.1, C.0
A.0, 3, _a0.0, Cn.0, 6, Cn.1, any.0, B.0, any.1, 4
B.0, 1, _b0.0, An.0, 4, An.1, any.0, C.0, any.1, 5
C.0, 2, _c0.0, Bn.0, 5, Bn.1, any.0, A.0, any.1, 6
1, 6, _a0.0, Cn.0, 6, Cn.1, any.0, B.0, any.1, 4
4, 6, _a0.0, Cn.0, 6, Cn.1, any.0, B.0, any.1, 1
2, 4, _b0.0, An.0, 4, An.1, any.0, C.0, any.1, 5
5, 4, _b0.0, An.0, 4, An.1, any.0, C.0, any.1, 2
3, 5, _c0.0, Bn.0, 5, Bn.1, any.0, A.0, any.1, 6
6, 5, _c0.0, Bn.0, 5, Bn.1, any.0, A.0, any.1, 3
A.0, 3, _a0.0, Cn.0, 3, Cn.1, _a0.1, _a0.2, _a0.3, A.0
B.0, 1, _b0.0, An.0, 1, An.1, _b0.1, _b0.2, _b0.3, B.0
C.0, 2, _c0.0, Bn.0, 2, Bn.1, _c0.1, _c0.2, _c0.3, C.0
A.0, 3, _a0.0, Cn.0, 6, Cn.1, _a0.1, _a0.2, _a0.3, 4
B.0, 1, _b0.0, An.0, 4, An.1, _b0.1, _b0.2, _b0.3, 5
C.0, 2, _c0.0, Bn.0, 5, Bn.1, _c0.1, _c0.2, _c0.3, 6
1, 6, _a0.0, Cn.0, 6, Cn.1, _a0.1, _a0.2, _a0.3, 4
4, 6, _a0.0, Cn.0, 6, Cn.1, _a0.1, _a0.2, _a0.3, 1
2, 4, _b0.0, An.0, 4, An.1, _b0.1, _b0.2, _b0.3, 5
5, 4, _b0.0, An.0, 4, An.1, _b0.1, _b0.2, _b0.3, 2
3, 5, _c0.0, Bn.0, 5, Bn.1, _c0.1, _c0.2, _c0.3, 6
6, 5, _c0.0, Bn.0, 5, Bn.1, _c0.1, _c0.2, _c0.3, 3
A.0, 1, An.0, An.1, A.1, An.2, An.3, An.4, An.5, A.0
B.0, 2, Bn.0, Bn.1, B.1, Bn.2, Bn.3, Bn.4, Bn.5, B.0
C.0, 3, Cn.0, Cn.1, C.1, Cn.2, Cn.3, Cn.4, Cn.5, C.0
A.1, 4, An.0, An.1, A.0, An.2, An.3, An.4, An.5, A.0
B.1, 5, Bn.0, Bn.1, B.0, Bn.2, Bn.3, Bn.4, Bn.5, B.0
C.1, 6, Cn.0, Cn.1, C.0, Cn.2, Cn.3, Cn.4, Cn.5, C.0
A.0, Cn.0, 3, Cn.1, _a0.0, Cn.2, 6, Cn.3, _a0.1, 4
B.0, An.0, 1, An.1, _b0.0, An.2, 4, An.3, _b0.1, 5
C.0, Bn.0, 2, Bn.1, _c0.0, Bn.2, 5, Bn.3, _c0.1, 6
A.1, An.0, A.0, An.1, An.2, An.3, A.0, An.4, An.5, 4
B.1, Bn.0, B.0, Bn.1, Bn.2, Bn.3, B.0, Bn.4, Bn.5, 5
C.1, Cn.0, C.0, Cn.1, Cn.2, Cn.3, C.0, Cn.4, Cn.5, 6
A.0, 3, _a0.0, _a0.1, _a0.2, 6, _a0.3, _a0.4, _a0.5, 4
B.0, 1, _b0.0, _b0.1, _b0.2, 4, _b0.3, _b0.4, _b0.5, 5
C.0, 2, _c0.0, _c0.1, _c0.2, 5, _c0.3, _c0.4, _c0.5, 6
A.1, A.0, An.0, An.1, An.2, A.0, An.3, An.4, An.5, 4
B.1, B.0, Bn.0, Bn.1, Bn.2, B.0, Bn.3, Bn.4, Bn.5, 5
C.1, C.0, Cn.0, Cn.1, Cn.2, C.0, Cn.3, Cn.4, Cn.5, 6
4, any.0, any.1, any.2, any.3, any.4, any.5, any.6, any.7, 1
5, any.0, any.1, any.2, any.3, any.4, any.5, any.6, any.7, 2
6, any.0, any.1, any.2, any.3, any.4, any.5, any.6, any.7, 3

@COLORS
1 175 88 0
2 155 78 0
3 135 68 0
4 255 255 255
5 215 215 215
6 175 175 175

Rule:Trine

2022-12-06T16:07:02Z

Freywa: expanded triangle rule

@RULE Trine

A hybrid of Wireworld Modern (https://conwaylife.com/forums/viewtopic.php?f=11&t=3640)
and Wireworld5 (https://conwaylife.com/forums/viewtopic.php?f=11&t=5035)
with truly inline inverters and rephasers.

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2:
3:
4:
5:
6:

@TABLE
neighborhood: Moore
symmetries: rotate4reflect
n_states: 7

var any.0 = {0,1,2,3,4,5,6}
var any.1 = any.0
var any.2 = any.0
var any.3 = any.0
var any.4 = any.0
var any.5 = any.0
var any.6 = any.0
var any.7 = any.0
var A.0 = {1,4}
var A.1 = A.0
var A.2 = A.0
var B.0 = {2,5}
var B.1 = B.0
var B.2 = B.0
var C.0 = {3,6}
var C.1 = C.0
var C.2 = C.0
var An.0 = {0,2,5}
var An.1 = An.0
var An.2 = An.0
var An.3 = An.0
var An.4 = An.0
var An.5 = An.0
var An.6 = An.0
var Bn.0 = {0,3,6}
var Bn.1 = Bn.0
var Bn.2 = Bn.0
var Bn.3 = Bn.0
var Bn.4 = Bn.0
var Bn.5 = Bn.0
var Bn.6 = Bn.0
var Cn.0 = {0,1,4}
var Cn.1 = Cn.0
var Cn.2 = Cn.0
var Cn.3 = Cn.0
var Cn.4 = Cn.0
var Cn.5 = Cn.0
var Cn.6 = Cn.0
var _a0.0 = {0,1,2,4,5}
var _a0.1 = _a0.0
var _a0.2 = _a0.0
var _a0.3 = _a0.0
var _a0.4 = _a0.0
var _a0.5 = _a0.0
var _a0.6 = _a0.0
var _b0.0 = {0,2,3,5,6}
var _b0.1 = _b0.0
var _b0.2 = _b0.0
var _b0.3 = _b0.0
var _b0.4 = _b0.0
var _b0.5 = _b0.0
var _b0.6 = _b0.0
var _c0.0 = {0,1,3,4,6}
var _c0.1 = _c0.0
var _c0.2 = _c0.0
var _c0.3 = _c0.0
var _c0.4 = _c0.0
var _c0.5 = _c0.0
var _c0.6 = _c0.0

A.0, 6, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, _a0.5, _a0.6, 4
A.0, _a0.0, 6, _a0.1, _a0.2, _a0.3, _a0.4, _a0.5, _a0.6, 4
B.0, 4, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, _b0.5, _b0.6, 5
B.0, _b0.0, 4, _b0.1, _b0.2, _b0.3, _b0.4, _b0.5, _b0.6, 5
C.0, 5, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, _c0.5, _c0.6, 6
C.0, _c0.0, 5, _c0.1, _c0.2, _c0.3, _c0.4, _c0.5, _c0.6, 6
A.0, 1, An.0, An.1, An.2, An.3, An.4, An.5, An.6, 4
A.0, An.0, 1, An.1, An.2, An.3, An.4, An.5, An.6, 4
A.0, 4, An.0, An.1, An.2, An.3, An.4, An.5, An.6, 1
A.0, An.0, 4, An.1, An.2, An.3, An.4, An.5, An.6, 1
B.0, 2, Bn.0, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, Bn.6, 5
B.0, Bn.0, 2, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, Bn.6, 5
B.0, 5, Bn.0, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, Bn.6, 2
B.0, Bn.0, 5, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, Bn.6, 2
C.0, 3, Cn.0, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, Cn.6, 6
C.0, Cn.0, 3, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, Cn.6, 6
C.0, 6, Cn.0, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, Cn.6, 3
C.0, Cn.0, 6, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, Cn.6, 3
A.0, 3, _a0.0, B.0, C.0, _a0.1, _a0.2, _a0.3, _a0.4, 1
A.0, 6, _a0.0, B.0, C.0, _a0.1, _a0.2, _a0.3, _a0.4, 4
A.0, B.0, C.0, _a0.0, _a0.1, Cn.0, 3, Cn.1, _a0.2, 1
A.0, B.0, C.0, _a0.0, _a0.1, Cn.0, 6, Cn.1, _a0.2, 4
A.0, 3, _a0.0, _a0.1, C.0, B.0, any.0, _a0.2, _a0.3, 1
A.0, 6, _a0.0, _a0.1, C.0, B.0, any.0, _a0.2, _a0.3, 4
A.0, B.0, C.0, Cn.0, 3, Cn.1, _a0.0, _a0.1, _a0.2, 1
A.0, B.0, C.0, Cn.0, 6, Cn.1, _a0.0, _a0.1, _a0.2, 4
B.0, 1, _b0.0, C.0, A.0, _b0.1, _b0.2, _b0.3, _b0.4, 2
B.0, 4, _b0.0, C.0, A.0, _b0.1, _b0.2, _b0.3, _b0.4, 5
B.0, An.0, 1, An.1, _b0.0, _b0.1, A.0, C.0, _b0.2, 2
B.0, An.0, 4, An.1, _b0.0, _b0.1, A.0, C.0, _b0.2, 5
B.0, 1, _b0.0, _b0.1, A.0, C.0, any.0, _b0.2, _b0.3, 2
B.0, 4, _b0.0, _b0.1, A.0, C.0, any.0, _b0.2, _b0.3, 5
B.0, An.0, 1, An.1, A.0, C.0, _b0.0, _b0.1, _b0.2, 2
B.0, An.0, 4, An.1, A.0, C.0, _b0.0, _b0.1, _b0.2, 5
C.0, 2, _c0.0, A.0, B.0, _c0.1, _c0.2, _c0.3, _c0.4, 3
C.0, 5, _c0.0, A.0, B.0, _c0.1, _c0.2, _c0.3, _c0.4, 6
C.0, A.0, B.0, _c0.0, _c0.1, Bn.0, 2, Bn.1, _c0.2, 3
C.0, A.0, B.0, _c0.0, _c0.1, Bn.0, 5, Bn.1, _c0.2, 6
C.0, 2, _c0.0, _c0.1, B.0, A.0, any.0, _c0.2, _c0.3, 3
C.0, 5, _c0.0, _c0.1, B.0, A.0, any.0, _c0.2, _c0.3, 6
C.0, A.0, B.0, Bn.0, 2, Bn.1, _c0.0, _c0.1, _c0.2, 3
C.0, A.0, B.0, Bn.0, 5, Bn.1, _c0.0, _c0.1, _c0.2, 6
A.0, 6, C.0, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, C.1, 4
B.0, 4, A.0, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, A.1, 5
C.0, 5, B.0, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, B.1, 6
A.0, 6, 6, A.1, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, 4
B.0, 4, 4, B.1, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, 5
C.0, 5, 5, C.1, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, 6
A.0, 3, 6, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, _a0.5, 4
B.0, 1, 4, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, _b0.5, 5
C.0, 2, 5, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, _c0.5, 6
A.0, 1, 4, An.0, An.1, An.2, An.3, An.4, An.5, 1
A.0, A.1, A.2, An.0, An.1, An.2, An.3, An.4, An.5, 4
B.0, 2, 5, Bn.0, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, 2
B.0, B.1, B.2, Bn.0, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, 5
C.0, 3, 6, Cn.0, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, 3
C.0, C.1, C.2, Cn.0, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, 6
A.0, _a0.0, 6, _a0.1, C.0, _a0.2, _a0.3, _a0.4, _a0.5, 4
B.0, _b0.0, 4, _b0.1, A.0, _b0.2, _b0.3, _b0.4, _b0.5, 5
C.0, _c0.0, 5, _c0.1, B.0, _c0.2, _c0.3, _c0.4, _c0.5, 6
A.0, An.0, 1, An.1, 1, An.2, An.3, An.4, An.5, 4
B.0, Bn.0, 2, Bn.1, 2, Bn.2, Bn.3, Bn.4, Bn.5, 5
C.0, Cn.0, 3, Cn.1, 3, Cn.2, Cn.3, Cn.4, Cn.5, 6
A.0, 6, _a0.0, 6, _a0.1, _a0.2, _a0.3, _a0.4, _a0.5, 4
B.0, 4, _b0.0, 4, _b0.1, _b0.2, _b0.3, _b0.4, _b0.5, 5
C.0, 5, _c0.0, 5, _c0.1, _c0.2, _c0.3, _c0.4, _c0.5, 6
A.0, 1, An.0, A.1, An.1, An.2, An.3, An.4, An.5, 4
B.0, 2, Bn.0, B.1, Bn.1, Bn.2, Bn.3, Bn.4, Bn.5, 5
C.0, 3, Cn.0, C.1, Cn.1, Cn.2, Cn.3, Cn.4, Cn.5, 6
1, 6, _a0.0, _a0.1, 6, _a0.2, _a0.3, _a0.4, _a0.5, 4
4, 6, _a0.0, _a0.1, 6, _a0.2, _a0.3, _a0.4, _a0.5, 1
2, 4, _b0.0, _b0.1, 4, _b0.2, _b0.3, _b0.4, _b0.5, 5
5, 4, _b0.0, _b0.1, 4, _b0.2, _b0.3, _b0.4, _b0.5, 2
3, 5, _c0.0, _c0.1, 5, _c0.2, _c0.3, _c0.4, _c0.5, 6
6, 5, _c0.0, _c0.1, 5, _c0.2, _c0.3, _c0.4, _c0.5, 3
A.0, 3, _a0.0, _a0.1, 6, _a0.2, _a0.3, _a0.4, _a0.5, 4
B.0, 1, _b0.0, _b0.1, 4, _b0.2, _b0.3, _b0.4, _b0.5, 5
C.0, 2, _c0.0, _c0.1, 5, _c0.2, _c0.3, _c0.4, _c0.5, 6
A.0, 6, _a0.0, _a0.1, 3, _a0.2, _a0.3, _a0.4, _a0.5, 1
B.0, 4, _b0.0, _b0.1, 1, _b0.2, _b0.3, _b0.4, _b0.5, 2
C.0, 5, _c0.0, _c0.1, 2, _c0.2, _c0.3, _c0.4, _c0.5, 3
A.0, 3, _a0.0, _a0.1, 3, _a0.2, _a0.3, _a0.4, _a0.5, A.0
B.0, 1, _b0.0, _b0.1, 1, _b0.2, _b0.3, _b0.4, _b0.5, B.0
C.0, 2, _c0.0, _c0.1, 2, _c0.2, _c0.3, _c0.4, _c0.5, C.0
A.0, 1, An.0, An.1, A.1, An.2, An.3, An.4, An.5, A.0
B.0, 2, Bn.0, Bn.1, B.1, Bn.2, Bn.3, Bn.4, Bn.5, B.0
C.0, 3, Cn.0, Cn.1, C.1, Cn.2, Cn.3, Cn.4, Cn.5, C.0
A.1, 4, An.0, An.1, A.0, An.2, An.3, An.4, An.5, A.0
B.1, 5, Bn.0, Bn.1, B.0, Bn.2, Bn.3, Bn.4, Bn.5, B.0
C.1, 6, Cn.0, Cn.1, C.0, Cn.2, Cn.3, Cn.4, Cn.5, C.0
A.0, _a0.0, 3, _a0.1, _a0.2, _a0.3, 6, _a0.4, _a0.5, 4
B.0, _b0.0, 1, _b0.1, _b0.2, _b0.3, 4, _b0.4, _b0.5, 5
C.0, _c0.0, 2, _c0.1, _c0.2, _c0.3, 5, _c0.4, _c0.5, 6
A.1, An.0, A.0, An.1, An.2, An.3, A.0, An.4, An.5, 4
B.1, Bn.0, B.0, Bn.1, Bn.2, Bn.3, B.0, Bn.4, Bn.5, 5
C.1, Cn.0, C.0, Cn.1, Cn.2, Cn.3, C.0, Cn.4, Cn.5, 6
A.0, 3, _a0.0, _a0.1, _a0.2, 6, _a0.3, _a0.4, _a0.5, 4
B.0, 1, _b0.0, _b0.1, _b0.2, 4, _b0.3, _b0.4, _b0.5, 5
C.0, 2, _c0.0, _c0.1, _c0.2, 5, _c0.3, _c0.4, _c0.5, 6
A.1, A.0, An.0, An.1, An.2, A.0, An.3, An.4, An.5, 4
B.1, B.0, Bn.0, Bn.1, Bn.2, B.0, Bn.3, Bn.4, Bn.5, 5
C.1, C.0, Cn.0, Cn.1, Cn.2, C.0, Cn.3, Cn.4, Cn.5, 6
4, any.0, any.1, any.2, any.3, any.4, any.5, any.6, any.7, 1
5, any.0, any.1, any.2, any.3, any.4, any.5, any.6, any.7, 2
6, any.0, any.1, any.2, any.3, any.4, any.5, any.6, any.7, 3

@COLORS
1 175 88 0
2 155 78 0
3 135 68 0
4 255 255 255
5 215 215 215
6 175 175 175

Kinetic symmetry

2022-12-05T17:24:03Z

Freywa: /* Oscillators */ it really is the champagne glass

{{stub}}
{{ambox|text=The pattern with oscillators displaying the 43 temporal symmetry types needs fully explanatory text/caption}}
A '''kinetic symmetry''' (contrast [[static symmetry]]) describes the spatial and temporal symmetries of [[still life]]s, [[oscillator]]s and [[spaceship]]s. It combines a pattern's spatial (rotational and reflectional) symmetries from the more general [[static symmetry]] with symmetrical transformations of said pattern arising from its evolution.<ref name="post138823" />

== On a square grid ==
There are a total of 43 different kinetic symmetries possible on a usual [[square grid]], comprised of the 16 static symmetries (D8_2 is excluded) with 27 possible time transformations.

Oscillators have a much wider range of possible kinetic symmetries than still lifes. It is very easy to see that the 27 time transformations cannot apply to still lifes by definition, as they require the pattern to have distinct phases which can be compared to each other, and therefore for the pattern to evolve, which still lifes do not. As such, oscillators can only have 16 of the possible 43 kinetic symmetry types, which therefore corresponds with the 16 different static symmetry types. The symmetry class is the symmetry class of the oscillator in a single generation followed by the symmetry class of the union of the generation and its congruent successors.<ref>{{CiteHickersonOscillators|accessdate=December 13, 2021}}</ref>

Both still lifes and oscillators can exhibit a wider range than spaceships can, at least as far as isotropic rules are concerned. Many higher kinetic symmetries, notably those involving rotation or with reflection happening on more than one axis, would forbid the pattern from having a nonzero displacement, as the symmetry would either force it to move in two directly opposing directions or redirect it back to its starting point. Many spaceships can have glide symmetry, which oscillators cannot have due to having no overall displacement, however glide symmetry very closely resembles certain mirror symmetries which oscillators do exhibit.

The ratio of a pattern's [[mod]] to its [[period]], for rules on a square grid, can only be 1, 2 or 4.

=== Kinetic symmetry naming system ===
[[Dean Hickerson]] invented a compact naming system for kinetic symmetries.

For still lifes, as well as oscillators and spaceships which have identical mods to periods, an initial symbol stand for a kind of transformation, and a symbol following it refers to the type of region where said transformation is centered.

Oscillators and spaceships of unequal period and mod will follow this string with another string detailing how the pattern is transformed after cycling through its mod.

Hickerson's naming scheme initially used "c" for the center of a cell and "k" for the vertex of a cell - these have been revised to "f" for the face of a cell and "v" for the vertex of a cell to clarify things and reduce any confusion that may arise due to homophones.

==== Symbols ====
{| class="wikitable"
! Hickerson name
! Wiki name
! Meaning
|-
! colspan="2" | n
| No symmetry
|-
! colspan="2" | -
| One line of orthogonal mirror symmetry
|-
! colspan="2" | /
| One line of diagonal mirror symmetry
|-
! colspan="2" | +
| Two lines of orthogonal mirror symmetry
|-
! colspan="2" | x
| Two lines of diagonal mirror symmetry
|-
! colspan="2" | *
| Two lines each of orthogonal and diagonal mirror symmetry
|-
! colspan="2" | r
| 90-degree rotational symmetry
|-
! colspan="2" | .
| 180-degree rotational symmetry
|-
! c
! f
| Transformation is centered on the center of a cell
|-
! colspan="2" | e
| Transformation is centered on the edge of a cell
|-
! k
! v
| Transformation is centered on the vertex of a cell
|}

=== Still lifes ===
These are equivalent to static symmetries (excluding D8_2). The corresponding static symmetries are detailed in the table for each type.

{| class="wikitable"
! Equivalent static symmetry
! Hickerson name
! Wiki name
! Description
! Diagram
! Example
|-
! C1
! colspan="2" | n
| No symmetry
| [[File:Symmetry C1.png|64px]]
| <center>[[File:eater1.png|64px]] [[Eater 1]]</center>
|-
! D2_+1
! -c
! -f
| One line of orthogonal mirror symmetry Line passes through cell centers and edges
| [[File:Symmetry D2_+1.png|64px]]
| <center>[[File:hat.png|64px]] [[Hat]]</center>
|-
! D2_+2
! colspan="2" | -e
| One line of orthogonal mirror symmetry Line passes through cell edges and vertices
| [[File:Symmetry D2_+2.png|64px]]
| <center>[[File:capandtable.png|64px]] [[Cap and table]]</center>
|-
! D2_x
! colspan="2" | /
| One line of diagonal mirror symmetry
| [[File:Symmetry D2_x.png|64px]]
| <center>[[File:boat.png|64px]] [[Boat]]</center>
|-
! C2_1
! .c
! .f
| 180-degree rotation Rotation is centered on the center of a cell
| [[File:Symmetry C2_1.png|64px]]
| <center>[[File:longsnake.png|64px]] [[Long snake]]</center>
|-
! C2_2
! colspan="2" | .e
| 180-degree rotation Rotation is centered on the edge of a cell
| [[File:Symmetry C2_2.png|64px]]
| <center>[[File:Aircraftcarrier.png|64px]] [[Aircraft carrier]]</center>
|-
! C2_4
! .k
! .v
| 180-degree rotation Rotation is centered on the vertex of a cell
| [[File:Symmetry C2_4.png|64px]]
| <center>[[File:Snake.png|64px]] [[Snake]]</center>
|-
! D4_+1
! +c
! +f
| Two lines of orthogonal mirror symmetry Both lines pass through cell centers and edges
| [[File:Symmetry D4_+1.png|64x]]
| <center>[[File:Hatcissiamesehat.png|64px]] [[Hat cis-siamese hat]] </center>
|-
! D4_+2
! colspan="2" | +e
| Two lines of orthogonal mirror symmetry One lines passes through cell centers and edges One line passes through cell edges and vertices
| [[File:Symmetry D4_+2.png|64px]]
| <center>[[File:beehive.png|64px]] [[Beehive]]</center>
|-[
! D4_+4
! +k
! +v
| Two lines of orthogonal mirror symmetry Both lines pass through cell edges and vertices
| [[File:Symmetry D4_+4.png|64px]]
| <center>[[File:xs32_8o6ll6o8z23cllc32.png|64px]] {{LinkCatagolue|code=xs32_8o6ll6o8z23cllc32|style=raw|patternname=unnamed}}</center>
|-
! D4_x1
! xc
! xf
| Two lines of diagonal mirror symmetry Lines meet at the center of a cell
| [[File:Symmetry D4_x1.png|64px]]
| <center>[[File:ship.png|64px]] [[Ship]]</center>
|-
! D4_x4
! xk
! xv
| Two lines of diagonal mirror symmetry Lines meet at the vertex of a cell
| [[File:Symmetry D4_x4.png|64px]]
| <center>[[File:barge.png|64px]] [[Barge]]</center>
|-
! C4_1
! rc
! rf
| 90-degree rotation Rotation is centered on the center of a cell
| [[File:Symmetry C4_1.png|64px]]
| <center>[[File:spiral.png|64px]] [[Spiral]]</center>
|-
! C4_4
! rk
! rv
| 90-degree rotation Rotation is centered on the vertex of a cell
| [[File:Symmetry C4_4.png|64px]]
| <center>[[File:xs36_354m88ge93zoie122d4ko.png|64px]] {{LinkCatagolue|code=xs36_354m88ge93zoie122d4ko|style=raw|patternname=unnamed}}</center>
|-
! D8_1
! *c
! *f
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell centers and edges
| [[File:Symmetry D8_1.png|64px]]
| <center>[[File:tub.png|64px]] [[Tub]]</center>
|-
! D8_4
! *k
! *v
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell edges and vertices
| [[File:Symmetry D8_4.png|64px]]
| <center>[[File:block.png|64px]] [[Block]]</center>
|}

=== Oscillators ===
For oscillators which have a mod identical to their period, refer to the still lifes table above.

"Composite symmetry" refers to the resulting symmetry of the pattern created from each of the oscillator's "identical" phases:
* for patterns with a mod half their period, the union of the pattern's initial state and the state it appears in at half its period
* for patterns with a mod a quarter their period, the union of the pattern's initial phase, generation (period/4), generation (period/2) and generation (3period/4)

{| class="wikitable"
! Hickerson name
! Wiki name
! Static symmetry
! Composite symmetry
! period/mod
! Description

! Example
|-
! n-c
! n-f
! C1
! D2_+1
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell centers and edges

| <center>[[File:xp2_466t186z6961696.png|64px]] [[xp2_466t186z6961696]]</center>
|-
! colspan="2" | n-e
! C1
! D2_+2
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell edges and vertices

| <center>[[File:Blockongriddle.png|64px]] [[Block on griddle]]</center>
|-
! colspan="2" | n/
! C1
! D2_x
| 2
| Pattern is asymmetric Appears flipped across a diagonal line during (period/2)

| <center>[[File:Mutteringmoat1.png|64px]] [[Muttering moat 1]]</center>
|-
! n.c
! n.f
! C1
! C2_1
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the center of a cell

| <center>[[File:xp2_0ml1ik8z1259a6.png|64px]] [[xp2_0ml1ik8z1259a6]]</center>
|-
! colspan="2" | n.e
! C1
! C2_2
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the edge of a cell

| <center>[[File:Laputa.png|64px]] [[Laputa]]</center>
|-
! n.k
! n.v
! C1
! C2_4
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the vertex of a cell

| <center>[[File:2.3.3.png|64px]] [[2.3.3]]</center>
|-
! nrc
! nrf
! C1
! C4_1
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the center of a cell

| <center>[[File:Sixtynine.png|64px]] [[Sixty-nine]]</center>
|-
! nrk
! nrv
! C1
! C4_4
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the vertex of a cell

| <center>[[File:Dinnertable.png|64px]] [[Dinner table]]</center>
|-
! -c+c
! -f+f
! D2_+1
! D4_+1
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges

| <center>[[File:Piston.png|64px]] [[Piston]]</center>
|-
! -c+e
! -f+e
! D2_+1
! D4_+2
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices

| <center>[[File:Byflops.png|64px]] [[by flops]]</center>
|-
! -e+e
! -e+e
! D2_+2
! D4_+2
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges

| <center>[[File:xp2_0giligz344k743zw121.png|64px]] [[xp2_0giligz344k743zw121]]</center>
|-
! -e+k
! -e+v
! D2_+2
! D4_+4
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices

| <center>[[File:2.5.6.png|64px]]{{br}}{{LinkCatagolue|code=xp2_g8j1qc6i0qdj8gz12pgb6c90bmp21|style=raw|patternname=unnamed}}</center>
|-
! /xc
! /xf
! D2_x
! D4_x1
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the center of a cell

| <center>[[File:xp2_066oo4g53zc8502046.png|64px]] [[xp2_066oo4g53zc8502046]]</center>
|-
! /xk
! /xv
! D2_x
! D4_x4
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the vertex of a cell

| <center>[[File:Tripole.png|64px]] [[Tripole]]</center>
|-
! .c+c
! .f+f
! C2_1
! D4_+1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges

| <center>[[File:xp2_g8j1cdj8gz01cb38c1.png|64px]] [[xp2_g8j1cdj8gz01cb38c1]]</center>
|-
! .cxc
! .fxf
! C2_1
! D4_x1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the center of a cell

| <center>[[File:Bipole.png|64px]] [[Bipole]]</center>
|-
! .crc
! .frf
! C2_1
! C4_1
| 2
| Pattern has C2_1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the center of a cell

| <center>[[File:xp2_2aa08060922zgg50p050lkgzw1.png|64px]] [[xp2_2aa08060922zgg50p050lkgzw1]]</center>
|-
! .e+e
! .e+e
! C2_2
! D4_+2
| 2
| Pattern has C2_2 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Line may pass through either cell centers and edges, or cell edges and vertices

| <center>[[File:2.6.0.png|64px]]{{br}}{{LinkCatagolue|code=xp2_0o4cjia3s4oz5t2q3hcei2t5zw11622611|style=raw|patternname=unnamed}}</center>
|-
! .k+k
! .v+v
! C2_4
! D4_+4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices

| <center>[[File:xp2_0e0j0944z44i0p0e.png|64px]] [[xp2_0e0j0944z44i0p0e]]</center>
|-
! .kxk
! .vxv
! C2_4
! D4_x4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the vertex of a cell

| <center>[[File:Clock.png|64px]] [[Clock]]</center>
|-
! .krk
! .vrv
! C2_4
! C4_4
| 2
| Pattern has C2_4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the vertex of a cell

| <center>[[File:2.6.3.png|64px]]{{br}}{{LinkCatagolue|code=xp2_g80c0gxcg2c0v1k4z11tp10244g084410gzx10g442014480gjnggzw45gv06816x106021|style=raw|patternname=unnamed}}</center>
|-
! +c*c
! +f*f
! D4_+1
! D8_1
| 2
| Pattern has D4_+1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell

| <center>[[File:Blinker.png|64px]] [[Blinker]]</center>
|-
! +k*k
! +v*v
! D4_+4
! D8_4
| 2
| Pattern has D4_+4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell

| <center>[[File:4.10.2.png|64px]]{{br}}{{LinkCatagolue|code=xp4_y1gs2ib8owo8bi2sgzgs2ib88g35i2222i53g88bi2sgzxji1wvwuwuwvw1ijz2egjk542h8iggggi8h245kjge2zy012egjl46w64ljge21zy51y21|style=raw|patternname=unnamed}}</center>
|-
! xc*c
! xf*f
! D4_x1
! D8_1
| 2
| Pattern has D4_x1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell

| <center>[[File:Washingmachine.png|64px]] [[Washing machine]]</center>
|-
! xk*k
! xv*v
! D4_x4
! D8_4
| 2
| Pattern has D4_x4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell

| <center>[[File:2.5.2.png|64px]]{{br}}{{LinkCatagolue|code=xp2_ggw392g5jwggzpi81k1g08281kpzy0ca049c|style=raw|patternname=unnamed}}</center>
|-
! rc*c
! rf*f
! C4_1
! D8_1
| 2
| Pattern has C4_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges

| <center>[[File:2.5.0.png|64px]]{{br}}{{LinkCatagolue|code=xp2_wc4oql2gkcz25ice08or1i52zw110252011|style=raw|patternname=unnamed}}</center>
|-
! rk*k
! rv*v
! C4_4
! D8_4
| 2
| Pattern has C4_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices

| <center>[[File:Quad.png|64px]] [[Quad]]</center>
|}

The following shows oscillators displaying each of the 43 temporal symmetry types:
{|style="margin:auto;width:300px;"
{{EmbedViewer
|viewerconfig = #C [[ GPS 20 THUMBSIZE 2 ZOOM 4 WIDTH 1640 HEIGHT 1000 ]]
|pname = temporalsymmetrytypes
|position = center
}}
|}
row 1: [[Caterer]], [[Honey thieves]], [[Beluchenko's p40]], [[22P36]], [[Kok's galaxy]], [[48P22.1]], [[1-2-3-4]], [[Short keys]], [[Heart]], [[Gray counter]], [[Pentadecathlon]], [[101]], [[Merzenich's p11]], [[Jason's p6]], [[Diamond ring]], [[Octagon 2]]{{br}}
row 2: [[Baker's dozen]], [[Merzenich's p64]], [[Achim's p144]], [[Windmill]], [[Achim's p16]], [[44P10]], [[Tumbler]], [[Heavyweight emulator]], [[46P10]], [[68P32.1]], [[A for all]], [[Washing machine]], [[Unicycle ]]{{br}}
row 3: [[Trans-queen bee shuttle]], [[2.2.6]], [[Two pre-L hasslers]], [[Eureka]], [[p30 traffic light hassler]], [[p24 shuttle]]{{br}}
row 4: [[Blocker]], [[Achim's p8]]{{br}}
row 5: [[Champagne glass]], [[p196 pi-heptomino hassler]]{{br}}
row 6: [[Rob's p16]]{{br}}
row 7: [[30P6.1]]{{br}}
row 8: [[Four eaters hassling lumps of muck]]{{br}}
row 9: [[Twirling T-tetsons 2]]

== On other grids ==
There are no known attempts at describing all possible oscillator and spaceship time symmetries on [[Hexagonal tiling|{6,3}]] or [[Triangular tiling|{3,6}]] so far.

== References ==
<references>
<ref name="post138823">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 138823
|author = GUYTU6J
|date = December 13, 2021
}}</ref>
</references>

[[Category:Everything else]]

Tutorials/Catagolue stdin symmetry

2022-11-29T01:12:52Z

Freywa: /* How to use the pipe command with apgluxe */ Demoggify the command

The program used for random soup searching and uploading census results to Catagolue, apgluxe, can also be used to census other patterns besides the standard 16x16 soups (and the various symmetric versions).

This can be done using a special-case "symmetry" -- which, as with some other custom input type settings (especially "C1") doesn't mean that anything about the input is actually symmetrical. It's just that the ability to choose different types of symmetry was the original reason why this input-type symmetry was added to apgsearch, so it got called '''--symmetry'''.

== Example use of stdin "symmetry" ==

Here's a walkthrough of what I did to make the "stdin" setting work correctly for the current octohash database. The octohash database is a text file containing RLE and hash "fingerprints" for 455,380 constellations of two well-separated small objects, with gliders hitting those constellations in all possible ways. The original format of the database looks like this:

<pre>2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo! 4VR.}_d9V 2Ix+b%WBR 3yxH8RZE. #0;<x`Uw5 ...
2o$2o5$6b2o$7bo$7bobo$8b2o2$10bo$9b2o$9bobo! %;PIz*v-2 4^3)fGg4d $ELjpBC|L +na$+!R;z ...
2o$2o5$6b2o$7bo$7bobo$8b2o$11b3o$11bo$12bo! +v_ZNH#oe -}^X[oicJ -R-?MafAS /_5rv;~OS ...
2o$2o5$6b2o$6bobo$8bo$8b2o2$9bo$8b2o$8bobo! *)96g6@`< )$19%$P-v 0;fHjqa6H 1kt!Xw0*B ...
2o$2o5$6b2o$6bobo$8bo$8b2o2$10b3o$10bo$11bo! )nqxL570R -[6bmsrmA /^gHjOSFo 1n3pM&bmw ...
...</pre>

For this project, we're not going to use the hash values that show up after the exclamation point on every line. We just need the RLE -- but we need it to be actual standard-format RLE, not headerless RLE. However, apgluxe doesn't care whether the x and y values are right or not, so we can just add the same standard header to each line.

We could do this by writing a Python or Lua script to read the original octohash database, split each string at the space, and write out a new text file with '''x = 0, y = 0, rule = B3/S23''' added before every line. But it's actually just as easy to do this kind of thing with a good text editor -- Notepad++ or TextPad, or any similar editor that support regular-expression search and replaces.

== Tangential note about the usefulness of regexp search-and-replace ==
First replace '''" .*"''' without the quotes -- space period asterisk -- with the empty string. That gets rid of the long strings of hashes. If you're trying this with the full database, this might take a little while since there are almost half a million lines of text in the database.

Then replace "^" without the quotes -- just a single carat character -- with "'''x = 0, y = 0, rule = B3/S23\n'''". "^" is a regexp shortcut for "the beginning of the line of text", just as "$" is a reference meaning "the end of the line of text". "\n" is just the standard syntax for a newline character.

You should end up with a new text file, which you can save with a new name. Let's call it '''octohashes.txt'''. Save it in the same folder with apgluxe.exe, to make things simpler (otherwise you have to specify the full path to it in your command-line invocation, below.) '''octohashes.txt''' should look like this now:

<pre>x = 0, y = 0, rule = B3/S23
2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
x = 0, y = 0, rule = B3/S23
2o$2o5$6b2o$7bo$7bobo$8b2o2$10bo$9b2o$9bobo!
x = 0, y = 0, rule = B3/S23
2o$2o5$6b2o$7bo$7bobo$8b2o$11b3o$11bo$12bo!
x = 0, y = 0, rule = B3/S23
2o$2o5$6b2o$6bobo$8bo$8b2o2$9bo$8b2o$8bobo!
x = 0, y = 0, rule = B3/S23
2o$2o5$6b2o$6bobo$8bo$8b2o2$10b3o$10bo$11bo!
...</pre>

== Different options for piping patterns into apgluxe ==
The above is a format -- chunks of RLE one right after another -- that we can feed directly into apgluxe, as long as we tell it that the symmetry is some arbitrary name containing the string "stdin". You pick the rest of the name, but make it unique and descriptive, and make sure it includes this string -- just "_stdin" at the end of the name for example. ("Stdin" is short for "standard input", and that's good terminology to know when you're working with command-line utilities like apgluxe.)

Really apgluxe can accept any '''stream''' of data that consists of chunks of RLE like this, one right after another. If you're familiar with the concept of piping the output of one shell command into the input of another, then you can write a program that generates RLE directly and prints it to the console -- a stream called "stdout", "standard output". A pipe character '''|''' then tells the shell interpreter to redirect the output of that program to be the input of another program, apgluxe.exe in this case.

Several people have written this kind of program to produce various types of enumerated patterns: partial spaceships, all possible NxN patterns for small N, etc. It's often useful to pipe these enumerated patterns through apgluxe, because that way you find out very quickly if any interesting still lifes, oscillators, spaceships, or growing patterns are produced.

In the case of the octohash database that we modified above, we can just use a shell command called "cat", short for "concatenate" but what it does is simply print whatever files you mention to the console (standard output), one after another. We'll only mention one file, '''octohashes.txt''', so it will just print the contents of the file, which is exactly what we want to pipe into apgluxe.

== How to use the pipe command with apgluxe ==
If you don't already have apgluxe installed, follow the standard instructions from the [https://gitlab.com/apgoucher/apgmera/-/blob/master/README.md apgmera README].

Once you've done that, recompile apgluxe with your chosen "stdin" symmetry name:

<pre>./apgluxe --symmetry octohash2obj12x12_stdin</pre>

Then you'll be all ready to run the actual command to census your list of RLEs:

<pre>./apgluxe -k MyPayoshaKey -t 1 -n 455380 < octohashes.txt</pre>

Translation:

<pre>< octohashes.txt</pre> – Use '''octohashes.txt''' as input to…

<pre> ./apgluxe </pre> – …apgluxe.exe (in Unix-like operating systems, you have to put the ./ in front of the name, because if you don't, it thinks that it's a shell command that it can't find, instead of an executable file name.)

<pre> -k MyPayoshaKey </pre> – you won't need this unless you change the next line, to upload your census results to Catagolue.

<pre> -t 1 </pre> – specifies 'testing' mode. Remove this option from the command to upload your stdin census to Catagolue.

<pre> -n 455380</pre> – specifies the number of patterns to process before uploading, or before completing the task that you're telling apgluxe to do here.

== Results from apgluxe ==
For my particular octohash database census, the result that came back from apgluxe after a few minutes (in the form of a log file named something long and unpronounceable) is shown below. You can check by running the sample soups in Golly, that those collisions do indeed produce explosions whose ash contains the referenced objects. For example,

{{EmbedViewer|rle = 2o$obo$2bo$2b2o3$6b2o$7bo$7bobo$8b2o2$8bo$7b2o$7bobo!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}

<pre>xp3_co9nas0san9oczgoldlo0oldlogz1047210127401 -2o$obo$2bo$2b2o3$6b2o$7bo$7bobo$8b2o2$8bo$7b2o$7bobo!</pre>

means that a glider hitting two 180-degree rotationally symmetric eaters will produce a pulsar (at T=1878, along with many other things).

<div class="mw-collapsible mw-collapsed">
Click on "Expand" to the right to view full content of the log file.
<div class="mw-collapsible-content">
<pre>testing
@VERSION v5.2-ll2.4.3
@MD5 678291a2bf974c9aeaf313e7171a9acb
@ROOT k_NCzsAkKecFzp
@RULE b3s23
@SYMMETRY octohash2obj12x12_stdin
@NUM_SOUPS 455380
@NUM_OBJECTS 6874903

@CENSUS TABLE
xs4_33 2138665
xp2_7 1930705
xs6_696 1125108
xq4_153 630131
xs7_2596 313936
xs5_253 307969
xs6_356 223659
xs8_6996 75167
xs4_252 63316
xs7_25ac 20223
xp2_7e 14256
xs12_g8o653z11 12841
xp2_318c 4204
xs6_25a4 3772
xs14_g88m952z121 3075
xs7_178c 1629
xs8_69ic 1578
xs8_25ak8 817
xq4_6frc 733
xp3_co9nas0san9oczgoldlo0oldlogz1047210127401 553
xs6_39c 450
xs14_69bqic 257
xs9_31ego 251
xs8_35ac 217
xq4_27dee6 167
xs6_bd 161
xs8_3pm 130
xs16_g88m996z1221 122
xs14_g88b96z123 113
xs10_g8o652z01 96
xs18_rhe0ehr 64
xs9_4aar 59
xs9_178ko 49
xs9_25ako 38
xs8_178k8 37
xp15_4r4z4r4 35
xs10_35ako 34
xq4_27deee6 26
xs11_g8o652z11 23
xs16_j1u0696z11 21
xs11_2530f9 17
xs15_354cgc453 14
xs14_j1u066z11 13
xs14_6970796 13
xs12_raar 13
xs11_g0s453z11 13
xs8_312ko 8
xs14_39e0e93 8
xs10_g0s252z11 8
xs10_178kk8 7
xs12_330fho 6
xs11_178kic 6
xs9_178kc 5
xs10_358gkc 5
xs7_3lo 4
xs17_2ege1ege2 4
xs12_o4q552z01 4
xs10_3542ac 4
xs10_32qr 4
xs16_69egmiczx1 3
xs14_69bo8a6 3
xs12_330f96 3
xs10_3215ac 3
xs9_312453 2
xs16_69bob96 2
xs15_j1u06a4z11 2
xs15_259e0eic 2
xs15_259e0e96 2
xs14_j1u413z11 2
xs14_6is079c 2
xs14_69e0eic 2
xs14_6960uic 2
xs13_g88m96z121 2
xs12_69iczx113 2
xs11_ggm952z1 2
xs10_g8ka52z01 2
xs10_1784ko 2
xs8_31248c 1
xs20_3lkkl3z32w23 1
xs19_0c88b96z6953 1
xs15_g88m596z121 1
xs15_4a9raic 1
xs15_3lkm96z01 1
xs15_3lk453z121 1
xs14_i5q453z11 1
xs14_g8o0e96z121 1
xs14_39e0eic 1
xs14_31egm96 1
xs13_3hu06a4 1
xs12_3hu066 1
xs12_0ggs252z32 1
xs12_0g8o652z121 1
xs12_08o653z32 1
xs11_ggka53z1 1
xs11_31461ac 1
xs10_69ar 1
xs10_0j96z32 1

@SAMPLE_SOUPIDS
xs4_33 -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xp2_7 -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xs6_696 -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xq4_153 -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xs7_2596 -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xs5_253 -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xs6_356 -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xs8_6996 -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xs4_252 -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xs7_25ac -2o$2o5$7b2o$6bo2bo$6bo2bo$7b2o2$9b3o$9bo$10bo!
xp2_7e -2o$2o6$8b2o$7bobo$8bo2$8b2o$8bobo$8bo!
xs12_g8o653z11 -2o$obo$bo4$8b2o$7bobo$7bo$6b2o2$8b2o$8bobo$8bo!
xp2_318c -2o$2o6$8b2o$7bobo$8bo2$8b2o$8bobo$8bo!
xs6_25a4 -2o$obo$2bo$2b2o4$8bo$7bobo$8bo2b2o$11bobo$11bo!
xs14_g88m952z121 -2o$obo$bo4$7b2o$6bo2bo$6bobo$7bo2$8b3o$8bo$9bo!
xs7_178c -2o$obo$bo5$7b2o$7bobo$8b2o2$8bo$7b2o$7bobo!
xs8_69ic -2o$2o5$6b2o$7bo$7bobo$8b2o2$9bo$8b2o$8bobo!
xs8_25ak8 -2o$obo$bo4$6b2o$7bo4b2o$7bobob2o$8b2o3bo!
xq4_6frc -b2o$o2bo$o2bo$b2o4$7b2o$7bobo$8b2o2$9bo$8b2o$8bobo!
xp3_co9nas0san9oczgoldlo0oldlogz1047210127401 -2o$obo$2bo$2b2o3$6b2o$7bo$7bobo$8b2o2$8bo$7b2o$7bobo!
xs6_39c -6bo$6b3o$9bo$8b2o2$9bo$8b2o$bo6bobo$obo$b2o!
xs14_69bqic -b2o$o2bo$bobo$2bo3$7b2o$6bo2bo$6bo2bo$7b2o2b2o$11bobo$11bo!
xs9_31ego -8b2o$7bobo$7b2o4$3bo$b3o$o$2o$3b2o$3bobo$3bo!
xs8_35ac -bo$obo$bobo$2b2o4$8bo$7bobo$7bobo$8bo2$6b2o$6bobo$6bo!
xq4_27dee6 -2b2o$3bo$3o$o3$7bo$6bobo$7bobo$8b2o2$9bo$8b2o$8bobo!
xs6_bd -b2o$o2bo$b2o4$8b2o$7bobo$6bobo$7bo2b2o$10bobo$10bo!
xs8_3pm -2b2o$3bo$3o$o3$7b2o$6bo2bo$6bo2bo$7b2o2$9b2o$9bobo$9bo!
xs16_g88m996z1221 -2b2o$3bo$3o$o3$7bo$6bobo$6bo2bo$7b2o2$8bo$7b2o$7bobo!
xs14_g88b96z123 -bo$obo$bo4$8bo$7bobo$7bobo$8bo2b3o$11bo$12bo!
xs10_g8o652z01 -7b2o$7bobo$8b2o2$8bo$7b2o$7bobo$b2o$o2bo$b2o!
xs18_rhe0ehr -b2o$obo$bo4$6bo$6b3o$9bo2b2o$8b2ob2o$13bo!
xs9_4aar -7b2o$6bo2bo$6bobo2b3o$7bo3bo$12bo4$2o$2o!
xs9_178ko -8b2o2b2o$7bobob2o$6bobo4bo$7bo5$bo$obo$b2o!
xs9_25ako -7b2o$7bobo$8bo6$2bo3b2o$bobob2o$o2bo3bo$b2o!
xs8_178k8 -2o$o$b3o$3bo4$6b2o$7bo$7bobo$8b2o2$10bo$9b2o$9bobo!
xp15_4r4z4r4 -b2o3b2o$o2bob2o$o2bo3bo$b2o4$6b2o$6bo$7b3o$9bo!
xs10_35ako -6b2o$7bo$7bobo$8b2o3$b2o$o2bo$bobo$2bo2$3b2o$3bobo$3bo!
xq4_27deee6 -2o$obo$b2o6$7b2o$6bo2bo$6bo2bo$7b2o2$9b3o$9bo$10bo!
xs11_g8o652z11 -bo$obo4b2o$obo4bobo$bo6bo2$9b3o$9bo$10bo!
xs16_j1u0696z11 -4b3o$bo2bo$obo2bo$2o6$8bo$7bobo$6bo2bo$7b2o!
xs11_2530f9 -2o$2o2$bo4b2o$2o4bobo$obo4bobo$8bo!
xs15_354cgc453 -8b2o$2b2o4b2o$bobo$obo7bo$bo7b2o$9bobo!
xs14_j1u066z11 -2o$o$b3o$3bo2$8bo$7bobob3o$7b2o2bo$12bo!
xs14_6970796 -bo$obo$obo4bo$bo4bobo$7bobo$8b2o2$7bo$6b2o$6bobo!
xs12_raar -7b2o$8bo$8bobo$2b2o5b2o$bobo$bo7bo$2o6b2o$8bobo!
xs11_g0s453z11 -b2o$bobo$2b2o2$bo5b2o$2o6bo$obo5bobo$9b2o!
xs8_312ko -2o$o8bo2b2o$b3o3b3ob2o$3bo2bo6bo$6b2o!
xs14_39e0e93 -8b2o2b2o$7bobob2o$6bobo4bo$7bo4$2b2o$2bo$obo$2o!
xs10_g0s252z11 -7b2o$2bo4bobo$bobo4bo$o2bo$b2o6b2o$9bobo$9bo!
xs10_178kk8 -2o$bo$bobo$2b2o4b2o$8bo2b2o$6bobo2bobo$6b2o3bo!
xs12_330fho -2o$obo$bo$8b2o$7bo2bo$7bobo2b3o$8bo3bo$13bo!
xs11_178kic -b2o$bobo$2b2o2$bo5b2o$2o5bobo$obo6bo$9b2o!
xs9_178kc -9b2o$8bobo$8bo$7b2o2$9b2o$9bobo$9bo$2b2o$3bo$3o$o!
xs10_358gkc -8b2o$7bo2bo$7bo2bo$8b2o$2bo$bobo3bo$obo3b2o$2o4bobo!
xs7_3lo -6b2o$3bo2bo$b3o3b3o$o8bo$2o4bo$5b2o$5bobo!
xs17_2ege1ege2 -7b2o$6bo2bo$b2o4b2o$o2bo$obo6b3o$bo7bo$10bo!
xs12_o4q552z01 -bo$obo$2o6bo$7bobo$8bobo$9b2o2$10bo$9b2o$9bobo!
xs10_3542ac -2o$obo$bo5bo$6bobo$2o4bo2bo$obo4b2o$o!
xs10_32qr -2o$o$b3o$3bo5$8b2o$7bo2bo$7bo2bo$8b2o2b2o$12bobo$12bo!
xs16_69egmiczx1 -2o$obo$b2o7bo$8b3o$bo5bo$2o5b2o$obo!
xs14_69bo8a6 -7bo$6bobo$7bobo$8b2o$b2o$o2bo$o2bo$b2o2b2o$5bobo$5bo!
xs12_330f96 -8b2o$7bobo$7b2o6$b2o$o2bo$o2bo$b2o2b2o$5bobo$5bo!
xs10_3215ac -bo$obo5bo$obo4bobo$bo4bobo$6b2o2$8b2o$8bobo$8bo!
xs9_312453 -o$o$o6bo3b2o$6bobob2o$5bo2bo3bo$6b2o!
xs16_69bob96 -6b2o$5bo2bo$5bo2bo$o5b2o$o$o$2b3o$2bo$3bo!
xs15_j1u06a4z11 -2bo$bobo$obo5bo$2o5bobo$8b2o$bo$2o$obo!
xs15_259e0eic -8bo$7bobo$6bobo$6b2o6$2o$obo2b2o$b2ob2o$6bo!
xs15_259e0e96 -b2o$obo$bo$10b2o$9bobo$9bo3b2o$8b2o3bobo$13bo!
xs14_j1u413z11 -2b2o$bobo$bo6b2o$2o6bobo$9b2o2$10bo$9b2o$9bobo!
xs14_6is079c -4b2o$4bobo2b2o$5b2ob2o$10bo2$b2o$o2bo$obo$bo!
xs14_69e0eic -b2o$obo$2o2$3b2o$2bo2bob3o$2bobo2bo$3bo4bo!
xs14_6960uic -o5b2o$o4bo2bo$o4bo2bo$6b2o2$6bo$5b2o$5bobo!
xs13_g88m96z121 -10bo$10bo$10bo$b2o$o2bo$b2o2b2o$5bobo$5bo!
xs12_69iczx113 -8bo$7bobo$7b2o$2b2o$bobo5b3o$bo7bo$2o8bo!
xs11_ggm952z1 -2b2o$2bobo$3bo2$5b3o$2bo2bo$bobo2bo$obo$2o!
xs10_g8ka52z01 -8b2o$8b2o$2bo$bobo$obo$2o2$bo$2o$obo!
xs10_1784ko -2o$bo$bobo$2b2o4bo$7bobo$7bobo$8bo2$9b2o$9bobo$9bo!
xs8_31248c -b2o5b2o$o2bo3bobo$obo5bo$bo$3b3o$3bo$4bo!
xs20_3lkkl3z32w23 -2bo$bobo$o2bo$b2o2$10bo$8b3o$7bo$7b2o2$7bo$6b2o$6bobo!
xs19_0c88b96z6953 -7b2o$7bobo$8bo6$2o$obo$b2o2$3bo$2b2o$2bobo!
xs15_g88m596z121 -6b2o$6bobo$b2o5bo$o2bo4b2o$obo$bo5bo$6b2o$6bobo!
xs15_4a9raic -4b2o$5bo$5bobo$6b2o3$2o$obo$b2o2$3bo$2b2o$2bobo!
xs15_3lkm96z01 -6b2o$6b2o3$3bo$b3o$o$2o2$2b3o$2bo$3bo!
xs15_3lk453z121 -2bo$bobo$2b2o3$2o$obo$b2o2$bo$2o$obo!
xs14_i5q453z11 -6b2o$6bo$7b3o$9bo4$2o$obo$b2o2b2o$4b2o$6bo!
xs14_g8o0e96z121 -b2o7bo$o2bo5bobo$o2bo6bo$b2o2$bo$2o$obo!
xs14_39e0eic -8b2o$2o5bobo$bo6bo$bobo$2b2o5b3o$9bo$10bo!
xs14_31egm96 -6b2o$5bo2bo$5bobo2b2o$6bo3bobo$10bo$2b2o$3bo$3o$o!
xs13_3hu06a4 -2o$2o7$10bo$8b3o$7bo$7b2o2$7bo$6b2o$6bobo!
xs12_3hu066 -7b2o$7bobo$8bo2$9b2o$9bobo$9bo$o$3o$3bo$2b2o!
xs12_0ggs252z32 -8b2o$2o5bobo$obo4bo$2bo3b2o$2b2o$6bo$5b2o$5bobo!
xs12_0g8o652z121 -7b2o$bo5bobo$obo5b2o$bobo$2b2o6bo$9b2o$9bobo!
xs12_08o653z32 -bo$obo$bobo5bo$2b2o3b3o$6bo$6b2o$9b2o$9bobo$9bo!
xs11_ggka53z1 -3bo$b3o$o$2o2$11b3o$7b2o2bo$6bo2bo2bo$7b2o!
xs11_31461ac -bo$obo$b2o3$5bo$4bobo$5bobo$6b2o2$8bo$7b2o$7bobo!
xs10_69ar -7b2o$7bobo$8b2o6$b2o$o2bo$b2o2b2o$5bobo$5bo!
xs10_0j96z32 -9b3o7$2b2o$bobo$bo3b2o$2o3bobo$5bo!</pre>
</div></div>

== See also ==
*[[Tutorials/Contributing to Catagolue]]

{{Tutorial}}
{{CatagolueNavbox}}

RLE:P4pipsquirter

2022-10-27T07:28:57Z

Freywa:

x = 18, y = 14, rule = B3/S23
5bo$5bo$2o8b3o$o2bob2o3b6o$bob5obo6bo$2bo6bo6bo$3b3o3b2o5b2o$5bo11bo$
12bob3o$12b2o$15b2o$16bo$14bo$14b2o!

Oscillator

2022-06-09T12:35:00Z

Freywa: SKOP143

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period).

[[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]].

== Important oscillators by period ==
A list of the first-discovered oscillator of each period,<ref>{{CiteHickersonOscillators|accessdate=April 11, 2009}}</ref> as well the current smallest-known oscillator of that period,<ref name="post132979" /> is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
| rowspan="500" style="border: none;" |
! Smallest known
! Minimum # of cells
|-
! {{period|2|brief}}
| [[blinker]]
|[[John Conway]]
| {{year|1969}}
| [[blinker]]
| {{cells|3}}
|-
! {{period|3|brief}}
| [[pulsar]]
|John Conway
| 1970
| [[caterer]]
| {{cells|12}}
|-
! {{period|4|brief}}
| [[pinwheel]]
|[[Simon Norton]]
| 1970
| [[mazing]], [[mold]]
| {{cells|12}}
|-
! {{period|5|brief}}
| [[octagon 2]]
|[[Sol Goodman]], [[Arthur Taber]]
| {{year|1971}}
| [[pseudo-barberpole]]
| {{cells|15}}
|-
! {{period|6|brief}}
| [[$rats]]
|[[David Buckingham]]
| {{year|1972}}
| [[unix]]
| {{cells|16}}
|-
! {{period|7|brief}}
| [[burloaferimeter]]
|David Buckingham
| 1972
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
| {{cells|28}}
|-
! {{period|8|brief}}
| [[figure eight]]
|Simon Norton
| 1970
| [[figure eight]]
| {{cells|12}}
|-
! {{period|9|brief}}
| [[worker bee]]
|David Buckingham
| 1972
| [[29P9]]
| {{cells|29}}
|-
! {{period|10|brief}}
| [[42P10.3]]
|David Buckingham
| ≤{{year|1976}}
| [[24P10]]
| {{cells|24}}
|-
! {{period|11|brief}}
| [[38P11.1]]
|David Buckingham
| {{year|1977}}
| [[rattlesnake]]
| {{cells|33}}
|-
! {{period|12|brief}}
| [[dinner table]]
|[[Robert Wainwright]]
| {{year|1972}}
| [[dinner table]]
| {{cells|33}}
|-
! {{period|13|brief}}
| [[Buckingham's p13]]
|David Buckingham
| 1976
| [[Beluchenko's p13]]
| {{cells|34}}
|-
! {{period|14|brief}}
| [[tumbler]]
|[[George Collins]]
| 1970
| [[tumbler]]
| {{cells|16}}
|-
! {{period|15|brief}}
| [[pentadecathlon]]
|John Conway
| 1970
| [[pentadecathlon]]
| {{cells|12}}
|-
! {{period|16|brief}}
| [[two pre-L hasslers]]
|Robert Wainwright
| {{year|1983}}
| [[Rob's p16]]
| {{cells|21}}
|-
! {{period|17|brief}}
| [[54P17.1]]
|[[Dean Hickerson]]
| {{year|1997}}
| [[honey thieves]]
| {{cells|36}}
|-
! {{period|18|brief}}
| [[117P18]]{{refn|group=note|name=lcm|[[Non-trivial]] oscillators of this period could have been constructed from two oscillators of lower period (usually [[sparker]]s), both of which were known by an earlier date. However, no such [[LCM oscillator]]s were attested prior to the discovery of this oscillator.}}
|David Buckingham
| ≤{{year|1991}}
| [[p18 bi-block hassler]], [https://catagolue.hatsya.com/object?apgcode=xp18_wc93xs112ogggzbdhe96kk801zw1213&rule=b3s23 p18 phase shifter]
| {{cells|43}}
|-
! class="red_td" | 19
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|20|brief}}
| [[145P20]]{{refn|group=note|name=lcm}}
|[[Noam Elkies]]
| {{year|1995}}
| [[mold on fumarole]]
| {{cells|30}}
|-
! {{period|21|brief}}
| [[124P21]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1995
| [[32P21]]
| {{cells|32}}
|-
! {{period|22|brief}}
| [[168P22.1]]
|Noam Elkies
| 1997
| [[Jason's p22]]
| {{cells|36}}
|-
! {{period|23|brief}}
| [[David Hilbert]]
|[[Luka Okanishi]], [[praosylen]]
| {{year|2019}}
| [[p23 honey farm hassler]]
| {{cells|76}}
|-
! {{period|24|brief}}
| [[186P24]]{{refn|group=note|name=lcm}}
|[[Bill Gosper]]
| {{year|1994}}
| [[caterer on figure eight]]
| {{cells|24}}
|-
! {{period|25|brief}}
| [[134P25]]
|Noam Elkies
| 1994
| [[30P25]]
| {{cells|30}}
|-
! {{period|26|brief}}
| [[p26 pre-pulsar shuttle]]
|David Buckingham
| 1983
| [[87P26]]
| {{cells|87}}
|-
! {{period|27|brief}}
| [[123P27.1]]
|Noam Elkies
| {{year|2002}}
| [[56P27]]
| {{cells|56}}
|-
! {{period|28|brief}}
| [[newshuttle]]
|David Buckingham
| {{year|1973}}
| [[mold on 34P14 shuttle]]
| {{cells|46}}
|-
! {{period|29|brief}}
| [[p29 pre-pulsar shuttle]]
|David Buckingham
| {{year|1980}}
| [[p29 pre-pulsar shuttle]]
| {{cells|54}}
|-
! {{period|30|brief}}
| [[queen bee shuttle]]
|Bill Gosper
| 1970
| [[queen bee shuttle]]
| {{cells|20}}
|-
! {{period|31|brief}}
| [[Merzenich's p31]]
|[[Matthias Merzenich]]
| {{year|2010}}
| [[Merzenich's p31]]
| {{cells|48}}
|-
! {{period|32|brief}}
| [[gourmet]]
|David Buckingham
| {{year|1978}}
| [[p32 honey farm hassler]]
| {{cells|45}}
|-
! {{period|33|brief}}
| [[258P3 on Achim's p11]]
|Noam Elkies, [[Achim Flammenkamp]]
| 1997
| [[caterer on rattlesnake]]
| {{cells|46}}
|-
! {{period|34|brief}}
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''No non-trivial examples found''
|-
! {{period|35|brief}}
| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
|Dean Hickerson
| 1995
| [[p35 honey farm hassler]]
| {{cells|44}}
|-
! {{period|36|brief}}
| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1984
| [[22P36]]
| {{cells|22}}
|-
! {{period|37|brief}}
| [[Beluchenko's p37]]
|[[Nicolay Beluchenko]]
| {{year|2009}}
| [[Beluchenko's p37]]
| {{cells|124}}
|-
! {{period|38|brief}}
| [[44P38]]
|[[David Raucci]]
| {{year|2022}}
| [[44P38]]
| {{cells|44}}
|-
! {{period|39|brief}}
| [[134P39.1]]
|Noam Elkies, David Buckingham
| {{year|2000}}
| [[caterer on Beluchenko's p13]]
|{{cells|46}}
|-
! {{period|40|brief}}
| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| 1991
| [[Beluchenko's p40]]
| {{cells|26}}
|-
! class="red_td" | 41
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|42|brief}}
| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
|Noam Elkies
| 1994
| [[unix on 34P14 shuttle]]
| {{cells|50}}
|-
! {{period|43|brief}}
| [[p43 Snark loop]]
|[[Mike Playle]]
| {{year|2013}}
| [[p43 Snark loop]]
|{{cells|228}}
|-
! {{period|44|brief}}
| [[p44 pi-heptomino hassler]]
|David Buckingham
| 1992
| [[mold on rattlesnake]]
| {{cells|45}}
|-
! {{period|45|brief}}
| [[pentadecathlon on snacker]]
| [[Mark Niemiec]], John Conway
| ≤1992
| [[pentadecathlon on thumb 1]]
| {{cells|48}}
|-
! {{period|46|brief}}
| [[twin bees shuttle]]
|Bill Gosper
| 1971
| [[twin bees shuttle]]
| {{cells|28}}
|-
! {{period|47|brief}}
| [[p47 pre-pulsar shuttle]]
|David Buckingham
| {{year|1982}}
| [[p47 pre-pulsar shuttle]]
| {{cells|84}}
|-
! {{period|48|brief}}
| [[p48 toad hassler]]
|Bill Gosper
| 1994
| [[30P3 on Rob's p16]]
| {{cells|51}}
|-
! {{period|49|brief}}
| [[p49 glider shuttle]]
|Noam Elkies
| {{year|1999}}
| {{LinkCatagolue|xp49_yzylc69h1hm4k8zyzyb8gy34b8q3034odzyzy972qngy61111g0s82u08k8zyzwsg8y4ggy488oxcc011w11zyzy76221y51zyqgzyo132yf532zyqgzy7ooxca8y46511y284sz8k80u28s26ya4kc0gzy011woci222c88gy37913zy38mgk7079grzy6122221|style=raw|patternname=p49 22hd reflector loop}}
| {{cells|188}}
|-
! {{period|50|brief}}
| [[p50 glider shuttle]]
|Dean Hickerson
| 1992
| [[24P10 on 30P25]]
| {{cells|58}}
|-
! {{period|51|brief}}
| [[Beluchenko's p51]]
|Nicolay Beluchenko
| 2009
| [[90P51]]
| {{cells|90}}
|-
! {{period|52|brief}}
| [[Four eaters hassling lumps of muck]]
|David Buckingham
| 1977
| [[four eaters hassling lumps of muck]]
| {{cells|35}}
|-
! {{period|53|brief}}
| [[p53 Snark loop]]
|Mike Playle
| {{year|2013}}
| [[p53 Snark loop]]
|{{cells|228}}
|-
! {{period|54|brief}}
| [[p54 shuttle]]
|David Buckingham
| {{year|1973}}
| [[p54 shuttle]]
| {{cells|48}}
|-
! {{period|55|brief}}
| [[p55 pre-pulsar hassler]]
|David Buckingham
| {{year|1986}}
| [[pseudo-barberpole on rattlesnake]]
| {{cells|49}}
|-
! {{period|56|brief}}
| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| ≤1991
| [[p56 B-heptomino shuttle]]
| {{cells|45}}
|-
! {{period|57|brief}}
| [[p57 Herschel loop 1]]
|[[Dietrich Leithner]]
| 1997
| p57 180° glider loop
|{{cells|146}}
|-
! {{period|58|brief}}
| [[p58 toadsucker]]
|Bill Gosper
| 1994
| [[p58 pre-pulsar shuttle]]
| {{cells|104}}
|-
! {{period|59|brief}}
| [[p59 Herschel loop 1]]
|David Buckingham
| 1997
| [[Adjustable glider loop|p59 Snark loop]]
|{{cells|228}}
|-
! {{period|60|brief}}
| [[p60 glider shuttle]]
| ?
| ≤1971
| [[mold on pentadecathlon]]
| {{cells|24}}
|-
! {{period|61|brief}}
| [[p61 Herschel loop 1]]
|David Buckingham
| {{year|1996}}
| [[Adjustable glider loop|p61 Snark loop]]
|{{cells|228}}
|-
! {{period|62|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[66P62]]
| {{cells|66}}
|-
! {{period|63|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[meatball on p9 thumb]]
| {{cells|74}}
|-
! {{period|64|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Merzenich's p64]]
| {{cells|34}}
|-
! {{period|65|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[fumarole on Beluchenko's p13]]
| {{cells|52}}
|-
! {{period|66|brief}}
| [[p42 glider shuttle|p66 glider shuttle]]
| Robert Wainwright
| 1984
| [[caterer on Jason's p22]]
| {{cells|48}}
|-
! {{period|67|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p67 Snark loop]]
|{{cells|228}}
|-
! {{period|68|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[72P68]]
|{{cells|72}}
|-
! {{period|69|brief}}
| Herschel loop
| David Buckingham
| 1996
| p69 180° glider loop
|{{cells|146}}
|-
! {{period|70|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[fumarole on 34P14 shuttle]]
| {{cells|52}}
|-
! {{period|71|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p71 Snark loop]]
|{{cells|228}}
|-
! {{period|72|brief}}
| [[two blockers hassling R-pentomino]]
|Robert Wainwright
| 1990
| [[figure eight on 22P36]]
| {{cells|36}}
|-
! {{period|73|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p73 Snark loop]]
|{{cells|228}}
|-
! {{period|74|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Raucci's p74]]
| {{cells|84}}
|-
! {{period|75|brief}}
| [[6 bits]]
| Robert Wainwright
| 1984
| [[pentadecathlon on 30P25]]
|{{cells|46}}
|-
! {{period|76|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[mold on 44P38]]
| {{cells|56}}
|-
! {{period|77|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[meatball on rattlesnake]]
|{{cells|71}}
|-
! {{period|78|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[p6 thumb on Beluchenko's p13]]
|{{cells|61}}
|-
! {{period|79|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p79 Snark loop]]
|{{cells|228}}
|-
! {{period|80|brief}}
| [[middleweight volcano]] on [[Achim's other p16]]
| Dean Hickerson, Achim Flammenkamp
| 1994
| [[fumarole on Rob's p16]]
| {{cells|39}}
|-
! {{period|81|brief}}
| Herschel loop
| David Buckingham
| 1996
| p81 180° glider loop
|{{cells|146}}
|-
! {{period|82|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p82 Snark loop]]
|{{cells|208}}
|-
! {{period|83|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p83 Snark loop]]
|{{cells|228}}
|-
! {{period|84|brief}}
| [[caterer]] on [[p28 pre-pulsar shuttle]] variant
| ?
| ≤1994
| [[p84 honey farm hassler]]
| {{cells|42}}
|-
! {{period|85|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[74P85]]
|{{cells|74}}
|-
! {{period|86|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p86 Snark loop]]
|{{cells|208}}
|-
! {{period|87|brief}}
| [[caterer]] on [[p29 pentadecathlon hassler]]
| Bill Gosper
| 1994
| [[84P87]]
| {{cells|84}}
|-
! {{period|88|brief}}
| p44n glider loop
|David Buckingham
| 1992
| [[figure eight on rattlesnake]]
| {{cells|45}}
|-
! {{period|89|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p89 Snark loop]]
|{{cells|228}}
|-
! {{period|90|brief}}
| p30n glider loop
| ?
| ≤1973
| [[thumb 1 on queen bee shuttle]]
| {{cells|56}}
|-
! {{period|91|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[meatball on Beluchenko's p13]]
|{{cells|72}}
|-
! {{period|92|brief}}
| p46n glider loop
| Bill Gosper
| 1971
| [[twin bees shuttle on 21P4.1]]
| {{cells|49}}
|-
! {{period|93|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[caterer on Merzenich's p31]]
|{{cells|60}}
|-
! {{period|94|brief}}
| capped [[P94S]]
| Dean Hickerson
| 1990
| {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]]
| {{cells|110}}
|-
! {{period|95|brief}}
| Herschel loop
| David Buckingham
| 1996
| p95 180° glider loop
| {{cells|166}}
|-
! {{period|96|brief}}
| [[p96 Hans Leo Hassler]]
| Noam Elkies
| 1995
| [[period-48 glider gun with boat-bit]]
| {{cells|59}}
|-
! {{period|97|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p97 Snark loop]]
|{{cells|228}}
|-
! {{period|98|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Gallus]]
| {{cells|105}}
|-
! {{period|99|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[48P9 on rattlesnake]]
|{{cells|82}}
|-
! {{period|100|brief}}
| [[centinal]]
|Bill Gosper
| ≤1987
| [[mold on 30P25]]
| {{cells|42}}
|-
! {{period|101|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p101 Snark loop]]
|{{cells|228}}
|-
! {{period|102|brief}}
| p102+6n [[traffic jam]]
| Noam Elkies
| ≤1996
| [[Raucci's p102]]
| {{cells|67}}
|-
! {{period|103|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[Adjustable glider loop|p103 Snark loop]]
|{{cells|228}}
|-
! {{period|104|brief}}
| p100+4n [[traffic jam]]
| Bill Gosper
| 1994
| [[figure eight on Beluchenko's p13]]
| {{cells|46}}
|-
! {{period|105|brief}}
| [[pentadecathlon]] on [[44P7.2]]
| ?
| ≤1992
| [[pentadecathlon on 37P7.1]]
|{{cells|49}}
|-
! {{period|106|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[rectifier|p106 rectifier loop]]
|{{cells|169}}
|-
! {{period|107|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[rectifier|p107 rectifier loop]]
|{{cells|136}}
|-
! {{period|108|brief}}
| [[p54 shuttle]] on [[figure eight]]
| ?
| ≤1992
| [[22P4.3 on 56P27]]
| {{cells|78}}
|-
! {{period|109|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[rectifier|p109 rectifier loop]]
| {{cells|156}}
|-
! {{period|110|brief}}
| [[p110 traffic jam]]
| Bill Gosper
| 1994
| [[pseudo-barberpole on Jason's p22]]
| {{cells|51}}
|-
! {{period|111|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[rectifier|p111 rectifier loop]]
| {{cells|136}}
|-
! {{period|112|brief}}
| p100+4n [[traffic jam]]
| Bill Gosper
| 1994
| [[tumbler on Rich's p16]]
| {{cells|50}}
|-
! {{period|113|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[nihonium]]
| {{cells|106}}
|-
! {{period|114|brief}}
| [[p42 glider shuttle|p66+24n glider shuttle]]
| Robert Wainwright
| 1984
| [[caterer on 44P38]]
| {{cells|57}}
|-
! {{period|115|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[rectifier|p115 rectifier loop]]
| {{cells|136}}
|-
! {{period|116|brief}}
| p100+4n [[traffic jam]]
| Bill Gosper
| 1994
| {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=102P116|style=raw}}
|{{cells|102}}
|-
! {{period|117|brief}}
| Herschel loop
| David Buckingham
| 1996
| {{LinkCatagolue|xp117_x32acxca23zggxg84448gxggy2g88cz14fes72x27sef41y211zyfeehrzyq33zyfo8gy5g33zyfopw11267608g3568w66zyseu4zyu3|patternname=112P117|style=raw}}
| {{cells|112}}
|-
! {{period|118|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[rectifier|p118 rectifier loop]]
| {{cells|154}}
|-
! {{period|119|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[rectifier|p119 rectifier loop]]
| {{cells|136}}
|-
! {{period|120|brief}}
| p30n glider loop
| ?
| ≤1973
| [[figure eight on pentadecathlon]]
| {{cells|24}}
|-
! {{period|124|brief}}
| [[p124 lumps of muck hassler]]
| Dean Hickerson
| 1994
| [[mold on Merzenich's p31]]
| {{cells|60}}
|-
! {{period|126|brief}}
| p102+6n [[traffic jam]]
| Noam Elkies
| ≤1996
| [[snacker on 34P14 shuttle]]
| {{cells|74}}
|-
! {{period|128|brief}}
| [[Period-256 glider gun#Gallery|spark-assisted p128 Herschel loop]]
| David Buckingham
| 1991
| [[p128 wing shuttle]], {{LinkCatagolue|xp128_ytokgyb6664abw66zyz8kk8y9ccwgc8gzyvggkcya33y473666zooogoy4ggyaca23w1zx134c2wcc011y64aa4zy3oowkk8oooyb2a6zy71|patternname=p128 Coe-blocker loop|style=raw}}
|{{cells|108}}
|-
! {{period|129|brief}}
| Herschel loop
| David Buckingham
| 1996
| p129 180° glider loop
|{{cells|146}}
|-
! {{period|130|brief}}
| [[p50 glider shuttle|p50+40n glider shuttle]]
| Dean Hickerson
| 1992
| [[55P10 on Beluchenko's p13]]
| {{cells|89}}
|-
! {{period|132|brief}}
| p44n glider loop
| David Buckingham
| 1992
| [[mold on Jason's p33]]
| {{cells|72}}
|-
! {{period|135|brief}}
| [[106P135]]
| Bill Gosper
| {{year|1989}}
| [[pentadecathlon on 56P27]]
|{{cells|68}}
|-
! {{period|136|brief}}
| [[p136 spark-assisted Herschel loop]]
| David Buckingham
| 1991
| {{LinkCatagolue|xp136_y3ca73oswcczy2ggwooy98m113czccwe192y166y7220o8zyq113y0oggzyz23088y7ccy18igew66zyz6oggd2y933w11zyzya66w73osa6|patternname=p136 Coe-blocker loop|style=raw}}
| {{cells|108}}
|-
! {{period|138|brief}}
| p46n glider loop
| Bill Gosper
| 1971
| [[Gabriel's p138]]
| {{cells|36}}
|-
! {{period|140|brief}}
| p100+10n traffic jam
| Bill Gosper
| 1994
| [[34P14 shuttle on dockyard]]
| {{cells|82}}
|-
! {{period|141|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[p47 pre-pulsar shuttle phase-shifting 28P7.1]]
| {{cells|114}}
|-
! {{period|143|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[p11 domino sparker on 66P13]]
| {{cells|107}}
|-
! {{period|144|brief}}
| capped p144 [[gunstar]]
| David Buckingham
| 1990
| [[Achim's p144]]
| {{cells|42}}
|-
! {{period|150|brief}}
| p30n glider loop
| ?
| ≤1973
| [[unix on 30P25]]
| {{cells|46}}
|-
! {{period|152|brief}}
| p136+8n Herschel loop
| David Buckingham
| 1991
| [[figure eight on 44P38]]
| {{cells|60}}
|-
! {{period|156|brief}}
| p156 [[traffic jam]] oscillator
| Bill Gosper
| 1994
| [[p156 unix loop]]
| {{cells|86}}
|-
! {{period|165|brief}}
| [[p165 glider shuttle]]
| Robert Wainwright
| ≤1989
| [[rattlesnake on pentadecathlon]]
| {{cells|45}}
|-
! {{period|168|brief}}
| p136+8n Herschel loop
| David Buckingham
| 1991
| [[figure eight on 32P21]]
| {{cells|44}}
|-
! {{period|177|brief}}
| ?
| ?
| ?
| [[Karel's p177]]
| {{cells|104}}
|-
! {{period|184|brief}}
| p46n glider loop
| Bill Gosper
| 1971
| [[figure eight on twin bees shuttle]]
| {{cells|40}}
|-
! {{period|186|brief}}
| [[p42 glider shuttle|p66+24n glider shuttle]]
| Robert Wainwright
| 1984
| [[unix on Merzenich's p31]]
| {{cells|64}}
|-
! {{period|188|brief}}
| p94n glider loop
| Dean Hickerson
| 1990
| [[AK-94 with boat-bits]]
| {{cells|108}}
|-
! {{period|196|brief}}
| ?
| ?
| ?
| [[p196 pi-heptomino hassler]]
| {{cells|66}}
|-
! {{period|200|brief}}
| p100n glider loop
| Bill Gosper
| ≤1987
| [[figure eight on 30P25]]
|{{cells|42}}
|-

! {{period|226|brief}}
| Herschel loop
| David Buckingham
| 1996
| [[nihonium*]]
| {{cells|107}}
|-
! {{period|230|brief}}
| p46n glider loop
| Bill Gosper
| 1971
| [[fumarole on twin bees shuttle]]
|{{cells|46}}
|-
! {{period|231|brief}}
| ?
| ?
| ?
| [[rattlesnake on 32P21]]
|{{cells|66}}
|-
! {{period|232|brief}}
| [[figure eight on p29 pre-pulsar shuttle]]
| ?
| ?
| [[figure eight on p29 pre-pulsar shuttle]]
|{{cells|66}}
|-
! {{period|240|brief}}
| p30n glider loop
| ?
| ≤1973
| [[pentadecathlon on Rob's p16]]
| {{cells|33}}
|-
! {{period|246|brief}}
| [[p42 glider shuttle#Gallery|p246 glider shuttle]]
| Dean Hickerson
| 1992
| [[period-246 glider gun#Gallery|period-246 glider gun variant]]
| {{cells|68}}
|-
! {{period|256|brief}}
| [[Period-256 glider gun#Gallery|spark-assisted p256 Herschel loop]]
| David Buckingham
| 1991
| {{LinkCatagolue|xp256_ytokgyb6664abw66zyz8kk8y9ccwgc8gzyvggkcya33y473666zooogoy4ggyaca23w1zx134c2wcc011y64aa4zy3oowkk8ooozy71|patternname=p256 Coe-blocker loop|style=raw}}
| {{cells|103}}
|-
! {{period|276|brief}}
| p46n glider loop
| Bill Gosper
| 1971
| [[caterer on 50P92.1]]
| {{cells|62}}
|-
! {{period|300|brief}}
| [[p60 glider shuttle|p60+120n glider shuttle]]
| ?
| ≤1971
| [[pentadecathlon on centinal]]
| {{cells|88}}
|-
! {{period|312|brief}}
| p136+8n Herschel loop
| David Buckingham
| 1991
| [[60P312]]
| {{cells|60}}
|-
! {{period|320|brief}}
| p136+8n Herschel loop
| David Buckingham
| 1991
| [[fumarole on Merzenich's p64]]
| {{cells|52}}
|-
! {{period|360|brief}}
| p30n glider loop
| ?
| ≤1973
| [[thumb 1 on Beluchenko's p40]]
| {{cells|62}}
|-
! {{period|368|brief}}
| p46n glider loop
| Bill Gosper
| 1971
| [[period-184 glider gun with boat-bits]]
| {{cells|50}}
|-
! {{period|460|brief}}
| p46n glider loop
| Bill Gosper
| 1971
| [[pseudo-barberpole on 50P92.1]]
| {{cells|65}}
|-
! {{period|492|brief}}
| ?
| ?
| ?
| [[period-246 glider gun with boat-bit]]
| {{cells|87}}
|-
! {{period|496|brief}}
| p136+8n Herschel loop
| David Buckingham
| 1991
| [[Rob's p16 on Merzenich's p31]]
| {{cells|69}}
|-
! {{period|512|brief}}
| p136+8n Herschel loop
| David Buckingham
| 1991
| [[period-256 glider gun with boat-bits]]
| {{cells|100}}
|-
! {{period|856|brief}}
| [[period-856 glider gun]]
| [[David Buckingham]]
| 1991
| {{LinkCatagolue|xp856_yzyzyrca8ya66wd52666zyzyzyw8kk8y9cccoszyzyzysggkcya33y11261w66zyzyzys1zzzzzzzzzzzzzzzooogoy4ggyaca23zx134c2wcc011y64aa4zy3oowkk8ooozy71|patternname=p856 Coe-blocker loop|style=raw}}
|{{cells|103}}
|}

==Flipper==
A '''flipper''' is any [[oscillator]] that forms its mirror image halfway through its [[period]]. For example, see [[Toad#Gallery|p60 toad flipper]].

==Notes==
<references group=note />

==References==
<references>
<ref name="post132979">{{LinkForumThread
|format = ref
|title = Re: Smallest Known Oscillators to p106 (and Beyond)
|p = 132979
|author = Jeremy Tan
|date = July 3, 2021
}}</ref>
</references>

==See also==
*[[List of common oscillators]]
*[[:Category:Flipping oscillators|List of flipping oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
*[[Table of oscillators by period]]
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]
*[[Almost oscillator]]
*[[Oscillizer]]-analyze and get vital statistics for an oscillator

==External links==
{{LinkWikipedia|Oscillator_(cellular_automaton)}}
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkLexicon|lex_f.htm#flipper|name=Flipper}}

===Forum threads===
{{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
{{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
{{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}

__NOTOC__

Static symmetry

2022-06-08T05:08:35Z

Freywa: /* C2 */ Only C2_2 exists in hexagonal INTs, not C2_4

A '''static symmetry'''<ref name="post138823" /> refers to the combined rotational and reflectional symmetries of an arrangement of cells on a grid. Most isotropic rules preserve all such symmetries.

This page specifically only covers purely geometric symmetries. Other preserved attributes which are not necessarily geometrical symmetries, notably gutters, are compiled on the [[Minor static symmetries]] page. Symmetries which apply to periodic objects, such as still lifes, oscillators and spaceships, which also includes time symmetries, are listed on the [[Kinetic symmetry]] page.

== Basic theory ==
The Life transition rule, like that of any [[Isotropic non-totalistic Life-like cellular automaton|isotropic cellular automaton]], is invariant under reflections and rotations. That is, the change in state of a cell remains the same if its [[neighbourhood]] is rotated or reflected. This implies there are '''symmetries''' which if present in a pattern are present in all its successors. Note that the converse is not true: a pattern need not have the full symmetry of one of its successor states.

== On a square grid ==
[[File:Symmetries.png|center|frame|Overview of symmetries (excluding D8_2).]]

=== Rotational ===
<div class="mw-collapsible mw-collapsed">
Rotational symmetries are prefixed with "C", referring to the [https://en.wikipedia.org/wiki/Cyclic_group cyclic groups]. Click on "Expand" to the right to view a list of them.
<div class="mw-collapsible-content">

==== C1 ====
'''C1''': Symmetric under 360° rotation. This is essentially no symmetry at all. Example: [[Eater 1]]

<center>{{Sym-demo
|rle = x = 16, y = 16, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o!
|width = 160
|height = 160
|caption = C1 symmetry
}}</center>

==== C2 ====
'''C2''': Symmetric under 180° rotation. There are three possibilities:

* '''C2_1''': Rotation around the center of a cell. The bounding rectangle of a C2_1 pattern is odd by odd. Example: [[Long snake]]
* '''C2_2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd. Example: [[Aircraft carrier]]
* '''C2_4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Snake]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$31o
$15bo14bo$15bo14bo$15bo9b2o3bo$15bo8b4o2bo$15bo8b4o2bo$15bo2b10o2bo$
15bo14bo$15bo14bo$15bo3b2o4b2o3bo$15bo2bo2bo2bo2bo2bo$15bo2bo2bo2bo2bo
2bo$15bo3b2o4b2o3bo$15bo14bo$15bo14bo$15b16o!
|width = 320
|height = 320
|caption = C2_1 symmetry}}
| {{Sym-demo
|rle = x = 31, y = 32, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$15b16o$15bo14bo$15bo14bo$15bo9b2o3bo$15bo8b4o2bo$15bo8b4o2bo$15bo2b
10o2bo$15bo14bo$15bo14bo$15bo3b2o4b2o3bo$15bo2bo2bo2bo2bo2bo$15bo2bo2b
o2bo2bo2bo$15bo3b2o4b2o3bo$15bo14bo$15bo14bo$15b16o!
|width = 320
|height = 320
|caption = C2_2 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$16b16o$16bo14bo$16bo14bo$16bo9b2o3bo$16bo8b4o2bo$16bo8b4o2bo$16bo2b
10o2bo$16bo14bo$16bo14bo$16bo3b2o4b2o3bo$16bo2bo2bo2bo2bo2bo$16bo2bo2b
o2bo2bo2bo$16bo3b2o4b2o3bo$16bo14bo$16bo14bo$16b16o!
|width = 320
|height = 320
|caption = C2_4 symmetry}}
|}

==== C4 ====
'''C4''': Symmetric under 90° rotation. There are two possibilities:

* '''C4_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd. Example: [[Shuriken]]
* '''C4_4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Quad]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o3b2o4b2o3bo3b3o3b2o3bo$o2bo2bo2bo2bo2bo2b4o2b
o2bo2bo$o2bo2bo2bo2bo2bo2b4o2bo2bo2bo$o3b2o4b2o3bo3b3o3b2o3bo$o14bo5bo
8bo$o14bo5bo8bo$o2b10o2bo5bo3b2o3bo$o2b4o8bo5bo2bo2bo2bo$o2b4o8bo5bo2b
o2bo2bo$o3b2o9bo5bo3b2o3bo$o14bo14bo$o14bo14bo$31o$o14bo14bo$o14bo14bo
$o3b2o3bo5bo9b2o3bo$o2bo2bo2bo5bo8b4o2bo$o2bo2bo2bo5bo8b4o2bo$o3b2o3bo
5bo2b10o2bo$o8bo5bo14bo$o8bo5bo14bo$o3b2o3b3o3bo3b2o4b2o3bo$o2bo2bo2b
4o2bo2bo2bo2bo2bo2bo$o2bo2bo2b4o2bo2bo2bo2bo2bo2bo$o3b2o3b3o3bo3b2o4b
2o3bo$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = C4_1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b3o3b2o3bo$o2bo2bo2bo2bo2b2o2b
4o2bo2bo2bo$o2bo2bo2bo2bo2b2o2b4o2bo2bo2bo$o3b2o4b2o3b2o3b3o3b2o3bo$o
14b2o5bo8bo$o14b2o5bo8bo$o2b10o2b2o5bo3b2o3bo$o2b4o8b2o5bo2bo2bo2bo$o
2b4o8b2o5bo2bo2bo2bo$o3b2o9b2o5bo3b2o3bo$o14b2o14bo$o14b2o14bo$32o$32o
$o14b2o14bo$o14b2o14bo$o3b2o3bo5b2o9b2o3bo$o2bo2bo2bo5b2o8b4o2bo$o2bo
2bo2bo5b2o8b4o2bo$o3b2o3bo5b2o2b10o2bo$o8bo5b2o14bo$o8bo5b2o14bo$o3b2o
3b3o3b2o3b2o4b2o3bo$o2bo2bo2b4o2b2o2bo2bo2bo2bo2bo$o2bo2bo2b4o2b2o2bo
2bo2bo2bo2bo$o3b2o3b3o3b2o3b2o4b2o3bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = C4_4 symmetry}}
|}
</div></div>

C4 tends to produce record [[diehard]]s and [[megasized]] soups compared to other symmetries.

=== Reflectional ===
<div class="mw-collapsible mw-collapsed">
Reflectional symmetries are prefixed with "D", referring to the [https://en.wikipedia.org/wiki/Dihedral_group dihedral groups]. Click on "Expand" to the right to view a list of them.
<div class="mw-collapsible-content">

==== D2 ====
'''D2''': Symmetric under reflection through a line. There are two possibilities:

* '''D2_+''' The line is orthogonal. There are two sub-possibilities:
** '''D2_+1''' The line bisects a row of cells. The bounding rectangle is odd by any.
** '''D2_+2''' The line lies between two rows of cells. The bounding rectangle is even by any.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 16, y = 31, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$o14bo$o14bo$o3b2o9bo$o2b4o8bo$o2b4o8bo$o2b10o2bo$o14bo$o14bo$o3b2o4b
2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b2o3bo$o14bo$o14bo$16o!
|width = 160
|height = 320
|caption = D2_+1 symmetry}}
| {{Sym-demo
|rle = x = 16, y = 32, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$16o$o14bo$o14bo$o3b2o9bo$o2b4o8bo$o2b4o8bo$o2b10o2bo$o14bo$o14bo$o3b
2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b2o3bo$o14bo$o14bo$
16o!
|width = 160
|height = 320
|caption = D2_+2 symmetry}}
|}

* '''D2_x''' The line is diagonal.

<center>{{Sym-demo
|rle = x = 16, y = 16, rule = B/S012345678
16o$o14bo$o14bo$o7bo6bo$o6bobo5bo$o7bo3bo2bo$o11bo2bo$o3bo7bo2bo$o2bob
o6bo2bo$o3bo6bo3bo$o9bo4bo$o8bo5bo$o4b4o6bo$o14bo$o14bo$16o!
|width = 160
|height = 160
|caption = D2_x symmetry}}</center>

==== D4 ====
'''D4''': Symmetric under both reflection and 180° rotation. The reflection symmetry will be with respect to two lines. There are two possibilities:

* '''D4_+''': The lines are orthogonal. There are three sub-possibilities:
** '''D4_+1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.
** '''D4_+2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd.
** '''D4_+4''': Rotation around a corner of a cell. The bounding rectangle is even by even.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o3b2o4b2o3bo3b2o4b2o3bo$o2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo$o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$o3b2o4b2o3bo3b2o4b2o3bo$o14b
o14bo$o14bo14bo$o2b10o2bo2b10o2bo$o2b4o8bo8b4o2bo$o2b4o8bo8b4o2bo$o3b
2o9bo9b2o3bo$o14bo14bo$o14bo14bo$31o$o14bo14bo$o14bo14bo$o3b2o9bo9b2o
3bo$o2b4o8bo8b4o2bo$o2b4o8bo8b4o2bo$o2b10o2bo2b10o2bo$o14bo14bo$o14bo
14bo$o3b2o4b2o3bo3b2o4b2o3bo$o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo$o3b2o4b2o3bo3b2o4b2o3bo$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = D4_+1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 31, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b2o2b
o2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b2o3b
o$o14b2o14bo$o14b2o14bo$o2b10o2b2o2b10o2bo$o2b4o8b2o8b4o2bo$o2b4o8b2o
8b4o2bo$o3b2o9b2o9b2o3bo$o14b2o14bo$o14b2o14bo$32o$o14b2o14bo$o14b2o
14bo$o3b2o9b2o9b2o3bo$o2b4o8b2o8b4o2bo$o2b4o8b2o8b4o2bo$o2b10o2b2o2b
10o2bo$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b
2o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b
2o3bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D4_+2 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b2o2b
o2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b2o3b
o$o14b2o14bo$o14b2o14bo$o2b10o2b2o2b10o2bo$o2b4o8b2o8b4o2bo$o2b4o8b2o
8b4o2bo$o3b2o9b2o9b2o3bo$o14b2o14bo$o14b2o14bo$32o$32o$o14b2o14bo$o14b
2o14bo$o3b2o9b2o9b2o3bo$o2b4o8b2o8b4o2bo$o2b4o8b2o8b4o2bo$o2b10o2b2o2b
10o2bo$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b
2o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b
2o3bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D4_+4 symmetry}}
|}

* '''D4_x''' The lines are diagonal. There are two sub-possibilities:
** '''D4_x1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.
** '''D4_x4''': Rotation around a corner of a cell. The bounding rectangle is even by even.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o7bo6bo5b3o6bo$o6bobo5bo5bobo6bo$o7bo3bo2bo2bo
2b3o6bo$o11bo2bo2b2o10bo$o3bo7bo2bo2b2o5b3o2bo$o2bobo6bo2bo2b3o4bobo2b
o$o3bo6bo3bo3b2o4b3o2bo$o9bo4bo3b4o7bo$o8bo5bo4b5o5bo$o4b4o6bo6b4o4bo$
o14bo14bo$o14bo14bo$31o$o14bo14bo$o14bo14bo$o4b4o6bo6b4o4bo$o5b5o4bo5b
o8bo$o7b4o3bo4bo9bo$o2b3o4b2o3bo3bo6bo3bo$o2bobo4b3o2bo2bo6bobo2bo$o2b
3o5b2o2bo2bo7bo3bo$o10b2o2bo2bo11bo$o6b3o2bo2bo2bo3bo7bo$o6bobo5bo5bob
o6bo$o6b3o5bo6bo7bo$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = D4_x1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o5b3o6bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo2b3o6bo$o11bo2b2o2b2o10bo$o3bo7bo2b2o2b2o5b3o2bo$o2bobo6bo2b2o2b
3o4bobo2bo$o3bo6bo3b2o3b2o4b3o2bo$o9bo4b2o3b4o7bo$o8bo5b2o4b5o5bo$o4b
4o6b2o6b4o4bo$o14b2o14bo$o14b2o14bo$32o$32o$o14b2o14bo$o14b2o14bo$o4b
4o6b2o6b4o4bo$o5b5o4b2o5bo8bo$o7b4o3b2o4bo9bo$o2b3o4b2o3b2o3bo6bo3bo$o
2bobo4b3o2b2o2bo6bobo2bo$o2b3o5b2o2b2o2bo7bo3bo$o10b2o2b2o2bo11bo$o6b
3o2bo2b2o2bo3bo7bo$o6bobo5b2o5bobo6bo$o6b3o5b2o6bo7bo$o14b2o14bo$o14b
2o14bo$32o!
|width = 320
|height = 320
|caption = D4_x4 symmetry}}
|}

==== D8 ====
'''D8''': Symmetric under both reflection and 90° rotation. The reflection symmetry will be with respect to horizontal, vertical, and diagonal lines. There are three possibilities:

* '''D8_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.
* '''D8_2''': Rotation around a edge of a cell. The bounding rectangle is even by odd. This symmetry is not preserved by Life (reverting to D4_+2), but is with most bilaterally symmetric rules.
* '''D8_4''': Rotation around a corner of a cell. The bounding rectangle is even by even.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o7bo6bo6bo7bo$o6bobo5bo5bobo6bo$o7bo3bo2bo2bo
3bo7bo$o11bo2bo2bo11bo$o3bo7bo2bo2bo7bo3bo$o2bobo6bo2bo2bo6bobo2bo$o3b
o6bo3bo3bo6bo3bo$o9bo4bo4bo9bo$o8bo5bo5bo8bo$o4b4o6bo6b4o4bo$o14bo14bo
$o14bo14bo$31o$o14bo14bo$o14bo14bo$o4b4o6bo6b4o4bo$o8bo5bo5bo8bo$o9bo
4bo4bo9bo$o3bo6bo3bo3bo6bo3bo$o2bobo6bo2bo2bo6bobo2bo$o3bo7bo2bo2bo7bo
3bo$o11bo2bo2bo11bo$o7bo3bo2bo2bo3bo7bo$o6bobo5bo5bobo6bo$o7bo6bo6bo7b
o$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = D8_1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 31, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o6bo7bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo3bo7bo$o11bo2b2o2bo11bo$o3bo7bo2b2o2bo7bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo6bo3b2o3bo6bo3bo$o9bo4b2o4bo9bo$o8bo5b2o5bo8bo$o4b4o6b2o6b4o
4bo$o14b2o14bo$o14b2o14bo$32o$o14b2o14bo$o14b2o14bo$o4b4o6b2o6b4o4bo$o
8bo5b2o5bo8bo$o9bo4b2o4bo9bo$o3bo6bo3b2o3bo6bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo7bo2b2o2bo7bo3bo$o11bo2b2o2bo11bo$o7bo3bo2b2o2bo3bo7bo$o6bobo
5b2o5bobo6bo$o7bo6b2o6bo7bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D8_2 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o6bo7bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo3bo7bo$o11bo2b2o2bo11bo$o3bo7bo2b2o2bo7bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo6bo3b2o3bo6bo3bo$o9bo4b2o4bo9bo$o8bo5b2o5bo8bo$o4b4o6b2o6b4o
4bo$o14b2o14bo$o14b2o14bo$32o$32o$o14b2o14bo$o14b2o14bo$o4b4o6b2o6b4o
4bo$o8bo5b2o5bo8bo$o9bo4b2o4bo9bo$o3bo6bo3b2o3bo6bo3bo$o2bobo6bo2b2o2b
o6bobo2bo$o3bo7bo2b2o2bo7bo3bo$o11bo2b2o2bo11bo$o7bo3bo2b2o2bo3bo7bo$o
6bobo5b2o5bobo6bo$o7bo6b2o6bo7bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D8_4 symmetry}}
|}

To preserve D8_2 symmetry, the following [[isotropic non-totalistic]] transitions must either all exist simultaneously with all other transitions in the same line or none should:<ref name="post143859" />

*B4i=B2a=B2i=B1e
*S6a=S7e=S4t=S6i
*S4c=S3y=S4q
*B1c=B2c=B4c
*S3a=S1e=S0
*S7c=S6c=S4e
*B5y=B4w=B4e
*B8=B7e=B5a
*B5e=B4n
*B4a=B5i
*B4t=B5r
*S5y=S5q
*S5e=S5j
*B6i=B3i
*B6c=B6k
*S4i=S3r
*B3j=B3e
*B3y=B3q
*S2k=S2c
*S4a=S3i
*S3e=S4r
*S5i=S2i
</div></div>

== On a hexagonal or triangular grid ==
[[Hexagonal neighbourhood|Hexagonal]] and [[triangular neighbourhood|triangular]] grids have the same set of admissible symmetries as each other (by [http://mathworld.wolfram.com/DualTessellation.html planar] or [https://en.wikipedia.org/wiki/Dual_polyhedron#Dual_polytopes_and_tessellations polytopic duality]), but these are not the same symmetries as square grids. Due to how hexagonal and triangular grids are handled by programs such as [[Golly]] and [[LifeViewer]], they will also appear markedly different in these respects. C2, D2, and D4 symmetries are still compatible, but C4 symmetries become meaningless because the cells no longer have a side count that is perfectly divisible by 4. Other symmetries are exclusive to these alternative grids, as indicated below:

* C1
* C2_1
* C2_4
* C3_1
* C3_3 (unsupported by apgsearch)
* C6
* D2_xo
* D2_x
* D4_x1
* D4_x4
* D6_1
* D6_1o
* D6_3 (unsupported by apgsearch)
* D12

[[apgsearch]] currently supports most higher symmetries for hexagonal rules; the rest (C3_3 and D6_3) will be added in a future version.<ref name="post66638" />

Another type of rotational symmetry which may not have been accounted for in the above list, arising as an alternate form of C2_2, was described in November 2021. Whether this is an actually distinct type of symmetry, however, is unknown and needs investigation.<ref name="post137220" />

=== Rotational ===
<div class="mw-collapsible mw-collapsed">
Click on "Expand" to the right to view a list of hexagonal/triangular rotational symmetries.
<div class="mw-collapsible-content">

==== C1 ====
'''C1''': Symmetric under 360° rotation. This is essentially no symmetry at all.

<center>{{Sym-demo
|rle = x = 16, y = 16, rule = B/S0123456H
16o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$o6b2o6bo$o2b2o10bo$o2bobo9bo$o3b2o
4b2o3bo$o8b2o4bo$o7b2o5bo$o7b3o4bo$o8b2o4bo$o14bo$o14bo$16o!
|width = 200
|height = 200
|caption = C1 symmetry
}}</center>

==== C2 ====
'''C2''': Symmetric under 180° rotation. There are two possibilities:

* '''C2_1''': Rotation around the center of a cell.
* '''C2_2''': Rotation around the midpoint of a side of a cell.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S0123456H
15b16o$15bo14bo$15bo14bo$15bo4b2o8bo$15bo4b3o7bo$15bo5b2o7bo$15bo4b2o
8bo$15bo3b2o4b2o3bo$15bo9bobo2bo$15bo10b2o2bo$15bo6b2o6bo$15bo6bobo5bo
$15bo7b2o5bo$15bo14bo$15bo14bo$31o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$o6b
2o6bo$o2b2o10bo$o2bobo9bo$o3b2o4b2o3bo$o8b2o4bo$o7b2o5bo$o7b3o4bo$o8b
2o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = C2_1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S0123456H
16b16o$16bo14bo$16bo14bo$16bo4b2o8bo$16bo4b3o7bo$16bo5b2o7bo$16bo4b2o
8bo$16bo3b2o4b2o3bo$16bo9bobo2bo$16bo10b2o2bo$16bo6b2o6bo$16bo6bobo5bo
$16bo7b2o5bo$16bo14bo$16bo14bo$16b16o$16o$o14bo$o14bo$o5b2o7bo$o5bobo
6bo$o6b2o6bo$o2b2o10bo$o2bobo9bo$o3b2o4b2o3bo$o8b2o4bo$o7b2o5bo$o7b3o
4bo$o8b2o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = C2_4 symmetry}}
|}

==== C3 ====
'''C3''': Symmetric under 120° rotation. There are two possibilities:

* '''C3_1''': Rotation around the center of a cell.
* '''C3_3''': Rotation around a corner of a cell. (unsupported by apgsearch)

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 46, y = 46, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o9bo$o6b2o2bo$o2b2o2bobo2b
o$o2b3o2b2o3bo$o3b2o8bo$o5bo8bo$bo4bo8bo$2bo4bo2b2o3bo$3bo3bo2bobo2bo$
4bo6b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo$
13bobo$14b2o$31o$o14b2o14bo$o14bobo14bo$o5b2o7bo2bo14bo$o5bobo6bo3bo7b
o6bo$o6b2o6bo4bo7b2ob2o2bo$o2b2o10bo5bo8b4o2bo$o2bobo9bo6bo3b2o4b2o3bo
$o3b2o4b2o3bo7bo2bobo9bo$o8b2o4bo8bo2b2o10bo$o7b2o5bo9bo6b2o6bo$o7b3o
4bo10bo5bobo6bo$o8b2o4bo11bo5b2o7bo$o14bo12bo14bo$o14bo13bo14bo$16o14b
16o!
|width = 400
|height = 400
|caption = C3_1 symmetry}}
| {{Sym-demo
|rle = x = 48, y = 48, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o9bo$o6b2o2bo$o2b2o2bobo2b
o$o2b3o2b2o3bo$o3b2o8bo$o5bo8bo$bo4bo8bo$2bo4bo2b2o3bo$3bo3bo2bobo2bo$
4bo6b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo$
13bobo$14b2o$15bo2$16ob16o$o14bo2bo14bo$o14bo3bo14bo$o5b2o7bo4bo14bo$o
5bobo6bo5bo7bo6bo$o6b2o6bo6bo7b2ob2o2bo$o2b2o10bo7bo8b4o2bo$o2bobo9bo
8bo3b2o4b2o3bo$o3b2o4b2o3bo9bo2bobo9bo$o8b2o4bo10bo2b2o10bo$o7b2o5bo
11bo6b2o6bo$o7b3o4bo12bo5bobo6bo$o8b2o4bo13bo5b2o7bo$o14bo14bo14bo$o
14bo15bo14bo$16o16b16o!
|width = 400
|height = 400
|caption = C3_3 symmetry}}
|}

==== C6 ====
'''C6''': Symmetric under 60° rotation.

<center>{{Sym-demo
|rle = x = 61, y = 61, rule = B/S0123456H
15bo$15b2o$15bobo$15bo2bo$15bo3bo$15bo4bo$15bo5bo$15bo6bo$15bo7bo$15bo
8bo$15bo9bo$15bo6b2o2bo$15bo2b2o2bobo2bo$15bo2b3o2b2o3bo$15bo3b2o8bo$
16o5bo8b16o$bo14bo4bo8bo14bo$2bo14bo4bo2b2o3bo14bo$3bo7b2o5bo3bo2bobo
2bo4b2o8bo$4bo6bobo5bo6b2o2bo4b3o7bo$5bo6b2o6bo9bo5b2o7bo$6bo10b2o2bo
8bo4b2o8bo$7bo9bobo2bo7bo3b2o4b2o3bo$8bo3b2o4b2o3bo6bo9bobo2bo$9bo2b4o
8bo5bo10b2o2bo$10bo2b2ob2o7bo4bo6b2o6bo$11bo6bo7bo3bo6bobo5bo$12bo14bo
2bo7b2o5bo$13bo14bobo14bo$14bo14b2o14bo$15b31o$15bo14b2o14bo$15bo14bob
o14bo$15bo5b2o7bo2bo14bo$15bo5bobo6bo3bo7bo6bo$15bo6b2o6bo4bo7b2ob2o2b
o$15bo2b2o10bo5bo8b4o2bo$15bo2bobo9bo6bo3b2o4b2o3bo$15bo3b2o4b2o3bo7bo
2bobo9bo$15bo8b2o4bo8bo2b2o10bo$15bo7b2o5bo9bo6b2o6bo$15bo7b3o4bo2b2o
6bo5bobo6bo$15bo8b2o4bo2bobo2bo3bo5b2o7bo$15bo14bo3b2o2bo4bo14bo$15bo
14bo8bo4bo14bo$15b16o8bo5b16o$31bo8b2o3bo$32bo3b2o2b3o2bo$33bo2bobo2b
2o2bo$34bo2b2o6bo$35bo9bo$36bo8bo$37bo7bo$38bo6bo$39bo5bo$40bo4bo$41bo
3bo$42bo2bo$43bobo$44b2o$45bo!
|width = 500
|height = 500
|caption = C6 symmetry}}</center>
</div></div>

=== Reflectional ===
<div class="mw-collapsible mw-collapsed">
Click on "Expand" to the right to view a list of hexagonal/triangular reflectional symmetries.
<div class="mw-collapsible-content">

==== D2 ====
'''D2''': There is line symmetry. There are two possibilities:

* '''D2_x''': Through the vertices of a cell.
* '''D2_xo''': Through the edges of a cell.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 16, y = 16, rule = B/S0123456H
16o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$o2bo3b2o6bo$o2bo11bo$o2bo6b2o3bo$o
2bo6bobo2bo$o3bo6b2o2bo$o4bo9bo$o5bo8bo$o6b4o4bo$o14bo$o14bo$16o!
|width = 300
|height = 300
|caption = D2_x symmetry}}
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S0123456H
16o$bo14bo$2bo14bo$3bo8b2o4bo$4bo7b3o4bo$5bo7b2o5bo$6bo8b2o4bo$7bo3b2o
4b2o3bo$8bo2bobo9bo$9bo2b2o10bo$10bo6b2o6bo$11bo5bobo6bo$12bo5b2o7bo$
13bo14bo$14bo14bo$15b16o$15bo14bo$15bo14bo$15bo5b2o7bo$15bo5bobo6bo$15b
o6b2o6bo$15bo2b2o10bo$15bo2bobo9bo$15bo3b2o4b2o3bo$15bo8b2o4bo$15bo7b
2o5bo$15bo7b3o4bo$15bo8b2o4bo$15bo14bo$15bo14bo$15b16o!
|width = 300
|height = 300
|caption = D2_xo symmetry}}
|}

==== D4 ====
'''D4''': Symmetric under both reflection and 180° rotation. The reflection symmetry will be with respect to two lines. There are two possibilities:

* '''D4_x1''': Rotation around the center of a cell.
* '''D4_x4''': Rotation around the edges of a cell.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S0123456H
15b16o$15bo14bo$15bo14bo$15bo4b4o6bo$15bo8bo5bo$15bo9bo4bo$15bo2b2o6bo
3bo$15bo2bobo6bo2bo$15bo3b2o6bo2bo$15bo11bo2bo$15bo6b2o3bo2bo$15bo6bob
o5bo$15bo7b2o5bo$15bo14bo$15bo14bo$31o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$
o2bo3b2o6bo$o2bo11bo$o2bo6b2o3bo$o2bo6bobo2bo$o3bo6b2o2bo$o4bo9bo$o5bo
8bo$o6b4o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = D4_x1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S0123456H
16b16o$16bo14bo$16bo14bo$16bo4b4o6bo$16bo8bo5bo$16bo9bo4bo$16bo2b2o6bo
3bo$16bo2bobo6bo2bo$16bo3b2o6bo2bo$16bo11bo2bo$16bo6b2o3bo2bo$16bo6bob
o5bo$16bo7b2o5bo$16bo14bo$16bo14bo$16b16o$16o$o14bo$o14bo$o5b2o7bo$o5b
obo6bo$o2bo3b2o6bo$o2bo11bo$o2bo6b2o3bo$o2bo6bobo2bo$o3bo6b2o2bo$o4bo
9bo$o5bo8bo$o6b4o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = D4_x4 symmetry}}
|}

==== D6 ====
'''D6''': Symmetric under both reflection and 120° rotation. The reflection symmetry will be with respect to three lines. There are three possibilities:

* '''D6_1''': Rotation around the center of a cell with lines going through the edges of cells.
* '''D6_1o''': Rotation around the center of a cell with lines going through the centers of cells.
* '''D6_3''': Rotation around the corner of a cell. (unsupported by apgsearch)

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 46, y = 46, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o2b5o2bo$o2bo4bo2bo$o2bo5b
o2bo$o2bo6bo2bo$o13bo$o14bo$bo13bo$2bo3b2o2b2o3bo$3bo2bobobobo2bo$4bo
2b2o2b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo
$13bobo$14b2o$31o$o14b2o14bo$o14bobo14bo$o5b2o7bo2bo7b2o5bo$o5bobo6bo
3bo6bobo5bo$o2bo3b2o6bo4bo6b2o3bo2bo$o2bo11bo5bo11bo2bo$o2bo6b2o3bo6bo
3b2o6bo2bo$o2bo6bobo2bo7bo2bobo6bo2bo$o3bo6b2o2bo8bo2b2o6bo3bo$o4bo9bo
9bo9bo4bo$o5bo8bo10bo8bo5bo$o6b4o4bo11bo4b4o6bo$o14bo12bo14bo$o14bo13b
o14bo$16o14b16o!
|width = 400
|height = 400
|caption = D6_1 symmetry}}
| {{Sym-demo
|rle = x = 31, y = 31, rule = B2/S34H
16o$2o14bo$obo14bo$o2bo4b5o5bo$o3bo8b2o4bo$o4bo9b2o3bo$o5bo3b2o5b2o2bo
$o6bo2bobo6bo2bo$o2bo4bo2b2o7bo2bo$o2bo5bo11bo2bo$o2bo2b2o2bo7b2o2bo2b
o$o2bo2bobo2bo6bobo5bo$o2bo3b2o3bo6b2o6bo$o3bo8bo14bo$o3bo9bo14bo$o4bo
9b16o$bo3bo9bo14bo$2bo3bo8bo14bo$3bo2bo3b2o3bo6b2o6bo$4bo2bo2bobo2bo6b
obo5bo$5bo2bo2b2o2bo7b2o2bo2bo$6bo2bo5bo11bo2bo$7bo2bo4bo2b2o7bo2bo$8b
o6bo2bobo6bo2bo$9bo5bo3b2o5b2o2bo$10bo4bo9b2o3bo$11bo3bo8b2o4bo$12bo2b
o4b5o5bo$13bobo14bo$14b2o14bo$15b16o!
|width = 400
|height = 400
|caption = D6_1o symmetry}}
| {{Sym-demo
|rle = x = 48, y = 48, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o2b5o2bo$o2bo4bo2bo$o2bo5b
o2bo$o2bo6bo2bo$o13bo$o14bo$bo13bo$2bo3b2o2b2o3bo$3bo2bobobobo2bo$4bo
2b2o2b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo
$13bobo$14b2o$15bo2$16ob16o$o14bo2bo14bo$o14bo3bo14bo$o5b2o7bo4bo7b2o
5bo$o5bobo6bo5bo6bobo5bo$o2bo3b2o6bo6bo6b2o3bo2bo$o2bo11bo7bo11bo2bo$o
2bo6b2o3bo8bo3b2o6bo2bo$o2bo6bobo2bo9bo2bobo6bo2bo$o3bo6b2o2bo10bo2b2o
6bo3bo$o4bo9bo11bo9bo4bo$o5bo8bo12bo8bo5bo$o6b4o4bo13bo4b4o6bo$o14bo
14bo14bo$o14bo15bo14bo$16o16b16o!
|width = 400
|height = 400
|caption = D6_3 symmetry}}
|}

==== D12 ====
'''D12''': Symmetric under both reflection and 60° rotation. The reflection symmetry will be with respect to six lines.

<center>{{Sym-demo
|rle = x = 61, y = 61, rule = B/S0123456H
15bo$15b2o$15bobo$15bo2bo$15bo3bo$15bo4bo$15bo5bo$15bo6bo$15bo7bo$15bo
8bo$15bo2b5o2bo$15bo2bo4bo2bo$15bo2bo5bo2bo$15bo2bo6bo2bo$15bo13bo$16o
14b16o$bo14bo13bo14bo$2bo14bo3b2o2b2o3bo14bo$3bo6b4o4bo2bobobobo2bo4b
4o6bo$4bo5bo8bo2b2o2b2o2bo8bo5bo$5bo4bo9bo9bo9bo4bo$6bo3bo6b2o2bo8bo2b
2o6bo3bo$7bo2bo6bobo2bo7bo2bobo6bo2bo$8bo2bo6b2o3bo6bo3b2o6bo2bo$9bo2b
o11bo5bo11bo2bo$10bo2bo3b2o6bo4bo6b2o3bo2bo$11bo5bobo6bo3bo6bobo5bo$
12bo5b2o7bo2bo7b2o5bo$13bo14bobo14bo$14bo14b2o14bo$15b31o$15bo14b2o14b
o$15bo14bobo14bo$15bo5b2o7bo2bo7b2o5bo$15bo5bobo6bo3bo6bobo5bo$15bo2bo
3b2o6bo4bo6b2o3bo2bo$15bo2bo11bo5bo11bo2bo$15bo2bo6b2o3bo6bo3b2o6bo2bo
$15bo2bo6bobo2bo7bo2bobo6bo2bo$15bo3bo6b2o2bo8bo2b2o6bo3bo$15bo4bo9bo
9bo9bo4bo$15bo5bo8bo2b2o2b2o2bo8bo5bo$15bo6b4o4bo2bobobobo2bo4b4o6bo$
15bo14bo3b2o2b2o3bo14bo$15bo14bo13bo14bo$15b16o14b16o$31bo13bo$32bo2bo
6bo2bo$33bo2bo5bo2bo$34bo2bo4bo2bo$35bo2b5o2bo$36bo8bo$37bo7bo$38bo6bo
$39bo5bo$40bo4bo$41bo3bo$42bo2bo$43bobo$44b2o$45bo!
|width = 500
|height = 500
|caption = D12 symmetry}}</center>
</div></div>

== References ==
<references>
<ref name="post138823">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 138823
|author = GUYTU6J
|date = December 13, 2021
}}</ref>
<ref name="post143859">{{LinkForumThread
|format = ref
|title = Re: Truly Bilateral Life-Like rules
|p = 143859
|author = LaundryPizza03
|date = April 6, 2022
}}</ref>
<ref name="post66638">{{LinkForumThread
|format = ref
|title = Re: apgsearch v4.0
|p = 66638
|author = Adam P. Goucher
|date = December 20, 2018
}}</ref>
<ref name="post137220">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 137220
|author = GUYTU6J
|date = November 2, 2021
}}</ref>
</references>

== External links ==
{{LinkLexicon|lex_s.htm#symmetric|name=Symmetric}}
{{LinkForumThread|f=7|t=1898|title=Help with symmetries}}

[[Category:Everything else]]

Table of oscillators by period

2022-06-07T20:26:31Z

Freywa: ???

This table provides a link to the '''S'''mallest '''K'''nown '''O'''scillator for each '''P'''eriod (SKOP). Smallness is by minimum population. Where there is more than one SKOP for a period, only one is linked.
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|- align=center valign=center
! colspan="24" | Smallest [[oscillator]] for each period
|- align=center valign=center
| style="background-color:#c6efce" | [[block|1]]
| style="background-color:#c6efce" | [[blinker|2]]
| style="background-color:#c6efce" | [[caterer|3]]
| style="background-color:#c6efce" | [[mold|4]]
| style="background-color:#c6efce" | [[pseudo-barberpole|5]]
| style="background-color:#c6efce" | [[unix|6]]
| style="background-color:#c6efce" | [[burloaferimeter|7]]
| style="background-color:#c6efce" | [[figure eight|8]]
| style="background-color:#c6efce" | [[29P9|9]]
| style="background-color:#c6efce" | [[24P10|10]]
| style="background-color:#c6efce" | [[rattlesnake|11]]
| style="background-color:#c6efce" | [[dinner table|12]]
| style="background-color:#c6efce" | [[Beluchenko's p13|13]]
| style="background-color:#c6efce" | [[tumbler|14]]
| style="background-color:#c6efce" | [[pentadecathlon|15]]
| style="background-color:#c6efce" | [[Rob's p16|16]]
| style="background-color:#c6efce" | [[honey thieves|17]]
| style="background-color:#c6efce" | [[p18 bi-block hassler|18]]
| style="background-color:#ff0000" | 19
| style="background-color:#80ff80" | [[mold on fumarole|20]]
| style="background-color:#c6efce" | [[32P21|21]]
| style="background-color:#c6efce" | [[Jason's p22|22]]
| style="background-color:#c6efce" | [[p23 honey farm hassler|23]]
| style="background-color:#80ff80" | [[caterer on figure eight|24]]
|- align=center valign=center
| style="background-color:#c6efce" | [[30P25|25]]
| style="background-color:#80ff80" | [[87P26|26]]
| style="background-color:#c6efce" | [[56P27|27]]
| style="background-color:#80ff80" | [[mold on 34P14 shuttle|28]]
| style="background-color:#c6efce" | [[pre-pulsar shuttle 29|29]]
| style="background-color:#c6efce" | [[queen bee shuttle|30]]
| style="background-color:#c6efce" | [[Merzenich's p31|31]]
| style="background-color:#c6efce" | [[p32 honey farm hassler|32]]
| style="background-color:#80ff80" | [[caterer on rattlesnake|33]]
| style="background-color:#ffff00" | [[honey thieves with test tube baby|34]]
| style="background-color:#c6efce" | [[p35 honey farm hassler|35]]
| style="background-color:#c6efce" | [[22P36|36]]
| style="background-color:#c6efce" | [[Beluchenko's p37|37]]
| style="background-color:#c6efce" | [[44P38|38]]
| style="background-color:#80ff80" | [[caterer on Beluchenko's p13|39]]
| style="background-color:#c6efce" | [[Beluchenko's p40|40]]
| style="background-color:#ff0000" | 41
| style="background-color:#80ff80" | [[unix on 34P14 shuttle|42]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|43]]
| style="background-color:#80ff80" | [[mold on rattlesnake|44]]
| style="background-color:#80ff80" | [[pentadecathlon on thumb 1|45]]
| style="background-color:#c6efce" | [[twin bees shuttle|46]]
| style="background-color:#c6efce" | [[p47 pre-pulsar shuttle|47]]
| style="background-color:#80ff80" | [[30P3 on Rob's p16|48]]
|- align=center valign=center
| style="background-color:#ccaaff" | {{LinkCatagolue|xp49_yzylc69h1hm4k8zyzyb8gy34b8q3034odzyzy972qngy61111g0s82u08k8zyzwsg8y4ggy488oxcc011w11zyzy76221y51zyqgzyo132yf532zyqgzy7ooxca8y46511y284sz8k80u28s26ya4kc0gzy011woci222c88gy37913zy38mgk7079grzy6122221|patternname=49|style=raw}}
| style="background-color:#80ff80" | [[24P10 on 30P25|50]]
| style="background-color:#80ff80" | [[90P51|51]]
| style="background-color:#c6efce" | [[Four eaters hassling lumps of muck|52]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|53]]
| style="background-color:#c6efce" | [[p54 shuttle|54]]
| style="background-color:#80ff80" | [[pseudo-barberpole on rattlesnake|55]]
| style="background-color:#c6efce" | [[p56 B-heptomino shuttle|56]]
| style="background-color:#ccaaff" | [[p57 bumper loop|57]]
| style="background-color:#c6efce" | [[p58 pre-pulsar shuttle|58]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|59]]
| style="background-color:#80ff80" | [[mold on pentadecathlon|60]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|61]]
| style="background-color:#c6efce" | [[66P62|62]]
| style="background-color:#80ff80" | [[meatball on p9 thumb|63]]
| style="background-color:#c6efce" | [[Merzenich's p64|64]]
| style="background-color:#80ff80" | [[fumarole on Beluchenko's p13|65]]
| style="background-color:#80ff80" | [[caterer on Jason's p22|66]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|67]]
| style="background-color:#80ff80" | [[72P68|68]]
| style="background-color:#ccaaff" | {{LinkCatagolue|xp69_yco08868y3ca23zyacb2807x6msy6ggzy6c453yj346co8oggz8oyz04t0vqgz0123ywog488w1zwgw22413ywo8gzw1bv0n4yz032zy0113236c4oyjok46zy811y67dcxs028q6zydo8a6y32c2203|patternname=69|style=raw}}
| style="background-color:#80ff80" | [[fumarole on 34P14 shuttle|70]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|71]]
| style="background-color:#80ff80" | [[figure eight on 22P36|72]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[Adjustable glider loops|73]]
| style="background-color:#c6efce" | [[Raucci's p74|74]]
| style="background-color:#80ff80" | [[Pentadecathlon on 30P25|75]]
| style="background-color:#80ff80" | [[Mold on 44P38|76]]
| style="background-color:#80ff80" | [[meatball on rattlesnake|77]]
| style="background-color:#80ff80" | [[p6 thumb on Beluchenko's p13|78]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|79]]
| style="background-color:#80ff80" | [[fumarole on Rich's p16|80]]
| style="background-color:#ccaaff" | {{LinkCatagolue|xp81_yh32acy386880ozyosm6x7082bczy8o8ym354czy080ki89121zws19073yzy1c871zy3ricywcimz0o4cyzy1ho040ez11yzxg044jb051zy8c88gym47011zya11ckg40oxoqezyd16045o4y3ckggzyu1|patternname=81|style=raw}}
| style="background-color:#ccaaff" | [[Adjustable glider loops|82]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|83]]
| style="background-color:#c6efce" | [[p84 honey farm hassler|84]]
| style="background-color:#80ff80" | [[74P85|85]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|86]]
| style="background-color:#c6efce" | [[84P87|87]]
| style="background-color:#80ff80" | [[figure eight on rattlesnake|88]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|89]]
| style="background-color:#80ff80" | [[thumb 1 on queen bee shuttle|90]]
| style="background-color:#80ff80" | [[meatball on Beluchenko's p13|91]]
| style="background-color:#80ff80" | [[Twin bees shuttle on 21P4.1|92]]
| style="background-color:#80ff80" | [[caterer on Merzenich's p31|93]]
| style="background-color:#c6efce" | [[AK-94|94]]
| style="background-color:#ccaaff" | {{LinkCatagolue|xp95_gwg6t1e8gz11dlka211feow8gzy38o0122221zy41230oows48y12552y7g0gzyo354cy431zzzzyz46ayhgkozzzzzyzyk351yhac4zzzzyzyzy5goy464kozyzyzy5101y78kk8y1247w330o8gzyzyzyvg8888g032zyzyzyv12w3eugg8a5lmggzyzyzyzw12egnc1w1|patternname=95|style=raw}}
| style="background-color:#c6efce" | [[period-48 glider gun|96]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[Adjustable glider loops|97]]
| style="background-color:#d0b65a" | [[Gallus|98]]
| style="background-color:#80ff80" | [[48P9 on rattlesnake|99]]
| style="background-color:#80ff80" | [[Mold on 30P25|100]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|101]]
| style="background-color:#c6efce" | [[Raucci's p102|102]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|103]]
| style="background-color:#80ff80" | [[figure eight on Beluchenko's p13|104]]
| style="background-color:#80ff80" | [[pentadecathlon on 37P7.1|105]]
| style="background-color:#ccaaff" | [[rectifier|106]]
| style="background-color:#ccaaff" | [[rectifier|107]]
| style="background-color:#80ff80" | [[22P4.3 on 56P27|108]]
| style="background-color:#ccaaff" | [[rectifier|109]]
| style="background-color:#80ff80" | [[pseudo-barberpole on Jason's p22|110]]
| style="background-color:#ccaaff" | [[rectifier|111]]
| style="background-color:#80ff80" | [[tumbler on Rich's p16|112]]
| style="background-color:#c6efce" | [[nihonium|113]]
| style="background-color:#80ff80" | [[Caterer on 44P38|114]]
| style="background-color:#ccaaff" | [[rectifier|115]]
| style="background-color:#80ff80" |  {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=116|style=raw}}
| style="background-color:#80ff80" | {{LinkCatagolue|xp117_x32acxca23zggxg84448gxggy2g88cz14fes72x27sef41y211zyfeehrzyq33zyfo8gy5g33zyfopw11267608g3568w66zyseu4zyu3|patternname=117|style=raw}}
| style="background-color:#ccaaff" | [[rectifier|118]]
| style="background-color:#ccaaff" | [[rectifier|119]]
| style="background-color:#80ff80" | [[figure eight on pentadecathlon|120]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|121]]
| style="background-color:#ccaaff" | [[rectifier|122]]
| style="background-color:#ccaaff" | [[rectifier|123]]
| style="background-color:#80ff80" | [[mold on Merzenich's p31|124]]
| style="background-color:#ccaaff" | [[rectifier|125]]
| style="background-color:#80ff80" | [[snacker on 34P14 shuttle|126]]
| style="background-color:#ccaaff" | [[rectifier|127]]
| style="background-color:#c6efce" | [[p128 wing shuttle|128]]
| style="background-color:#ccaaff" | {{LinkCatagolue|xp129_yro08868y3ca23zypcb2807x6mszylc453zzyzynggzyzyo346co8oggz8oyzyr4t0vqgz0123yzynog488w1zwgw22413yzyno8gzw1bv0n4yzyr32zy0113236c4ozy811zzyzy8ok46zyz7dcxs028q6zyso8a6y32c2203|patternname=129|style=raw}}
| style="background-color:#80ff80" | [[55P10 on Beluchenko's p13|130]]
| style="background-color:#ccaaff" | [[rectifier|131]]
| style="background-color:#80ff80" | [[mold on Jason's p33|132]]
| style="background-color:#ccaaff" | [[rectifier|133]]
| style="background-color:#ccaaff" | [[rectifier|134]]
| style="background-color:#80ff80" | [[pentadecathlon on 56P27|135]]
| style="background-color:#d0b65a" | [[Shuttle#Glider_shuttle|136]]
| style="background-color:#ccaaff" | [[rectifier|137]]
| style="background-color:#c6efce" | [[Gabriel's p138|138]]
| style="background-color:#ccaaff" | [[rectifier|139]]
| style="background-color:#80ff80" | [[34P14 shuttle on dockyard|140]]
| style="background-color:#c6efce" | [[p47 pre-pulsar shuttle phase-shifting 28P7.1|141]]
| style="background-color:#ccaaff" | [[rectifier|142]]
| style="background-color:#ccaaff" | [[rectifier|143]]
| style="background-color:#c6efce" | [[Achim's p144|144]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|145]]
| style="background-color:#ccaaff" | [[rectifier|146]]
| style="background-color:#ccaaff" | [[rectifier|147]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|148]]
| style="background-color:#ccaaff" | [[rectifier|149]]
| style="background-color:#80ff80" | [[Unix on 30P25|150]]
| style="background-color:#ccaaff" | [[rectifier|151]]
| style="background-color:#80ff80" | [[Figure eight on 44P38|152]]
| style="background-color:#ccaaff" | [[rectifier|153]]
| style="background-color:#d0b65a" | [[34P14 shuttle|154]]
| style="background-color:#ccaaff" | [[rectifier|155]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|156]]
| style="background-color:#ccaaff" | [[rectifier|157]]
| style="background-color:#ccaaff" | [[rectifier|158]]
| style="background-color:#ccaaff" | [[rectifier|159]]
| style="background-color:#80ff80" | [[Heavyweight volcano on p32 honey farm hassler|160]]
| style="background-color:#ccaaff" | [[rectifier|161]]
| style="background-color:#d0b65a" | [[p6 thumb|162]]
| style="background-color:#ccaaff" | [[rectifier|163]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|164]]
| style="background-color:#80ff80" | [[Rattlesnake on pentadecathlon|165]]
| style="background-color:#ccaaff" | [[rectifier|166]]
| style="background-color:#ccaaff" | [[rectifier|167]]
| style="background-color:#80ff80" | [[Figure eight on 32P21|168]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|169]]
| style="background-color:#d0b65a" | {{LinkCatagolue|xp170_y6438g0ia4zx66w66xac4zxggo4c4oggyh66x66zca16888188861acya358mhh181hhm853zy066x66yj12321zyv66w66zym252x66|patternname=170|style=raw}}
| style="background-color:#ccaaff" | [[rectifier|171]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|172]]
| style="background-color:#ccaaff" | [[rectifier|173]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|174]]
| style="background-color:#80ff80" | [[meatball on 30P25|175]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|176]]
| style="background-color:#c6efce" | [[Karel's p177|177]]
| style="background-color:#ccaaff" | [[rectifier|178]]
| style="background-color:#ccaaff" | [[rectifier|179]]
| style="background-color:#d0b65a" | [[p60 glider shuttle|180]]
| style="background-color:#ccaaff" | [[rectifier|181]]
| style="background-color:#ccaaff" | [[rectifier|182]]
| style="background-color:#ccaaff" | [[rectifier|183]]
| style="background-color:#c6efce" | [[period-184 glider gun|184]]
| style="background-color:#ccaaff" | [[rectifier|185]]
| style="background-color:#80ff80" | [[unix on Merzenich's p31|186]]
| style="background-color:#ccaaff" | [[rectifier|187]]
| style="background-color:#c6efce" | [[AK-94|188]]
| style="background-color:#80ff80" | [[56P27#LCM oscillators|189]]
| style="background-color:#80ff80" | [[44P38#Gallery|190]]
| style="background-color:#ccaaff" | [[rectifier|191]]
| style="background-color:#80ff80" | [[hotcrystal0_reaction#Generalized_form|192]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|193]]
| style="background-color:#ccaaff" | [[rectifier|194]]
| style="background-color:#d0b65a" | [[6 bits|195]]
| style="background-color:#c6efce" | [[p196 pi-heptomino hassler|196]]
| style="background-color:#ccaaff" | [[rectifier|197]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|198]]
| style="background-color:#ccaaff" | [[rectifier|199]]
| style="background-color:#80ff80" | [[Figure eight on 30P25|200]]
| style="background-color:#ccaaff" | [[rectifier|201]]
| style="background-color:#ccaaff" | [[rectifier|202]]
| style="background-color:#ccaaff" | [[rectifier|203]]
| style="background-color:#80ff80" | [[Mold on Raucci's p102|204]]
| style="background-color:#ccaaff" | [[rectifier|205]]
| style="background-color:#ccaaff" | [[rectifier|206]]
| style="background-color:#ccaaff" | [[rectifier|207]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|208]]
| style="background-color:#ccaaff" | [[rectifier|209]]
| style="background-color:#d0b65a" | [[Pentadecathlon|210]]
| style="background-color:#ccaaff" | [[rectifier|211]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|212]]
| style="background-color:#ccaaff" | [[rectifier|213]]
| style="background-color:#ccaaff" | [[rectifier|214]]
| style="background-color:#ccaaff" | [[rectifier|215]]
| style="background-color:#80ff80" | [[56P27#Gallery|216]]
|- align=center valign=center
| style="background-color:#80ff80" | [[meatball on Merzenich's p31|217]]
| style="background-color:#ccaaff" | [[rectifier|218]]
| style="background-color:#ccaaff" | [[rectifier|219]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|220]]
| style="background-color:#ccaaff" | [[rectifier|221]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|222]]
| style="background-color:#ccaaff" | [[rectifier|223]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|224]]
| style="background-color:#80ff80" | [[48P9 on 30P25|225]]
| style="background-color:#c6efce" | [[nihonium*|226]]
| style="background-color:#ccaaff" | [[rectifier|227]]
| style="background-color:#80ff80" | [[unix on p76 pi-heptomino hassler|228]]
| style="background-color:#ccaaff" | [[rectifier|229]]
| style="background-color:#80ff80" | [[fumarole on twin bees shuttle|230]]
| style="background-color:#80ff80" | [[Rattlesnake on 32P21|231]]
| style="background-color:#80ff80" | [[figure eight on p29 pre-pulsar shuttle|232]]
| style="background-color:#ccaaff" | [[rectifier|233]]
| style="background-color:#d0b65a" | [[p6 thumb|234]]
| style="background-color:#ccaaff" | [[rectifier|235]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|236]]
| style="background-color:#ccaaff" | [[rectifier|237]]
| style="background-color:#ccaaff" | [[rectifier|238]]
| style="background-color:#ccaaff" | [[rectifier|239]]
| style="background-color:#80ff80" | [[pentadecathlon on Rob's p16|240]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|241]]
| style="background-color:#ccaaff" | [[rectifier|242]]
| style="background-color:#ccaaff" | [[rectifier|243]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|244]]
| style="background-color:#ccaaff" | [[rectifier|245]]
| style="background-color:#c6efce" | [[period-246 glider gun|246]]
| style="background-color:#ccaaff" | [[rectifier|247]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|248]]
| style="background-color:#ccaaff" | [[rectifier|249]]
| style="background-color:#d0b65a" | {{LinkCatagolue|xp250_y1ooy2o4a9jwggzy1ccy0elh4wrwhhz33x6a2y134aipw11z252zzzzykggy94a4zygoowp452sgy6cczygoowtw2oa7y0jjzykc9521y211|patternname=250|style=raw}}
| style="background-color:#ccaaff" | [[rectifier|251]]
| style="background-color:#80ff80" | [[p84 honey farm hassler#Gallery|252]]
| style="background-color:#ccaaff" | [[rectifier|253]]
| style="background-color:#ccaaff" | [[rectifier|254]]
| style="background-color:#d0b65a" | [[Pentadecathlon|255]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|256]]
| style="background-color:#ccaaff" | [[rectifier|257]]
| style="background-color:#d0b65a" | [[p6 thumb|258]]
| style="background-color:#ccaaff" | [[rectifier|259]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|260]]
| style="background-color:#ccaaff" | [[rectifier|261]]
| style="background-color:#ccaaff" | [[rectifier|262]]
| style="background-color:#ccaaff" | [[rectifier|263]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|264]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|265]]
| style="background-color:#80ff80" | [[44P38#Gallery|266]]
| style="background-color:#ccaaff" | [[rectifier|267]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|268]]
| style="background-color:#ccaaff" | [[rectifier|269]]
| style="background-color:#d0b65a" | [[Buckaroo|270]]
| style="background-color:#ccaaff" | [[rectifier|271]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|272]]
| style="background-color:#ccaaff" | [[rectifier|273]]
| style="background-color:#ccaaff" | [[rectifier|274]]
| style="background-color:#80ff80" | [[p11 domino sparker on 30P25|275]]
| style="background-color:#80ff80" | [[caterer on 50P92.1|276]]
| style="background-color:#ccaaff" | [[rectifier|277]]
| style="background-color:#ccaaff" | [[rectifier|278]]
| style="background-color:#ccaaff" | [[rectifier|279]]
| style="background-color:#80ff80" | [[p35 honey farm hassler#Gallery|280]]
| style="background-color:#ccaaff" | [[rectifier|281]]
| style="background-color:#d0b65a" | [[92P114|282]]
| style="background-color:#ccaaff" | [[rectifier|283]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|284]]
| style="background-color:#d0b65a" | [[Pentadecathlon|285]]
| style="background-color:#ccaaff" | [[rectifier|286]]
| style="background-color:#ccaaff" | [[rectifier|287]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|288]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|289]]
| style="background-color:#ccaaff" | [[rectifier|290]]
| style="background-color:#ccaaff" | [[rectifier|291]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|292]]
| style="background-color:#ccaaff" | [[rectifier|293]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|294]]
| style="background-color:#ccaaff" | [[rectifier|295]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|296]]
| style="background-color:#80ff80" | [[56P27#LCM oscillators|297]]
| style="background-color:#ccaaff" | [[rectifier|298]]
| style="background-color:#ccaaff" | [[rectifier|299]]
| style="background-color:#d0b65a" | [[p60 glider shuttle|300]]
| style="background-color:#ccaaff" | [[rectifier|301]]
| style="background-color:#ccaaff" | [[rectifier|302]]
| style="background-color:#ccaaff" | [[rectifier|303]]
| style="background-color:#80ff80" | [[Rob's p16 on p76 pi-heptomino hassler|304]]
| style="background-color:#ccaaff" | [[rectifier|305]]
| style="background-color:#d0b65a" | [[p6 thumb|306]]
| style="background-color:#ccaaff" | [[rectifier|307]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|308]]
| style="background-color:#ccaaff" | [[rectifier|309]]
| style="background-color:#ccaaff" | [[rectifier|310]]
| style="background-color:#ccaaff" | [[rectifier|311]]
| style="background-color:#c6efce" | [[60P312|312]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|313]]
| style="background-color:#ccaaff" | [[rectifier|314]]
| style="background-color:#d0b65a" | [[6 bits|315]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|316]]
| style="background-color:#ccaaff" | [[rectifier|317]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|318]]
| style="background-color:#ccaaff" | [[rectifier|319]]
| style="background-color:#80ff80" | [[fumarole on Merzenich's p64|320]]
| style="background-color:#ccaaff" | [[rectifier|321]]
| style="background-color:#d0b65a" | [[Twin bees shuttle|322]]
| style="background-color:#ccaaff" | [[rectifier|323]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|324]]
| style="background-color:#80ff80" | [[66P13 on 30P25|325]]
| style="background-color:#ccaaff" | [[rectifier|326]]
| style="background-color:#ccaaff" | [[rectifier|327]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|328]]
| style="background-color:#ccaaff" | [[rectifier|329]]
| style="background-color:#d0b65a" | [[Pentadecathlon|330]]
| style="background-color:#ccaaff" | [[rectifier|331]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|332]]
| style="background-color:#ccaaff" | [[rectifier|333]]
| style="background-color:#ccaaff" | [[rectifier|334]]
| style="background-color:#ccaaff" | [[rectifier|335]]
| style="background-color:#80ff80" | [[Rich's p16 on p84 honey farm hassler|336]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|337]]
| style="background-color:#ccaaff" | [[rectifier|338]]
| style="background-color:#ccaaff" | [[rectifier|339]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|340]]
| style="background-color:#ccaaff" | [[rectifier|341]]
| style="background-color:#80ff80" | [[44P38#Gallery|342]]
| style="background-color:#ccaaff" | [[rectifier|343]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|344]]
| style="background-color:#ccaaff" | [[rectifier|345]]
| style="background-color:#ccaaff" | [[rectifier|346]]
| style="background-color:#ccaaff" | [[rectifier|347]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|348]]
| style="background-color:#ccaaff" | [[rectifier|349]]
| style="background-color:#ccaaff" | [[rectifier|350]]
| style="background-color:#ccaaff" | [[rectifier|351]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|352]]
| style="background-color:#ccaaff" | [[rectifier|353]]
| style="background-color:#d0b65a" | [[p6 thumb|354]]
| style="background-color:#ccaaff" | [[rectifier|355]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|356]]
| style="background-color:#ccaaff" | [[rectifier|357]]
| style="background-color:#ccaaff" | [[rectifier|358]]
| style="background-color:#ccaaff" | [[rectifier|359]]
| style="background-color:#80ff80" | [[thumb 1 on Beluchenko's p40|360]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|361]]
| style="background-color:#ccaaff" | [[rectifier|362]]
| style="background-color:#ccaaff" | [[rectifier|363]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|364]]
| style="background-color:#ccaaff" | [[rectifier|365]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|366]]
| style="background-color:#ccaaff" | [[rectifier|367]]
| style="background-color:#c6efce" | [[period-184 glider gun|368]]
| style="background-color:#ccaaff" | [[rectifier|369]]
| style="background-color:#ccaaff" | [[rectifier|370]]
| style="background-color:#ccaaff" | [[rectifier|371]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|372]]
| style="background-color:#ccaaff" | [[rectifier|373]]
| style="background-color:#ccaaff" | [[rectifier|374]]
| style="background-color:#ccaaff" | [[rectifier|375]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|376]]
| style="background-color:#ccaaff" | [[rectifier|377]]
| style="background-color:#d0b65a" | [[p6 thumb|378]]
| style="background-color:#ccaaff" | [[rectifier|379]]
| style="background-color:#80ff80" | [[Fumarole on p76 pi-heptomino hassler|380]]
| style="background-color:#ccaaff" | [[rectifier|381]]
| style="background-color:#ccaaff" | [[rectifier|382]]
| style="background-color:#ccaaff" | [[rectifier|383]]
| style="background-color:#ccaaff" | [[hotcrystal0_reaction#Generalized_form|384]]
|-
! colspan="24" |
|- align=center valign=center
| colspan="3" | Key:
| colspan="3" style="background-color:#c6efce" | known
| colspan="3" style="background-color:#80ff80" | [[LCM]]
| colspan="3" style="background-color:#ddaaff" | [[glider loop]]
| colspan="3" style="background-color:#d0b65a" | [[shuttle|glider shuttle]]
| colspan="3" style="background-color:#ff0000" | undiscovered
| colspan="3" style="background-color:#ffff00" | [[trivial]]
| colspan="3" style="background-color:#ffffff" | unknown

|}

==Higher periods==
Links for SKOPs for selected higher periods.

{|class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
! period !! min. pop.
|-
| {{LinkCatagolue|xp460_033y133zzzckgsxsgkczzy979102cy733zy9e98043y7ccz31c08zy01050kgzy623|patternname=460|style=raw}} || 65
|-
| {{LinkCatagolue|xp480_y5osq596z4r4y7oy0c871z4r4y6525zy366zy3gggeeezy3333|patternname=480|style=raw}} || 57
|-
| {{LinkCatagolue|xp492_y0o4qa344ozx118f0dc3z8oyago0ab2sycc871z0123y9126e431zy8ooz0mqzyt66w7bcczyy66|patternname=492|style=raw}} || 87
|-
| {{LinkCatagolue|xp496_ccy04ajaeweaja4y0cczz66y04apaeweapa4y066zzy2oo0o8i22zy368wov|patternname=496|style=raw}} || 69
|-
| {{LinkCatagolue|xp512_yr33y166z0ggy033y16426ye33y0ccz011w66yuggz66yz56zzzy2mqyz66zygckgk2a21ya66woozy133y0ccye6426y1cczy566y1cc|patternname=512|style=raw}} || 100
|-
| {{LinkCatagolue|xp532_033y133zo4maxam4oylg88cz1ppy1pp1yggy01hzyf557y53088803zyaggy4ggzy8ckla26eeee62alkc|patternname=532|style=raw}} || 91
|-
| [[30P25#LCM oscillators|550]] || 76
|-
| {{LinkCatagolue|xp690_0ooy9vtvzyc757zok4sxs4kozzzz033y133|patternname=690|style=raw}} || 40
|-
| {{LinkCatagolue|xp836_ydog8oy1o8ehe8zcieg8oye46ll21z0suvy5sg2a4y465zg9jfgoz123zy7s0111zy9222x31e8|patternname=836|style=raw}} || 90
|-
| {{LinkCatagolue|xp992_ccy04ajaeweaja4y0cczz66y04apaeweapa4y066zyeggy2gggzwg8keey711xsss333zw1221y022525zy3o8a6|patternname=992|style=raw}} || 93
|-
| {{LinkCatagolue|xp1008_y48oyc356zy432yi696y9o8gozyjc871zzy12552yg2bq4y4o8zca6y3oggyp113y3ca6zy823ys8kk8zzyogs26zx3123y9cicyi8ozymckoyc32|patternname=1008|style=raw}} ||107
|}

==External links==
*[https://github.com/Parcly-Taxel/Skopje Skopje repository]

[[Category:Oscillators]]

Hotcrystal0 reaction

2022-06-07T16:34:48Z

Freywa: /* Generalized form */ new 8n+4 SKOPs using this reaction have been committed to Skopje

{{DISPLAYTITLE:hotcrystal0 reaction}}
The '''hotcrystal0 reaction''' is a [[periodic]] [[glider]]-receiving mechanism that has been used for creating [[glider gun]]s of various [[period]]s.

== Unix-specific form ==

On November 13, {{year|2021}}, a forums user with pseudonym [[hotcrystal0]] found a [[partial]] [[conduit]] in a Life-related [[cellular automaton]] known as Symbiosis.<ref name="post137613" /> A glider hitting a [[bait]] [[block]] triggers a [[honey farm]] [[predecessor]] explosion, and some peripheral [[alien]] [[catalyst]]s perturb it to restore the block and emit an additional [[octomino II]].
{{EmbedViewer
|pname = period174glidergun
|position = right
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 8 AUTOSTART PAUSE 2 GPS 10 LOOP 174 ]]
|caption = Period 174+24N glider gun (174 shown) 
}}
A fortnight later, [[wwei23]] found that a [[toad]] can turn a premature octomino II into a 90-degree glider, and completed the conduit in plain Life with a couple of [[unix|unices]] as [[sparker]]s.<ref name="post138145" /> The first unix provides a [[dot]] [[spark]] to suppress a B3a birth. The second one can be placed in either of two possible locations, one of which produces an additional 180-degree glider along with the aforementioned one; this results in an adjustable p174+24N glider [[shuttle]]/[[relay]].<ref name="post138147" /> Below is given a list of high periods where the smallest gun by bounding box uses this reaction. The four rows are by itself and with a period doubler, tripler, and quadrupler.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|- align=center valign=center
| style="background-color:#c6efce" | 174
| style="background-color:#c6efce" | 198
| style="background-color:#c6efce" | 222
| style="background-color:#ffffff" | 246
| style="background-color:#ffffff" | 270
| style="background-color:#c6efce" | 294
| style="background-color:#c6efce" | 318
| style="background-color:#c6efce" | 342
|- align=center valign=center
| style="background-color:#c6efce" | 348
| style="background-color:#c6efce" | 396
| style="background-color:#c6efce" | 444
| style="background-color:#ffffff" | 492
| style="background-color:#ffffff" | 540
| style="background-color:#c6efce" | 588
| style="background-color:#c6efce" | 636
| style="background-color:#c6efce" | 684
|- align=center valign=center
| style="background-color:#c6efce" | 522
| style="background-color:#c6efce" | 594
| style="background-color:#c6efce" | 666
| style="background-color:#ffffff" | 738
| style="background-color:#ffffff" | 810
| style="background-color:#c6efce" | 882
| style="background-color:#c6efce" | 954
|- align=center valign=center
| style="background-color:#c6efce" | 696
| style="background-color:#c6efce" | 792
| style="background-color:#c6efce" | 888
| style="background-color:#ffffff" | 984
|- align=center valign=center
| colspan="2" | Key:
| colspan="3" style="background-color:#c6efce" | hotcrystal0 reaction
| colspan="3" style="background-color:#ffffff" | Something else
|}

== Generalized form ==
A few hours after wwei23's post, [[Luka Okanishi]] modified the mechanism and created a true period-51 glider gun.<ref name="post138155" /> The second unix described above is replaced with the eater1-with-[[beehive]] [[constellation]] used in [[p5 quinti-Snark]]; this emits the 180-degree output glider on another [[transparent lane]], 22 [[half-diagonal]]s away from input, but destroys the octomino II. More notably, Luka collided sparks from two copies of this new reflector and added an eater 1, obtaining an extra glider parallel to both inputs and outputs. This [[over-unity reaction]] with a [[repeat time]] of 49 turns out to be suitable for building lower-period glider guns.

Since then, various people have found other compatible sparkers of various periods. Collaborative efforts have managed to construct the first [[true-period]] guns with periods 49 and 51, as well as to reduce in bounding box for several true gun periods including 52, 57, 65. On May 28, {{year|2022}}, the p49 gun was significantly reduced due to the discovery of [[meatball]], a slightly smaller sparker which could be used in place of [[38P7.2]].<ref name="message980248018651578398" />

{|
|{{EmbedViewer
|pname = period49glidergun
|position = center
|viewerconfig = #C [[ GPS 25 THUMBSIZE 2 ZOOM 8 WIDTH 800 HEIGHT 800 LOOP 49 ]]
|caption = p49 glider gun 
}}
|{{EmbedViewer
|pname = period51glidergun
|position = center
|viewerconfig = #C [[ GPS 25 THUMBSIZE 2 ZOOM 8 WIDTH 800 HEIGHT 800 LOOP 51 ]]
|caption = p51 glider gun 
}}
|}

Apart from coupling to give guns, this new 180-degree reflector is also capable of constituting the smallest known oscillator by population of several periods.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Base !! Sparker !! Periods
|-
| 3 || || 57, 69, 81, 129
|-
| 4 || || 148, 164, 172, 212, 220, 236, 244, 260, 268, 284, 292, 308, 316, 332, 340, 356, 364, 388, 404, 436, 452, 484, 500
|-
| 5 || || 95
|-
| 6 || unix || 156, 174, 192, 198, 222, 264, 288, 294, 318, 324, 348, 366, 372, 384
|-
| 7 || meatball || 49
|-
| 8 || blocker || 128, 136, 176, 208, 224, 248, 256, 272, 296, 328, 344, 352, 376, 400, 416, 424, 464, 472, 488
|}

{{EmbedViewer
|pname = P156unixloop
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 600 ]]
|caption = Smallest p156 oscillator 
}}

== References ==
<references>
<ref name="post137613">{{LinkForumThread
|format = ref
|title = Re: Symbiosis
|p = 137613
|author = hotcrystal0
|date = November 13, 2021
}}</ref>
<ref name="post138145">{{LinkForumThread
|format = ref
|title = Re: Thread for your reactions that might be useful for conduits
|p = 138145
|author = wwei23
|date = November 27, 2021
}}</ref>
<ref name="post138147">{{LinkForumThread
|format = ref
|title = Re: Execution of Old Guns by Variable-Speed Firing Squad
|p = 138147
|author = wwei23
|date = November 27, 2021
}}</ref>
<ref name="post138155">{{LinkForumThread
|format = ref
|title = Re: Gun Discussion Thread
|p = 138155
|author = Luka Okanishi
|date = November 27, 2021
}}</ref>
<ref name="message980248018651578398">{{CiteDiscord
|author = iNoMed
|date = May 28, 2022
|channel = cgol
|id = 980248018651578398
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found by hotcrystal0]]
[[Category:Patterns found by wwei23]]
[[Category:Patterns found in 2021]]
[[Category:Guns]]
[[Category:Linear growth]]
[[Category:Infinite growth]]
[[Category:Patterns discovered by pseudonymous users]]
__NOTOC__
{{GliderNavbox}}

P7 bumper

2022-06-06T10:30:35Z

Freywa: Wrong count

{{Reflector
|name = p7 bumper
|pname = p7bumper
|c = 52
|bx = 25
|by = 12
|family = Bumper
|a = 90
|p = 7
|rotor = [[38P7.2]]
|discoverer = Tanner Jacobi
|discoveryear = 2016
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-y/S23-y
|isorulemax = B34c5ce6c7e8/S234cez5r6ei7e8
|rle = true
|viewerconfig = #C [[ THUMBSIZE 2 X -15 Y 10 ZOOM 10 GPS 14 HEIGHT 480 AUTOSTART LOOP 112 ]]
}}

'''p7 [[bumper]]''' is a periodic [[colour-preserving]] [[glider]] [[reflector]] with a minimum [[repeat time]] of 35 [[tick]]s. For an equivalent [[colour-changing]] periodic glider reflector see [[p7 bouncer]]. A [[stable]] [[Snark]] reflector can be substituted for any bumper. This changes the timing of the output glider, which can be useful for rephasing periodic glider [[stream]]s.

[[38P7.2]] can be replaced with [[37P7.1]], allowing for a lower [[population]] but a larger [[bounding box]]. This variant was used in a 206-cell p49 bumper loop, the formerly smallest period-49 [[oscillator]], which has now been superseded by a 188-cell glider shuttle with [[hotcrystal0_reaction#Generalized_form|a new mechanism]].

{|
|{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 15 LOOP 112 X -10 Y 10 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 480 ]]
|pname = alternativep7bumper
|position = center
|caption = A p7 bumper with a slightly smaller population but a slightly larger bounding box 
}}
|{{EmbedViewer
|pname = p49bumperloopnew
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 14 ZOOM 12 HEIGHT 600 WIDTH 600 LOOP 50 ]]
|caption = 206-cell p49 bumper loop 
}}
|}

==External links==
{{LinkLexicon|filename=lex_p.htm#p7bumper|name=p7 bumper}}
{{DISPLAYTITLE:p7 bumper}}
{{GliderNavbox}}

Hotcrystal0 reaction

2022-05-30T05:41:07Z

Freywa: /* Generalized form */ the "Coe-blocker loop" is really just another instance of this mechanism, feel free to add more periods

{{DISPLAYTITLE:hotcrystal0 reaction}}
The '''hotcrystal0 reaction''' is a [[periodic]] [[glider]]-receiving mechanism that has been used for creating [[glider gun]]s of various [[period]]s.

== Unix-specific form ==

On November 13, {{year|2021}}, a forums user with pseudonym [[hotcrystal0]] found a [[partial]] [[conduit]] in a Life-related [[cellular automaton]] known as Symbiosis.<ref name="post137613" /> A glider hitting a [[bait]] [[block]] triggers a [[honey farm]] [[predecessor]] explosion, and some peripheral [[alien]] [[catalyst]]s perturb it to restore the block and emit an additional [[octomino II]].
{{EmbedViewer
|pname = period174glidergun
|position = right
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 8 AUTOSTART PAUSE 2 GPS 10 LOOP 174 ]]
|caption = Period 174+24N glider gun (174 shown) 
}}
A fortnight later, [[wwei23]] found that a [[toad]] can turn a premature octomino II into a 90-degree glider, and completed the conduit in plain Life with a couple of [[unix|unices]] as [[sparker]]s.<ref name="post138145" /> The first unix provides a [[dot]] [[spark]] to suppress a B3a birth. The second one can be placed in either of two possible locations, one of which produces an additional 180-degree glider along with the aforementioned one; this results in an adjustable p174+24N glider [[shuttle]]/[[relay]].<ref name="post138147" /> Below is given a list of high periods where the smallest gun by bounding box uses this reaction. The four rows are by itself and with a period doubler, tripler, and quadrupler.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|- align=center valign=center
| style="background-color:#c6efce" | 174
| style="background-color:#c6efce" | 198
| style="background-color:#c6efce" | 222
| style="background-color:#ffffff" | 246
| style="background-color:#ffffff" | 270
| style="background-color:#c6efce" | 294
| style="background-color:#c6efce" | 318
| style="background-color:#c6efce" | 342
|- align=center valign=center
| style="background-color:#c6efce" | 348
| style="background-color:#c6efce" | 396
| style="background-color:#c6efce" | 444
| style="background-color:#ffffff" | 492
| style="background-color:#ffffff" | 540
| style="background-color:#c6efce" | 588
| style="background-color:#c6efce" | 636
| style="background-color:#c6efce" | 684
|- align=center valign=center
| style="background-color:#c6efce" | 522
| style="background-color:#c6efce" | 594
| style="background-color:#c6efce" | 666
| style="background-color:#ffffff" | 738
| style="background-color:#ffffff" | 810
| style="background-color:#c6efce" | 882
| style="background-color:#c6efce" | 954
|- align=center valign=center
| style="background-color:#c6efce" | 696
| style="background-color:#c6efce" | 792
| style="background-color:#c6efce" | 888
| style="background-color:#ffffff" | 984
|- align=center valign=center
| colspan="2" | Key:
| colspan="3" style="background-color:#c6efce" | hotcrystal0 reaction
| colspan="3" style="background-color:#ffffff" | Something else
|}

== Generalized form ==
A few hours after wwei23's post, [[Luka Okanishi]] modified the mechanism and created a true period-51 glider gun.<ref name="post138155" /> The second unix described above is replaced with the eater1-with-[[beehive]] [[constellation]] used in [[p5 quinti-Snark]]; this emits the 180-degree output glider on another [[transparent lane]], 22 [[half-diagonal]]s away from input, but destroys the octomino II. More notably, Luka collided sparks from two copies of this new reflector and added an eater 1, obtaining an extra glider parallel to both inputs and outputs. This [[over-unity reaction]] with a [[repeat time]] of 49 turns out to be suitable for building lower-period glider guns.

Since then, various people have found other compatible sparkers of various periods. Collaborative efforts have managed to construct the first [[true-period]] guns with periods 49 and 51, as well as to reduce in bounding box for several true gun periods including 52, 57, 65. On May 28, {{year|2022}}, the p49 gun was significantly reduced due to the discovery of [[meatball]], a slightly smaller sparker which could be used in place of [[38P7.2]].<ref name="message980248018651578398" />

{|
|{{EmbedViewer
|pname = period49glidergun
|position = center
|viewerconfig = #C [[ GPS 25 THUMBSIZE 2 ZOOM 8 WIDTH 800 HEIGHT 800 LOOP 49 ]]
|caption = p49 glider gun 
}}
|{{EmbedViewer
|pname = period51glidergun
|position = center
|viewerconfig = #C [[ GPS 25 THUMBSIZE 2 ZOOM 8 WIDTH 800 HEIGHT 800 LOOP 51 ]]
|caption = p51 glider gun 
}}
|}

Apart from coupling to give guns, this new 180-degree reflector is also capable of constituting the smallest known oscillator by population of several periods.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Base !! Sparker !! Periods
|-
| 3 || || 57, 69, 81, 129
|-
| 5 || || 95
|-
| 6 || unix || 174, 192, 198, 222, 264, 288, 294, 318, 324, 348, 366, 372, 384
|-
| 7 || meatball || 49
|-
| 8 || blocker || 128, 136…
|}

{{EmbedViewer
|pname = P156unixloop
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 600 ]]
|caption = Smallest p156 oscillator 
}}

== References ==
<references>
<ref name="post137613">{{LinkForumThread
|format = ref
|title = Re: Symbiosis
|p = 137613
|author = hotcrystal0
|date = November 13, 2021
}}</ref>
<ref name="post138145">{{LinkForumThread
|format = ref
|title = Re: Thread for your reactions that might be useful for conduits
|p = 138145
|author = wwei23
|date = November 27, 2021
}}</ref>
<ref name="post138147">{{LinkForumThread
|format = ref
|title = Re: Execution of Old Guns by Variable-Speed Firing Squad
|p = 138147
|author = wwei23
|date = November 27, 2021
}}</ref>
<ref name="post138155">{{LinkForumThread
|format = ref
|title = Re: Gun Discussion Thread
|p = 138155
|author = Luka Okanishi
|date = November 27, 2021
}}</ref>
<ref name="message980248018651578398">{{CiteDiscord
|author = iNoMed
|date = May 28, 2022
|channel = cgol
|id = 980248018651578398
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found by hotcrystal0]]
[[Category:Patterns found by wwei23]]
[[Category:Patterns found in 2021]]
[[Category:Guns]]
[[Category:Linear growth]]
[[Category:Infinite growth]]
[[Category:Patterns discovered by pseudonymous users]]
__NOTOC__
{{GliderNavbox}}

Hotcrystal0 reaction

2022-05-30T05:33:14Z

Freywa: /* Generalized form */ the p3s are in Skopje too

{{DISPLAYTITLE:hotcrystal0 reaction}}
The '''hotcrystal0 reaction''' is a [[periodic]] [[glider]]-receiving mechanism that has been used for creating [[glider gun]]s of various [[period]]s.

== Unix-specific form ==

On November 13, {{year|2021}}, a forums user with pseudonym [[hotcrystal0]] found a [[partial]] [[conduit]] in a Life-related [[cellular automaton]] known as Symbiosis.<ref name="post137613" /> A glider hitting a [[bait]] [[block]] triggers a [[honey farm]] [[predecessor]] explosion, and some peripheral [[alien]] [[catalyst]]s perturb it to restore the block and emit an additional [[octomino II]].
{{EmbedViewer
|pname = period174glidergun
|position = right
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 8 AUTOSTART PAUSE 2 GPS 10 LOOP 174 ]]
|caption = Period 174+24N glider gun (174 shown) 
}}
A fortnight later, [[wwei23]] found that a [[toad]] can turn a premature octomino II into a 90-degree glider, and completed the conduit in plain Life with a couple of [[unix|unices]] as [[sparker]]s.<ref name="post138145" /> The first unix provides a [[dot]] [[spark]] to suppress a B3a birth. The second one can be placed in either of two possible locations, one of which produces an additional 180-degree glider along with the aforementioned one; this results in an adjustable p174+24N glider [[shuttle]]/[[relay]].<ref name="post138147" /> Below is given a list of high periods where the smallest gun by bounding box uses this reaction. The four rows are by itself and with a period doubler, tripler, and quadrupler.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|- align=center valign=center
| style="background-color:#c6efce" | 174
| style="background-color:#c6efce" | 198
| style="background-color:#c6efce" | 222
| style="background-color:#ffffff" | 246
| style="background-color:#ffffff" | 270
| style="background-color:#c6efce" | 294
| style="background-color:#c6efce" | 318
| style="background-color:#c6efce" | 342
|- align=center valign=center
| style="background-color:#c6efce" | 348
| style="background-color:#c6efce" | 396
| style="background-color:#c6efce" | 444
| style="background-color:#ffffff" | 492
| style="background-color:#ffffff" | 540
| style="background-color:#c6efce" | 588
| style="background-color:#c6efce" | 636
| style="background-color:#c6efce" | 684
|- align=center valign=center
| style="background-color:#c6efce" | 522
| style="background-color:#c6efce" | 594
| style="background-color:#c6efce" | 666
| style="background-color:#ffffff" | 738
| style="background-color:#ffffff" | 810
| style="background-color:#c6efce" | 882
| style="background-color:#c6efce" | 954
|- align=center valign=center
| style="background-color:#c6efce" | 696
| style="background-color:#c6efce" | 792
| style="background-color:#c6efce" | 888
| style="background-color:#ffffff" | 984
|- align=center valign=center
| colspan="2" | Key:
| colspan="3" style="background-color:#c6efce" | hotcrystal0 reaction
| colspan="3" style="background-color:#ffffff" | Something else
|}

== Generalized form ==
A few hours after wwei23's post, [[Luka Okanishi]] modified the mechanism and created a true period-51 glider gun.<ref name="post138155" /> The second unix described above is replaced with the eater1-with-[[beehive]] [[constellation]] used in [[p5 quinti-Snark]]; this emits the 180-degree output glider on another [[transparent lane]], 22 [[half-diagonal]]s away from input, but destroys the octomino II. More notably, Luka collided sparks from two copies of this new reflector and added an eater 1, obtaining an extra glider parallel to both inputs and outputs. This [[over-unity reaction]] with a [[repeat time]] of 49 turns out to be suitable for building lower-period glider guns.

Since then, various people have found other compatible sparkers of various periods. Collaborative efforts have managed to construct the first [[true-period]] guns with periods 49 and 51, as well as to reduce in bounding box for several true gun periods including 52, 57, 65. On May 28, {{year|2022}}, the p49 gun was significantly reduced due to the discovery of [[meatball]], a slightly smaller sparker which could be used in place of [[38P7.2]].<ref name="message980248018651578398" />

{|
|{{EmbedViewer
|pname = period49glidergun
|position = center
|viewerconfig = #C [[ GPS 25 THUMBSIZE 2 ZOOM 8 WIDTH 800 HEIGHT 800 LOOP 49 ]]
|caption = p49 glider gun 
}}
|{{EmbedViewer
|pname = period51glidergun
|position = center
|viewerconfig = #C [[ GPS 25 THUMBSIZE 2 ZOOM 8 WIDTH 800 HEIGHT 800 LOOP 51 ]]
|caption = p51 glider gun 
}}
|}

Apart from coupling to give guns, this new 180-degree reflector is also capable of constituting the smallest known oscillator by population of several periods.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Base !! Sparker !! Periods
|-
| 3 || || 57, 69, 81, 129
|-
| 5 || || 95
|-
| 6 || unix || 174, 192, 198, 222, 264, 288, 294, 318, 324, 348, 366, 372, 384
|-
| 7 || meatball || 49
|}

{{EmbedViewer
|pname = P156unixloop
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 600 ]]
|caption = Smallest p156 oscillator 
}}

== References ==
<references>
<ref name="post137613">{{LinkForumThread
|format = ref
|title = Re: Symbiosis
|p = 137613
|author = hotcrystal0
|date = November 13, 2021
}}</ref>
<ref name="post138145">{{LinkForumThread
|format = ref
|title = Re: Thread for your reactions that might be useful for conduits
|p = 138145
|author = wwei23
|date = November 27, 2021
}}</ref>
<ref name="post138147">{{LinkForumThread
|format = ref
|title = Re: Execution of Old Guns by Variable-Speed Firing Squad
|p = 138147
|author = wwei23
|date = November 27, 2021
}}</ref>
<ref name="post138155">{{LinkForumThread
|format = ref
|title = Re: Gun Discussion Thread
|p = 138155
|author = Luka Okanishi
|date = November 27, 2021
}}</ref>
<ref name="message980248018651578398">{{CiteDiscord
|author = iNoMed
|date = May 28, 2022
|channel = cgol
|id = 980248018651578398
}}</ref>
</references>

[[Category:Patterns]]
[[Category:Patterns found by hotcrystal0]]
[[Category:Patterns found by wwei23]]
[[Category:Patterns found in 2021]]
[[Category:Guns]]
[[Category:Linear growth]]
[[Category:Infinite growth]]
[[Category:Patterns discovered by pseudonymous users]]
__NOTOC__
{{GliderNavbox}}

Oscillator

2022-05-29T12:08:49Z

Freywa: EV's bumper loop is no longer SKOP49

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period).

[[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]].

== Important oscillators by period ==
A list of the first-discovered oscillator of each period,<ref>{{CiteHickersonOscillators|accessdate=April 11, 2009}}</ref> as well the current smallest-known oscillator of that period,<ref name="post132979" /> is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
| rowspan="500" style="border: none;" |
! Smallest known
! Minimum # of cells
|-
! {{period|2|brief}}
| [[blinker]]
|[[John Conway]]
| {{year|1970}}
| [[blinker]]
| {{cells|3}}
|-
! {{period|3|brief}}
| [[pulsar]]
|John Conway
| 1970
| [[caterer]]
| {{cells|12}}
|-
! {{period|4|brief}}
| [[pinwheel]]
|[[Simon Norton]]
| 1970
| [[mazing]], [[mold]]
| {{cells|12}}
|-
! {{period|5|brief}}
| [[octagon 2]]
|[[Sol Goodman]], [[Arthur Taber]]
| {{year|1971}}
| [[pseudo-barberpole]]
| {{cells|15}}
|-
! {{period|6|brief}}
| [[$rats]]
|[[David Buckingham]]
| {{year|1972}}
| [[unix]]
| {{cells|16}}
|-
! {{period|7|brief}}
| [[burloaferimeter]]
|David Buckingham
| 1972
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
| {{cells|28}}
|-
! {{period|8|brief}}
| [[figure eight]]
|Simon Norton
| 1970
| [[figure eight]]
| {{cells|12}}
|-
! {{period|9|brief}}
| [[worker bee]]
|David Buckingham
| 1972
| [[29P9]]
| {{cells|29}}
|-
! {{period|10|brief}}
| [[42P10.3]]
|David Buckingham
| ≤{{year|1976}}
| [[24P10]]
| {{cells|24}}
|-
! {{period|11|brief}}
| [[38P11.1]]
|David Buckingham
| {{year|1977}}
| [[rattlesnake]]
| {{cells|33}}
|-
! {{period|12|brief}}
| [[dinner table]]
|[[Robert Wainwright]]
| {{year|1972}}
| [[dinner table]]
| {{cells|33}}
|-
! {{period|13|brief}}
| [[Buckingham's p13]]
|David Buckingham
| 1976
| [[Beluchenko's p13]]
| {{cells|34}}
|-
! {{period|14|brief}}
| [[tumbler]]
|[[George Collins]]
| 1970
| [[tumbler]]
| {{cells|16}}
|-
! {{period|15|brief}}
| [[pentadecathlon]]
|John Conway
| 1970
| [[pentadecathlon]]
| {{cells|12}}
|-
! {{period|16|brief}}
| [[two pre-L hasslers]]
|Robert Wainwright
| {{year|1983}}
| [[Rob's p16]]
| {{cells|21}}
|-
! {{period|17|brief}}
| [[54P17.1]]
|[[Dean Hickerson]]
| {{year|1997}}
| [[honey thieves]]
| {{cells|36}}
|-
! {{period|18|brief}}
| [[117P18]]{{refn|group=note|name=lcm|[[Non-trivial]] oscillators of this period could have been constructed from two oscillators of lower period (usually [[sparker]]s), both of which were known by an earlier date. However, no such [[LCM oscillator]]s were attested prior to the discovery of this oscillator.}}
|David Buckingham
| ≤{{year|1991}}
| [[p18 bi-block hassler]], [https://catagolue.hatsya.com/object?apgcode=xp18_wc93xs112ogggzbdhe96kk801zw1213&rule=b3s23 p18 phase shifter]
| {{cells|43}}
|-
! class="red_td" | 19
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|20|brief}}
| [[145P20]]{{refn|group=note|name=lcm}}
|[[Noam Elkies]]
| {{year|1995}}
| [[mold on fumarole]]
| {{cells|30}}
|-
! {{period|21|brief}}
| [[124P21]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1995
| [[32P21]]
| {{cells|32}}
|-
! {{period|22|brief}}
| [[168P22.1]]
|Noam Elkies
| 1997
| [[Jason's p22]]
| {{cells|36}}
|-
! {{period|23|brief}}
| [[David Hilbert]]
|[[Luka Okanishi]], [[praosylen]]
| {{year|2019}}
| [[p23 honey farm hassler]]
| {{cells|76}}
|-
! {{period|24|brief}}
| [[186P24]]{{refn|group=note|name=lcm}}
|[[Bill Gosper]]
| {{year|1994}}
| [[caterer on figure eight]]
| {{cells|24}}
|-
! {{period|25|brief}}
| [[134P25]]
|Noam Elkies
| 1994
| [[30P25]]
| {{cells|30}}
|-
! {{period|26|brief}}
| [[p26 pre-pulsar shuttle]]
|David Buckingham
| 1983
| [[87P26]]
| {{cells|87}}
|-
! {{period|27|brief}}
| [[123P27.1]]
|Noam Elkies
| {{year|2002}}
| [[56P27]]
| {{cells|56}}
|-
! {{period|28|brief}}
| [[newshuttle]]
|David Buckingham
| {{year|1973}}
| [[mold on 34P14 shuttle]]
| {{cells|46}}
|-
! {{period|29|brief}}
| [[p29 pre-pulsar shuttle]]
|David Buckingham
| {{year|1980}}
| [[p29 pre-pulsar shuttle]]
| {{cells|54}}
|-
! {{period|30|brief}}
| [[queen bee shuttle]]
|Bill Gosper
| 1970
| [[queen bee shuttle]]
| {{cells|20}}
|-
! {{period|31|brief}}
| [[Merzenich's p31]]
|[[Matthias Merzenich]]
| {{year|2010}}
| [[Merzenich's p31]]
| {{cells|48}}
|-
! {{period|32|brief}}
| [[gourmet]]
|David Buckingham
| {{year|1978}}
| [[p32 honey farm hassler]]
| {{cells|45}}
|-
! {{period|33|brief}}
| [[258P3 on Achim's p11]]
|Noam Elkies, [[Achim Flammenkamp]]
| 1997
| [[caterer on rattlesnake]]
| {{cells|46}}
|-
! {{period|34|brief}}
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''No non-trivial examples found''
|-
! {{period|35|brief}}
| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
|Dean Hickerson
| 1995
| [[p35 honey farm hassler]]
| {{cells|44}}
|-
! {{period|36|brief}}
| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1984
| [[22P36]]
| {{cells|22}}
|-
! {{period|37|brief}}
| [[Beluchenko's p37]]
|[[Nicolay Beluchenko]]
| {{year|2009}}
| [[Beluchenko's p37]]
| {{cells|124}}
|-
! {{period|38|brief}}
| [[44P38]]
|[[David Raucci]]
| {{year|2022}}
| [[44P38]]
| {{cells|44}}
|-
! {{period|39|brief}}
| [[134P39.1]]
|David Buckingham, Noam Elkies
| {{year|2000}}
| [[caterer on Beluchenko's p13]]
|{{cells|46}}
|-
! {{period|40|brief}}
| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| 1991
| [[Beluchenko's p40]]
| {{cells|26}}
|-
! class="red_td" | 41
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|42|brief}}
| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
|Noam Elkies
| 1994
| [[unix on 34P14 shuttle]]
| {{cells|50}}
|-
! {{period|43|brief}}
| [[p43 Snark loop]]
|[[Mike Playle]]
| {{year|2013}}
| [[p43 Snark loop]]
|{{cells|228}}
|-
! {{period|44|brief}}
| [[p44 pi-heptomino hassler]]
|David Buckingham
| 1992
| [[mold on rattlesnake]]
| {{cells|45}}
|-
! {{period|45|brief}}
| [[pentadecathlon on snacker]]
| [[Mark Niemiec]], John Conway
| ≤1995
| [[pentadecathlon on thumb 1]]
| {{cells|48}}
|-
! {{period|46|brief}}
| [[twin bees shuttle]]
|Bill Gosper
| 1971
| [[twin bees shuttle]]
| {{cells|28}}
|-
! {{period|47|brief}}
| [[p47 pre-pulsar shuttle]]
|David Buckingham
| {{year|1982}}
| [[p47 pre-pulsar shuttle]]
| {{cells|84}}
|-
! {{period|48|brief}}
| [[p48 toad hassler]]
|Bill Gosper
| 1994
| [[30P3 on Rob's p16]]
| {{cells|51}}
|-
! {{period|49|brief}}
| [[p49 glider shuttle]]
|Noam Elkies
| {{year|1999}}
| {{LinkCatagolue|xp49_yzylc69h1hm4k8zyzyb8gy34b8q3034odzyzy972qngy61111g0s82u08k8zyzwsg8y4ggy488oxcc011w11zyzy76221y51zyqgzyo132yf532zyqgzy7ooxca8y46511y284sz8k80u28s26ya4kc0gzy011woci222c88gy37913zy38mgk7079grzy6122221|style=raw|patternname=p49 22hd reflector loop}}
| {{cells|188}}
|-
! {{period|50|brief}}
| [[p50 glider shuttle]]
|Dean Hickerson
| 1992
| [[24P10 on 30P25]]
| {{cells|58}}
|-
! {{period|51|brief}}
| [[Beluchenko's p51]]
|Nicolay Beluchenko
| 2009
| [[90P51]]
| {{cells|90}}
|-
! {{period|52|brief}}
| [[Four eaters hassling lumps of muck]]
|David Buckingham
| 1977
| [[four eaters hassling lumps of muck]]
| {{cells|35}}
|-
! {{period|53|brief}}
| [[p53 Snark loop]]
|Mike Playle
| {{year|2013}}
| [[p53 Snark loop]]
|{{cells|228}}
|-
! {{period|54|brief}}
| [[p54 shuttle]]
|David Buckingham
| {{year|1973}}
| [[p54 shuttle]]
| {{cells|48}}
|-
! {{period|55|brief}}
| [[p55 pre-pulsar hassler]]
|David Buckingham
| {{year|1986}}
| [[pseudo-barberpole on rattlesnake]]
| {{cells|49}}
|-
! {{period|56|brief}}
| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| ≤1991
| [[p56 B-heptomino shuttle]]
| {{cells|45}}
|-
! {{period|57|brief}}
| [[p57 Herschel loop 1]]
|[[Dietrich Leithner]]
| 1997
| p57 180° glider loop
|{{cells|146}}
|-
! {{period|58|brief}}
| [[p58 toadsucker]]
|Bill Gosper
| 1994
| [[p58 pre-pulsar shuttle]]
| {{cells|104}}
|-
! {{period|59|brief}}
| [[p59 Herschel loop 1]]
|David Buckingham
| 1997
| [[Adjustable glider loop|p59 Snark loop]]
|{{cells|228}}
|-
! {{period|60|brief}}
| [[p60 glider shuttle]]
|David Buckingham
| ≤ 1971
| [[mold on pentadecathlon]]
| {{cells|24}}
|-
! {{period|61|brief}}
| [[p61 Herschel loop 1]]
|David Buckingham
| {{year|1996}}
| [[Adjustable glider loop|p61 Snark loop]]
|{{cells|228}}
|-
! {{period|62|brief}}
| ?
| ?
| ?
| [[66P62]]
| {{cells|66}}
|-
! {{period|63|brief}}
| ?
| ?
| ?
| [[meatball on p9 thumb]]
| {{cells|74}}
|-
! {{period|64|brief}}
| ?
| ?
| ?
| [[Merzenich's p64]]
| {{cells|34}}
|-
! {{period|65|brief}}
| ?
| ?
| ?
| [[fumarole on Beluchenko's p13]]
| {{cells|52}}
|-
! {{period|66|brief}}
| ?
| ?
| ?
| [[caterer on Jason's p22]]
| {{cells|48}}
|-
! {{period|67|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p67 Snark loop]]
|{{cells|228}}
|-
! {{period|68|brief}}
| ?
| ?
| ?
| [[72P68]]
|{{cells|72}}
|-
! {{period|69|brief}}
| ?
| ?
| ?
| p69 180° glider loop
|{{cells|146}}
|-
! {{period|70|brief}}
| ?
| ?
| ?
| [[fumarole on 34P14 shuttle]]
| {{cells|52}}
|-
! {{period|71|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p71 Snark loop]]
|{{cells|228}}
|-
! {{period|72|brief}}
| [[two blockers hassling R-pentomino]]
|Robert Wainwright
| 1990
| [[figure eight on 22P36]]
| {{cells|36}}
|-
! {{period|73|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p73 Snark loop]]
|{{cells|228}}
|-
! {{period|74|brief}}
| p74 Herschel loop
|David Buckingham
| 1996
| [[Raucci's p74]]
| {{cells|84}}
|-
! {{period|75|brief}}
| [[6 bits]]
| Robert Wainwright
| 1984
| [[pentadecathlon on 30P25]]
|{{cells|46}}
|-
! {{period|76|brief}}
| ?
| ?
| ?
| [[mold on 44P38]]
| {{cells|56}}
|-
! {{period|77|brief}}
| ?
| ?
| ?
| [[meatball on rattlesnake]]
|{{cells|71}}
|-
! {{period|78|brief}}
| ?
| ?
| ?
| [[p6 thumb on Beluchenko's p13]]
|{{cells|61}}
|-
! {{period|79|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p79 Snark loop]]
|{{cells|228}}
|-
! {{period|80|brief}}
| ?
| ?
| ?
| [[fumarole on Rob's p16]]
| {{cells|39}}
|-
! {{period|81|brief}}
| ?
| ?
| ?
| p81 180° glider loop
|{{cells|146}}
|-
! {{period|82|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p82 Snark loop]]
|{{cells|208}}
|-
! {{period|83|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p83 Snark loop]]
|{{cells|228}}
|-
! {{period|84|brief}}
| ?
| ?
| ?
| [[p84 honey farm hassler]]
| {{cells|42}}
|-
! {{period|85|brief}}
| ?
| ?
| ?
| [[74P85]]
|{{cells|74}}
|-
! {{period|86|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p86 Snark loop]]
|{{cells|208}}
|-
! {{period|87|brief}}
| ?
| ?
| ?
| [[84P87]]
| {{cells|84}}
|-
! {{period|88|brief}}
| p88 glider loop
|David Buckingham
| 1992
| [[figure eight on rattlesnake]]
| {{cells|45}}
|-
! {{period|89|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p89 Snark loop]]
|{{cells|228}}
|-
! {{period|90|brief}}
| ?
| ?
| ?
| [[thumb 1 on queen bee shuttle]]
| {{cells|56}}
|-
! {{period|91|brief}}
| ?
| ?
| ?
| [[meatball on Beluchenko's p13]]
|{{cells|72}}
|-
! {{period|92|brief}}
| ?
| ?
| ?
| [[twin bees shuttle on 21P4.1]]
| {{cells|49}}
|-
! {{period|93|brief}}
| ?
| ?
| ?
| [[caterer on Merzenich's p31]]
|{{cells|60}}
|-
! {{period|94|brief}}
| capped [[AK-47 reaction|AK-47]] gun
|Dean Hickerson
| 1990
| {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]]
| {{cells|110}}
|-
! {{period|95|brief}}
| ?
| ?
| ?
| p95 180° glider loop
| {{cells|166}}
|-
! {{period|96|brief}}
| ?
| ?
| ?
| [[period-48 glider gun with boat-bit]]
| {{cells|59}}
|-
! {{period|97|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p97 Snark loop]]
|{{cells|228}}
|-
! {{period|98|brief}}
| ?
| ?
| ?
| [[Gallus]]
| {{cells|105}}
|-
! {{period|99|brief}}
| ?
| ?
| ?
| [[48P9 on rattlesnake]]
|{{cells|82}}
|-
! {{period|100|brief}}
| [[centinal]]
|Bill Gosper
| ≤1987
| [[mold on 30P25]]
| {{cells|42}}
|-
! {{period|101|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p101 Snark loop]]
|{{cells|228}}
|-
! {{period|102|brief}}
| ?
| ?
| ?
| [[Raucci's p102]]
| {{cells|67}}
|-
! {{period|103|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p103 Snark loop]]
|{{cells|228}}
|-
! {{period|104|brief}}
| ?
| ?
| ?
| [[figure eight on Beluchenko's p13]]
| {{cells|46}}
|-
! {{period|105|brief}}
| ?
| ?
| ?
| [[pentadecathlon on 37P7.1]]
|{{cells|49}}
|-
! {{period|106|brief}}
| ?
| ?
| ?
| [[rectifier|p106 rectifier loop]]
|{{cells|169}}
|-
! {{period|107|brief}}
| ?
| ?
| ?
| [[rectifier|p107 rectifier loop]]
|{{cells|136}}
|-
! {{period|108|brief}}
| ?
| ?
| ?
| [[22P4.3 on 56P27]]
| {{cells|78}}
|-
! {{period|109|brief}}
| ?
| ?
| ?
| [[rectifier|p109 rectifier loop]]
| {{cells|156}}
|-
! {{period|110|brief}}
| [[p110 traffic jam]]
| Bill Gosper
| 1994
| [[pseudo-barberpole on Jason's p22]]
| {{cells|51}}
|-
! {{period|111|brief}}
| ?
| ?
| ?
| [[rectifier|p111 rectifier loop]]
| {{cells|136}}
|-
! {{period|112|brief}}
| ?
| ?
| ?
| [[tumbler on Rich's p16]]
| {{cells|50}}
|-
! {{period|113|brief}}
| ?
| ?
| ?
| [[nihonium]]
| {{cells|106}}
|-
! {{period|114|brief}}
| ?
| ?
| ?
| [[caterer on 44P38]]
| {{cells|57}}
|-
! {{period|115|brief}}
| ?
| ?
| ?
| [[rectifier|p115 rectifier loop]]
| {{cells|136}}
|-
! {{period|116|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=102P116|style=raw}}
|{{cells|102}}
|-
! {{period|117|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp117_x32acxca23zggxg84448gxggy2g88cz14fes72x27sef41y211zyfeehrzyq33zyfo8gy5g33zyfopw11267608g3568w66zyseu4zyu3|patternname=112P117|style=raw}}
| {{cells|112}}
|-
! {{period|118|brief}}
| ?
| ?
| ?
| [[rectifier|p118 rectifier loop]]
| {{cells|154}}
|-
! {{period|119|brief}}
| ?
| ?
| ?
| [[rectifier|p119 rectifier loop]]
| {{cells|136}}
|-
! {{period|120|brief}}
| ?
| ?
| ?
| [[figure eight on pentadecathlon]]
| {{cells|24}}
|-
! {{period|124|brief}}
| [[p124 lumps of muck hassler]]
| Dean Hickerson
| 1994
| [[mold on Merzenich's p31]]
| {{cells|60}}
|-
! {{period|126|brief}}
| ?
| ?
| ?
| [[snacker on 34P14 shuttle]]
| {{cells|74}}
|-
! {{period|128|brief}}
| ?
| ?
| ?
| [[p128 wing shuttle]], {{LinkCatagolue|xp128_ytokgyb6664abw66zyz8kk8y9ccwgc8gzyvggkcya33y473666zooogoy4ggyaca23w1zx134c2wcc011y64aa4zy3oowkk8oooyb2a6zy71|patternname=p128 Coe-blocker loop|style=raw}}
|{{cells|108}}
|-
! {{period|129|brief}}
| ?
| ?
| ?
| p129 180° glider loop
|{{cells|146}}
|-
! {{period|130|brief}}
| ?
| ?
| ?
| [[55P10 on Beluchenko's p13]]
| {{cells|89}}
|-
! {{period|132|brief}}
| p132 glider loop
| David Buckingham
| 1992
| [[mold on Jason's p33]]
| {{cells|72}}
|-
! {{period|135|brief}}
| [[106P135]]
| Bill Gosper
| {{year|1989}}
| [[pentadecathlon on 56P27]]
|{{cells|68}}
|-
! {{period|136|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp136_y3ca73oswcczy2ggwooy98m113czccwe192y166y7220o8zyq113y0oggzyz23088y7ccy18igew66zyz6oggd2y933w11zyzya66w73osa6|patternname=p136 Coe-blocker loop|style=raw}}
| {{cells|108}}
|-
! {{period|138|brief}}
| ?
| ?
| ?
| [[Gabriel's p138]]
| {{cells|36}}
|-
! {{period|140|brief}}
| p140 traffic jam
| Bill Gosper
| 1994
| [[34P14 shuttle on dockyard]]
| {{cells|82}}
|-
! {{period|141|brief}}
| ?
| ?
| ?
| [[p47 pre-pulsar shuttle phase-shifting 28P7.1]]
| {{cells|114}}
|-
! {{period|143|brief}}
| ?
| ?
| ?
| [[p143 Bandersnatch loop]]
| {{cells|144}}
|-
! {{period|144|brief}}
| capped p144 [[gunstar]]
| David Buckingham
| 1990
| [[Achim's p144]]
| {{cells|42}}
|-
! {{period|150|brief}}
| ?
| ?
| ?
| [[unix on 30P25]]
| {{cells|46}}
|-
! {{period|152|brief}}
| ?
| ?
| ?
| [[figure eight on 44P38]]
| {{cells|60}}
|-
! {{period|156|brief}}
| p156 [[traffic jam]] oscillator
|Bill Gosper
| 1994
| [[p156 unix loop]]
| {{cells|86}}
|-
! {{period|165|brief}}
| ?
| ?
| ?
| [[rattlesnake on pentadecathlon]]
| {{cells|45}}
|-
! {{period|168|brief}}
| ?
| ?
| ?
| [[figure eight on 32P21]]
| {{cells|44}}
|-
! {{period|177|brief}}
| ?
| ?
| ?
| [[Karel's p177]]
| {{cells|104}}
|-
! {{period|184|brief}}
| ?
| ?
| ?
| [[figure eight on twin bees shuttle]]
| {{cells|40}}
|-
! {{period|186|brief}}
| ?
| ?
| ?
| [[unix on Merzenich's p31]]
| {{cells|64}}
|-
! {{period|188|brief}}
| ?
| ?
| ?
| [[AK-94 with boat-bits]]
| {{cells|108}}
|-
! {{period|196|brief}}
| ?
| ?
| ?
| [[p196 pi-heptomino hassler]]
| {{cells|66}}
|-
! {{period|200|brief}}
| p200 glider loop
|Bill Gosper
| ≤1987
| [[figure eight on 30P25]]
|{{cells|42}}
|-

! {{period|226|brief}}
| ?
| ?
| ?
| [[nihonium*]]
| {{cells|107}}
|-
! {{period|230|brief}}
| ?
| ?
| ?
| [[fumarole on twin bees shuttle]]
|{{cells|46}}
|-
! {{period|231|brief}}
| ?
| ?
| ?
| [[rattlesnake on 32P21]]
|{{cells|66}}
|-
! {{period|232|brief}}
| ?
| ?
| ?
| [[figure eight on p29 pre-pulsar shuttle]]
|{{cells|66}}
|-
! {{period|240|brief}}
| ?
| ?
| ?
| [[pentadecathlon on Rob's p16]]
| {{cells|33}}
|-
! {{period|246|brief}}
| ?
| ?
| ?
| [[period-246 glider gun#Gallery|period-246 glider gun variant]]
| {{cells|68}}
|-
! {{period|256|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp256_ytokgyb6664abw66zyz8kk8y9ccwgc8gzyvggkcya33y473666zooogoy4ggyaca23w1zx134c2wcc011y64aa4zy3oowkk8ooozy71|patternname=p256 Coe-blocker loop|style=raw}}
| {{cells|103}}
|-
! {{period|276|brief}}
| ?
| ?
| ?
| [[caterer on 50P92.1]]
| {{cells|62}}
|-
! {{period|300|brief}}
| ?
| ?
| ?
| [[pentadecathlon on centinal]]
| {{cells|88}}
|-
! {{period|312|brief}}
| ?
| ?
| ?
| [[60P312]]
| {{cells|60}}
|-
! {{period|320|brief}}
| ?
| ?
| ?
| [[fumarole on Merzenich's p64]]
| {{cells|52}}
|-
! {{period|360|brief}}
| ?
| ?
| ?
| [[thumb 1 on Beluchenko's p40]]
| {{cells|62}}
|-
! {{period|368|brief}}
| ?
| ?
| ?
| [[period-184 glider gun with boat-bits]]
| {{cells|50}}
|-
! {{period|460|brief}}
| ?
| ?
| ?
| [[pseudo-barberpole on 50P92.1]]
| {{cells|65}}
|-
! {{period|492|brief}}
| ?
| ?
| ?
| [[period-246 glider gun with boat-bit]]
| {{cells|87}}
|-
! {{period|496|brief}}
| ?
| ?
| ?
| [[Rob's p16 on Merzenich's p31]]
| {{cells|69}}
|-
! {{period|512|brief}}
| ?
| ?
| ?
| [[period-256 glider gun with boat-bits]]
| {{cells|100}}
|-
! {{period|856|brief}}
| [[period-856 glider gun]]
| [[David Buckingham]]
| 1991
| {{LinkCatagolue|xp856_yzyzyrca8ya66wd52666zyzyzyw8kk8y9cccoszyzyzysggkcya33y11261w66zyzyzys1zzzzzzzzzzzzzzzooogoy4ggyaca23zx134c2wcc011y64aa4zy3oowkk8ooozy71|patternname=p856 Coe-blocker loop|style=raw}}
|{{cells|103}}
|}

==Flipper==
A '''flipper''' is any [[oscillator]] that forms its mirror image halfway through its [[period]]. For example, see [[Toad#Gallery|p60 toad flipper]].

==Notes==
<references group=note />

==References==
<references>
<ref name="post132979">{{LinkForumThread
|format = ref
|title = Re: Smallest Known Oscillators to p106 (and Beyond)
|p = 132979
|author = Jeremy Tan
|date = July 3, 2021
}}</ref>
</references>

==See also==
*[[List of common oscillators]]
*[[:Category:Flipping oscillators|List of flipping oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
*[[Table of oscillators by period]]
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]
*[[Almost oscillator]]
*[[Oscillizer]]-analyze and get vital statistics for an oscillator

==External links==
{{LinkWikipedia|Oscillator_(cellular_automaton)}}
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkLexicon|lex_f.htm#flipper|name=Flipper}}

===Forum threads===
{{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
{{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
{{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}

__NOTOC__

P128 wing shuttle

2022-01-17T05:11:32Z

Freywa: flesh out more details

{{Oscillator
|name = p128 wing shuttle
|pname = p128wingshuttle
|f1 = Shuttle
|c = 108
|bx = 42
|by = 35
|p = 128
|m = 64
|h = 92.7
|v = 0.97
|sv = 0.37
|discoverer = David Raucci
|discoveryear = 2021
|rulemin = B3/S23
|rulemax = B38/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B36c8/S234c6i7e
|synthesis = 48
|synthesisRLE = true
|plaintext = true
|rle = true
|viewerconfig = #C [[ GPS 32 THUMBSIZE 2 ]]
|apgcode = xp128_y3ca73oswcczyqg88gzy1ggyh6bbcxca4z8ko010onmcy04eewuscy26dt30g0352z4a6x6qqcyh11zy01221zyh66w73osa6
}}
The '''p128 wing shuttle''' is a {{period|128}} [[oscillator]] found by [[David Raucci]] on August 24, 2021.<ref name="post135248" /> It consists of a [[wing]] being hassled back and forth by 2 [[Rich's p16]]s and 2 [[blocker]]s. In terms of its {{cells|108}} cells, it is tied with the {{LinkCatagolue|xp128_ytokgyb6664abw66zyz8kk8y9ccwgc8gzyvggkcya33y473666zooogoy4ggyaca23w1zx134c2wcc011y64aa4zy3oowkk8oooyb2a6zy71|patternname=p128 Coe-blocker loop|style=raw}} as the smallest known period-128 oscillator.

==References==
<references>
<ref name="post135248">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 135248
|author = David Raucci
|date = August 24, 2021
}}</ref>
</references>

==External links==
{{LinkCatagolue|xp128_y3ca73oswcczyqg88gzy1ggyh6bbcxca4z8ko010onmcy04eewuscy26dt30g0352z4a6x6qqcyh11zy01221zyh66w73osa6|patternname=p128 wing shuttle}}
{{Symmetry|osc=turn180}}
{{DISPLAYTITLE:p128 wing shuttle}}

Table of oscillators by period

2022-01-16T21:41:26Z

Freywa: the capgun is no longer SKOP

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|- align=center valign=center
! colspan="24" | Smallest [[oscillator]]s for each period
|- align=center valign=center
| style="background-color:#c6efce" | [[block|1]]
| style="background-color:#c6efce" | [[blinker|2]]
| style="background-color:#c6efce" | [[caterer|3]]
| style="background-color:#c6efce" | [[mold|4]]
| style="background-color:#c6efce" | [[pseudo-barberpole|5]]
| style="background-color:#c6efce" | [[unix|6]]
| style="background-color:#c6efce" | [[burloaferimeter|7]]
| style="background-color:#c6efce" | [[figure eight|8]]
| style="background-color:#c6efce" | [[29P9|9]]
| style="background-color:#c6efce" | [[24P10|10]]
| style="background-color:#c6efce" | [[rattlesnake|11]]
| style="background-color:#c6efce" | [[dinner table|12]]
| style="background-color:#c6efce" | [[Beluchenko's p13|13]]
| style="background-color:#c6efce" | [[tumbler|14]]
| style="background-color:#c6efce" | [[pentadecathlon|15]]
| style="background-color:#c6efce" | [[Rob's p16|16]]
| style="background-color:#c6efce" | [[honey thieves|17]]
| style="background-color:#c6efce" | [[p18 bi-block hassler|18]]
| style="background-color:#ff0000" | 19
| style="background-color:#80ff80" | [[mold on fumarole|20]]
| style="background-color:#80ff80" | [[Caterer on 28P7.3|21]]
| style="background-color:#c6efce" | [[Jason's p22|22]]
| style="background-color:#c6efce" | [[David Hilbert|23]]
| style="background-color:#80ff80" | [[caterer on figure eight|24]]
|- align=center valign=center
| style="background-color:#c6efce" | [[p25 pre-pulsar shuttle|25]]
| style="background-color:#80ff80" | [[87P26|26]]
| style="background-color:#c6efce" | [[56P27|27]]
| style="background-color:#80ff80" | [[mold on 34P14 shuttle|28]]
| style="background-color:#c6efce" | [[pre-pulsar shuttle 29|29]]
| style="background-color:#c6efce" | [[queen bee shuttle|30]]
| style="background-color:#c6efce" | [[Merzenich's p31|31]]
| style="background-color:#c6efce" | [[p32 honey farm hassler|32]]
| style="background-color:#80ff80" | [[caterer on rattlesnake|33]]
| style="background-color:#ffff00" | [[honey thieves with test tube baby|34]]
| style="background-color:#c6efce" | [[p35 honey farm hassler|35]]
| style="background-color:#c6efce" | [[22P36|36]]
| style="background-color:#c6efce" | [[Beluchenko's p37|37]]
| style="background-color:#c6efce" | [[44P38|38]]
| style="background-color:#80ff80" | [[caterer on Beluchenko's p13|39]]
| style="background-color:#c6efce" | [[Beluchenko's p40|40]]
| style="background-color:#ff0000" | 41
| style="background-color:#80ff80" | [[unix on 34P14 shuttle|42]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|43]]
| style="background-color:#80ff80" | [[mold on rattlesnake|44]]
| style="background-color:#80ff80" | [[pentadecathlon on thumb 1|45]]
| style="background-color:#c6efce" | [[twin bees shuttle|46]]
| style="background-color:#c6efce" | [[p47 pre-pulsar shuttle|47]]
| style="background-color:#80ff80" | [[unix on Rich's p16|48]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[p49 bumper loop|49]]
| style="background-color:#c6efce" | [[p50 traffic jam|50]]
| style="background-color:#80ff80" | [[90P51|51]]
| style="background-color:#c6efce" | [[Four eaters hassling lumps of muck|52]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|53]]
| style="background-color:#c6efce" | [[p54 shuttle|54]]
| style="background-color:#80ff80" | [[pseudo-barberpole on rattlesnake|55]]
| style="background-color:#c6efce" | [[p56 B-heptomino shuttle|56]]
| style="background-color:#ccaaff" | [[p57 bumper loop|57]]
| style="background-color:#c6efce" | [[p58 pre-pulsar shuttle|58]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|59]]
| style="background-color:#80ff80" | [[mold on pentadecathlon|60]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|61]]
| style="background-color:#c6efce" | [[110P62|62]]
| style="background-color:#80ff80" | [[snacker on 38P7.2|63]]
| style="background-color:#c6efce" | [[Merzenich's p64|64]]
| style="background-color:#80ff80" | [[fumarole on Beluchenko's p13|65]]
| style="background-color:#80ff80" | [[caterer on Jason's p22|66]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|67]]
| style="background-color:#80ff80" | [[72P68|68]]
| style="background-color:#ccaaff" | [[p57 bumper loop|69]]
| style="background-color:#80ff80" | [[fumarole on 34P14 shuttle|70]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|71]]
| style="background-color:#80ff80" | [[figure eight on 22P36|72]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[Adjustable glider loops|73]]
| style="background-color:#c6efce" | [[Raucci's p74|74]]
| style="background-color:#d0b65a" | [[6 bits|75]]
| style="background-color:#80ff80" | [[Mold on 44P38|76]]
| style="background-color:#80ff80" | [[77P77|77]]
| style="background-color:#80ff80" | [[p6 thumb on Beluchenko's p13|78]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|79]]
| style="background-color:#80ff80" | [[fumarole on Rich's p16|80]]
| style="background-color:#ccaaff" | [[p57 bumper loop|81]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|82]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|83]]
| style="background-color:#c6efce" | [[52P84|84]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|85]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|86]]
| style="background-color:#c6efce" | [[84P87|87]]
| style="background-color:#80ff80" | [[figure eight on rattlesnake|88]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|89]]
| style="background-color:#80ff80" | [[thumb 1 on queen bee shuttle|90]]
| style="background-color:#80ff80" | [[44P7 on Beluchenko's p13|91]]
| style="background-color:#80ff80" | [[Twin bees shuttle on 21P4.1|92]]
| style="background-color:#80ff80" | [[caterer on Merzenich's p31|93]]
| style="background-color:#c6efce" | [[AK-94|94]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|95]]
| style="background-color:#c6efce" | [[period-48 glider gun|96]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[Adjustable glider loops|97]]
| style="background-color:#d0b65a" | [[Gallus|98]]
| style="background-color:#80ff80" | [[48P9 on rattlesnake|99]]
| style="background-color:#c6efce" | [[centinal|100]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|101]]
| style="background-color:#ccaaff" | [[p6 bumper|102]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|103]]
| style="background-color:#80ff80" | [[figure eight on Beluchenko's p13|104]]
| style="background-color:#80ff80" | [[pentadecathlon on 37P7.1|105]]
| style="background-color:#ccaaff" | [[rectifier|106]]
| style="background-color:#ccaaff" | [[rectifier|107]]
| style="background-color:#80ff80" | [[22P4.3 on 56P27|108]]
| style="background-color:#ccaaff" | [[rectifier|109]]
| style="background-color:#80ff80" | [[pseudo-barberpole on Jason's p22|110]]
| style="background-color:#ccaaff" | [[rectifier|111]]
| style="background-color:#80ff80" | [[tumbler on Rich's p16|112]]
| style="background-color:#c6efce" | [[nihonium|113]]
| style="background-color:#80ff80" | [[Caterer on 44P38|114]]
| style="background-color:#ccaaff" | [[rectifier|115]]
| style="background-color:#80ff80" | [[102P116|116]]
| style="background-color:#80ff80" | [[117P117|117]]
| style="background-color:#ccaaff" | [[rectifier|118]]
| style="background-color:#ccaaff" | [[rectifier|119]]
| style="background-color:#80ff80" | [[figure eight on pentadecathlon|120]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|121]]
| style="background-color:#ccaaff" | [[rectifier|122]]
| style="background-color:#ccaaff" | [[rectifier|123]]
| style="background-color:#80ff80" | [[mold on Merzenich's p31|124]]
| style="background-color:#ccaaff" | [[rectifier|125]]
| style="background-color:#80ff80" | [[snacker on 34P14 shuttle|126]]
| style="background-color:#ccaaff" | [[rectifier|127]]
| style="background-color:#c6efce" | [[p128 wing shuttle|128]]
| style="background-color:#ccaaff" | [[p57 bumper loop|129]]
| style="background-color:#80ff80" | [[55P10 on Beluchenko's p13|130]]
| style="background-color:#ccaaff" | [[rectifier|131]]
| style="background-color:#80ff80" | [[mold on Jason's p33|132]]
| style="background-color:#ccaaff" | [[rectifier|133]]
| style="background-color:#ccaaff" | [[rectifier|134]]
| style="background-color:#80ff80" | [[pentadecathlon on 56P27|135]]
| style="background-color:#d0b65a" | 136
| style="background-color:#ccaaff" | [[rectifier|137]]
| style="background-color:#c6efce" | [[Gabriel's p138|138]]
| style="background-color:#ccaaff" | [[rectifier|139]]
| style="background-color:#80ff80" | [[34P14 shuttle on dockyard|140]]
| style="background-color:#c6efce" | [[114P141|141]]
| style="background-color:#ccaaff" | [[rectifier|142]]
| style="background-color:#ccaaff" | [[rectifier|143]]
| style="background-color:#c6efce" | [[Achim's p144|144]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|145]]
| style="background-color:#ccaaff" | [[rectifier|146]]
| style="background-color:#ccaaff" | [[rectifier|147]]
| style="background-color:#ccaaff" | [[p4 bumper|148]]
| style="background-color:#ccaaff" | [[rectifier|149]]
| style="background-color:#d0b65a" | [[buckaroo|150]]
| style="background-color:#ccaaff" | [[rectifier|151]]
| style="background-color:#80ff80" | [[Figure eight on 44P38|152]]
| style="background-color:#ccaaff" | [[rectifier|153]]
| style="background-color:#d0b65a" | [[34P14 shuttle|154]]
| style="background-color:#ccaaff" | [[rectifier|155]]
| style="background-color:#ccaaff" | 156
| style="background-color:#ccaaff" | [[rectifier|157]]
| style="background-color:#ccaaff" | [[rectifier|158]]
| style="background-color:#ccaaff" | [[rectifier|159]]
| style="background-color:#80ff80" | [[Heavyweight volcano on p32 honey farm hassler|160]]
| style="background-color:#ccaaff" | [[rectifier|161]]
| style="background-color:#d0b65a" | [[p6 thumb|162]]
| style="background-color:#ccaaff" | [[rectifier|163]]
| style="background-color:#ccaaff" | [[p4 bumper|164]]
| style="background-color:#80ff80" | [[Rattlesnake on pentadecathlon|165]]
| style="background-color:#ccaaff" | [[rectifier|166]]
| style="background-color:#ccaaff" | [[rectifier|167]]
| style="background-color:#80ff80" | [[Figure eight on p21 honey farm hassler|168]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|169]]
| style="background-color:#d0b65a" | 170
| style="background-color:#ccaaff" | [[rectifier|171]]
| style="background-color:#ccaaff" | [[p4 bumper|172]]
| style="background-color:#ccaaff" | [[rectifier|173]]
| style="background-color:#ccaaff" | 174
| style="background-color:#ccaaff" | [[rectifier|175]]
| style="background-color:#d0b65a" | 176
| style="background-color:#c6efce" | [[Karel's p177|177]]
| style="background-color:#ccaaff" | [[rectifier|178]]
| style="background-color:#ccaaff" | [[rectifier|179]]
| style="background-color:#d0b65a" | [[p60 glider shuttle|180]]
| style="background-color:#ccaaff" | [[rectifier|181]]
| style="background-color:#ccaaff" | [[rectifier|182]]
| style="background-color:#ccaaff" | [[rectifier|183]]
| style="background-color:#c6efce" | [[period-184 glider gun|184]]
| style="background-color:#ccaaff" | [[rectifier|185]]
| style="background-color:#80ff80" | [[unix on Merzenich's p31|186]]
| style="background-color:#ccaaff" | [[rectifier|187]]
| style="background-color:#c6efce" | [[AK-94|188]]
| style="background-color:#ccaaff" | [[rectifier|189]]
| style="background-color:#80ff80" | [[Fumarole on 44P38|190]]
| style="background-color:#ccaaff" | [[rectifier|191]]
| style="background-color:#ccaaff" | 192
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|193]]
| style="background-color:#ccaaff" | [[rectifier|194]]
| style="background-color:#d0b65a" | [[6 bits|195]]
| style="background-color:#c6efce" | [[p196 pi-heptomino hassler|196]]
| style="background-color:#ccaaff" | [[rectifier|197]]
| style="background-color:#ccaaff" | 198
| style="background-color:#ccaaff" | [[rectifier|199]]
| style="background-color:#80ff80" | [[figure eight on centinal|200]]
| style="background-color:#ccaaff" | [[rectifier|201]]
| style="background-color:#ccaaff" | [[rectifier|202]]
| style="background-color:#ccaaff" | [[rectifier|203]]
| style="background-color:#ccaaff" | 204
| style="background-color:#ccaaff" | [[rectifier|205]]
| style="background-color:#ccaaff" | [[rectifier|206]]
| style="background-color:#ccaaff" | [[rectifier|207]]
| style="background-color:#d0b65a" | 208
| style="background-color:#ccaaff" | [[rectifier|209]]
| style="background-color:#d0b65a" | [[Pentadecathlon|210]]
| style="background-color:#ccaaff" | [[rectifier|211]]
| style="background-color:#ccaaff" | [[p4 bumper|212]]
| style="background-color:#ccaaff" | [[rectifier|213]]
| style="background-color:#ccaaff" | [[rectifier|214]]
| style="background-color:#ccaaff" | [[rectifier|215]]
| style="background-color:#80ff80" | [[figure eight on 56P27|216]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|217]]
| style="background-color:#ccaaff" | [[rectifier|218]]
| style="background-color:#ccaaff" | [[rectifier|219]]
| style="background-color:#ccaaff" | [[p4 bumper|220]]
| style="background-color:#ccaaff" | [[rectifier|221]]
| style="background-color:#ccaaff" | 222
| style="background-color:#ccaaff" | [[rectifier|223]]
| style="background-color:#d0b65a" | 224
| style="background-color:#ccaaff" | [[rectifier|225]]
| style="background-color:#c6efce" | [[nihonium*|226]]
| style="background-color:#ccaaff" | [[rectifier|227]]
| style="background-color:#80ff80" | [[unix on p76 pi-heptomino hassler|228]]
| style="background-color:#ccaaff" | [[rectifier|229]]
| style="background-color:#80ff80" | [[fumarole on twin bees shuttle|230]]
| style="background-color:#ccaaff" | [[rectifier|231]]
| style="background-color:#80ff80" | [[figure eight on p29 pre-pulsar shuttle|232]]
| style="background-color:#ccaaff" | [[rectifier|233]]
| style="background-color:#d0b65a" | [[p6 thumb|234]]
| style="background-color:#ccaaff" | [[rectifier|235]]
| style="background-color:#ccaaff" | [[p4 bumper|236]]
| style="background-color:#ccaaff" | [[rectifier|237]]
| style="background-color:#ccaaff" | [[rectifier|238]]
| style="background-color:#ccaaff" | [[rectifier|239]]
| style="background-color:#80ff80" | [[pentadecathlon on Rob's p16|240]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|241]]
| style="background-color:#ccaaff" | [[rectifier|242]]
| style="background-color:#ccaaff" | [[rectifier|243]]
| style="background-color:#ccaaff" | [[p4 bumper|244]]
| style="background-color:#ccaaff" | [[rectifier|245]]
| style="background-color:#c6efce" | [[period-246 glider gun|246]]
| style="background-color:#ccaaff" | [[rectifier|247]]
| style="background-color:#d0b65a" | 248
| style="background-color:#ccaaff" | [[rectifier|249]]
| style="background-color:#d0b65a" | 250
| style="background-color:#ccaaff" | [[rectifier|251]]
| style="background-color:#ccaaff" | 252
| style="background-color:#ccaaff" | [[rectifier|253]]
| style="background-color:#ccaaff" | [[rectifier|254]]
| style="background-color:#d0b65a" | [[Pentadecathlon|255]]
| style="background-color:#ccaaff" | [[Coe's p8|256]]
| style="background-color:#ccaaff" | [[rectifier|257]]
| style="background-color:#d0b65a" | [[p6 thumb|258]]
| style="background-color:#ccaaff" | [[rectifier|259]]
| style="background-color:#ccaaff" | [[p4 bumper|260]]
| style="background-color:#ccaaff" | [[rectifier|261]]
| style="background-color:#ccaaff" | [[rectifier|262]]
| style="background-color:#ccaaff" | [[rectifier|263]]
| style="background-color:#ccaaff" | 264
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|265]]
| style="background-color:#80ff80" | [[34P14 shuttle on 44P38|266]]
| style="background-color:#ccaaff" | [[rectifier|267]]
| style="background-color:#ccaaff" | [[p4 bumper|268]]
| style="background-color:#ccaaff" | [[rectifier|269]]
| style="background-color:#d0b65a" | [[Buckaroo|270]]
| style="background-color:#ccaaff" | [[rectifier|271]]
| style="background-color:#d0b65a" | 272
| style="background-color:#ccaaff" | [[rectifier|273]]
| style="background-color:#ccaaff" | [[rectifier|274]]
| style="background-color:#ccaaff" | [[rectifier|275]]
| style="background-color:#80ff80" | [[caterer on 50P92.1|276]]
| style="background-color:#ccaaff" | [[rectifier|277]]
| style="background-color:#ccaaff" | [[rectifier|278]]
| style="background-color:#ccaaff" | [[rectifier|279]]
| style="background-color:#80ff80" | [[figure eight on p35 honey farm hassler|280]]
| style="background-color:#ccaaff" | [[rectifier|281]]
| style="background-color:#d0b65a" | [[92P114|282]]
| style="background-color:#ccaaff" | [[rectifier|283]]
| style="background-color:#ccaaff" | [[p4 bumper|284]]
| style="background-color:#d0b65a" | [[Pentadecathlon|285]]
| style="background-color:#ccaaff" | [[rectifier|286]]
| style="background-color:#ccaaff" | [[rectifier|287]]
| style="background-color:#ccaaff" | 288
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|289]]
| style="background-color:#ccaaff" | [[rectifier|290]]
| style="background-color:#ccaaff" | [[rectifier|291]]
| style="background-color:#ccaaff" | [[p4 bumper|292]]
| style="background-color:#ccaaff" | [[rectifier|293]]
| style="background-color:#ccaaff" | 294
| style="background-color:#ccaaff" | [[rectifier|295]]
| style="background-color:#d0b65a" | 296
| style="background-color:#80ff80" | [[p11 domino sparker on 56P27|297]]
| style="background-color:#ccaaff" | [[rectifier|298]]
| style="background-color:#ccaaff" | [[rectifier|299]]
| style="background-color:#d0b65a" | [[p60 glider shuttle|300]]
| style="background-color:#ccaaff" | [[rectifier|301]]
| style="background-color:#ccaaff" | [[rectifier|302]]
| style="background-color:#ccaaff" | [[rectifier|303]]
| style="background-color:#80ff80" | [[Rob's p16 on p76 pi-heptomino hassler|304]]
| style="background-color:#ccaaff" | [[rectifier|305]]
| style="background-color:#d0b65a" | [[p6 thumb|306]]
| style="background-color:#ccaaff" | [[rectifier|307]]
| style="background-color:#ccaaff" | [[p4 bumper|308]]
| style="background-color:#ccaaff" | [[rectifier|309]]
| style="background-color:#ccaaff" | [[rectifier|310]]
| style="background-color:#ccaaff" | [[rectifier|311]]
| style="background-color:#c6efce" | [[60P312|312]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|313]]
| style="background-color:#ccaaff" | [[rectifier|314]]
| style="background-color:#d0b65a" | [[6 bits|315]]
| style="background-color:#ccaaff" | [[p4 bumper|316]]
| style="background-color:#ccaaff" | [[rectifier|317]]
| style="background-color:#ccaaff" | 318
| style="background-color:#ccaaff" | [[rectifier|319]]
| style="background-color:#80ff80" | [[fumarole on Merzenich's p64|320]]
| style="background-color:#ccaaff" | [[rectifier|321]]
| style="background-color:#d0b65a" | [[Twin bees shuttle|322]]
| style="background-color:#ccaaff" | [[rectifier|323]]
| style="background-color:#ccaaff" | 324
| style="background-color:#ccaaff" | [[rectifier|325]]
| style="background-color:#ccaaff" | [[rectifier|326]]
| style="background-color:#ccaaff" | [[rectifier|327]]
| style="background-color:#d0b65a" | 328
| style="background-color:#ccaaff" | [[rectifier|329]]
| style="background-color:#d0b65a" | [[Pentadecathlon|330]]
| style="background-color:#ccaaff" | [[rectifier|331]]
| style="background-color:#ccaaff" | [[p4 bumper|332]]
| style="background-color:#ccaaff" | [[rectifier|333]]
| style="background-color:#ccaaff" | [[rectifier|334]]
| style="background-color:#ccaaff" | [[rectifier|335]]
| style="background-color:#ccaaff" | 336
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|337]]
| style="background-color:#ccaaff" | [[rectifier|338]]
| style="background-color:#ccaaff" | [[rectifier|339]]
| style="background-color:#ccaaff" | [[p4 bumper|340]]
| style="background-color:#ccaaff" | [[rectifier|341]]
| style="background-color:#80ff80" | [[p18 bi-block hassler on 44P38|342]]
| style="background-color:#ccaaff" | [[rectifier|343]]
| style="background-color:#d0b65a" | 344
| style="background-color:#ccaaff" | [[rectifier|345]]
| style="background-color:#ccaaff" | [[rectifier|346]]
| style="background-color:#ccaaff" | [[rectifier|347]]
| style="background-color:#ccaaff" | 348
| style="background-color:#ccaaff" | [[rectifier|349]]
| style="background-color:#ccaaff" | [[rectifier|350]]
| style="background-color:#ccaaff" | [[rectifier|351]]
| style="background-color:#d0b65a" | 352
| style="background-color:#ccaaff" | [[rectifier|353]]
| style="background-color:#d0b65a" | [[p6 thumb|354]]
| style="background-color:#ccaaff" | [[rectifier|355]]
| style="background-color:#ccaaff" | [[p4 bumper|356]]
| style="background-color:#ccaaff" | [[rectifier|357]]
| style="background-color:#ccaaff" | [[rectifier|358]]
| style="background-color:#ccaaff" | [[rectifier|359]]
| style="background-color:#80ff80" | [[thumb 1 on Beluchenko's p40|360]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[rectifier|361]]
| style="background-color:#ccaaff" | [[rectifier|362]]
| style="background-color:#ccaaff" | [[rectifier|363]]
| style="background-color:#ccaaff" | [[p4 bumper|364]]
| style="background-color:#ccaaff" | [[rectifier|365]]
| style="background-color:#ccaaff" | 366
| style="background-color:#ccaaff" | [[rectifier|367]]
| style="background-color:#c6efce" | [[period-184 glider gun|368]]
| style="background-color:#ccaaff" | [[rectifier|369]]
| style="background-color:#ccaaff" | [[rectifier|370]]
| style="background-color:#ccaaff" | [[rectifier|371]]
| style="background-color:#ccaaff" | 372
| style="background-color:#ccaaff" | [[rectifier|373]]
| style="background-color:#ccaaff" | [[rectifier|374]]
| style="background-color:#ccaaff" | [[rectifier|375]]
| style="background-color:#d0b65a" | 376
| style="background-color:#ccaaff" | [[rectifier|377]]
| style="background-color:#d0b65a" | [[p6 thumb|378]]
| style="background-color:#ccaaff" | [[rectifier|379]]
| style="background-color:#80ff80" | [[Fumarole on p76 pi-heptomino hassler|380]]
| style="background-color:#ccaaff" | [[rectifier|381]]
| style="background-color:#ccaaff" | [[rectifier|382]]
| style="background-color:#ccaaff" | [[rectifier|383]]
| style="background-color:#ccaaff" | 384
|-
! colspan="24" |
|- align=center valign=center
| colspan="3" | Key:
| colspan="3" style="background-color:#c6efce" | known
| colspan="3" style="background-color:#80ff80" | LCM
| colspan="3" style="background-color:#ddaaff" | glider loop
| colspan="3" style="background-color:#d0b65a" | glider shuttle
| colspan="3" style="background-color:#ff0000" | undiscovered
| colspan="3" style="background-color:#ffff00" | [[trivial]]
| colspan="3" style="background-color:#ffffff" | unknown
|}

[[Category:Oscillators| ]]

Raucci's p217

2022-01-16T21:37:38Z

Freywa: Conked

{{Oscillator
|name = Raucci's p217
|pname = rauccisp217
|c = 236
|bx = 74
|by = 74
|p = 217
|m = 217
|h = 345.7
|v = 0.99
|sv = 0.45
|discoverer = David Raucci
|discoveryear = 2021
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B3/S23
|synthesis = 160
|plaintext =
|rle = true
|apgcode = xp217_ygccy068cd1w1dc86y0cczzyg66y0c26mgwgm62cy066zzyzyk33y333zyl8oo0gya8sm7y9g2qsy3sq2gzwccy3ccya131yrp0ggy3gg0pz088gy3g88yzy5453y3354z6033y33306ysgybccy3ccz3gmey3emg3y9oqe4ya31764zwggy3ggyb1zw11y311zysooy0cgoq2w2qogcy0oozzysccy0o4ccy0cc4oy0cczyzw11w11
|viewerconfig = #C [[ ZOOM 3 GPS 60 ]]
}}
'''Raucci's p217''' is a {{period|217}} [[oscillator]] found by [[David Raucci]] on May 5, {{year|2021}}. It consists of four [[U-turner]]s (which had no name at the time)<ref name="post129552" /> being hassled by four [[Merzenich's p31]]s.<ref name="post129618" />

The bounding box can be reduced from 74×74 to 72×72 by using the diagonal sparks of Merzenich's p31 instead of the domino sparks, but this increases its minimum population from 236 to 256 due to a change in phase.<ref name="post130447" />

It, along with an {{LinkCatagolue|xp132_y7iu0e1j0gg0ggy4g88czy6haq2dl57glkjgw22aqo0c96zy612269ssst86221y04s4y2oe1d6geh6kkmzw17842qcgwgykgf0v0n4nqw23zy1cc155013yk178701226zy0c88g0s2sgy6ocogwcy2o0408oihazo8wbt4t0v0u1y8111y4102024ab52sgz0d55che1cmge3y2susy0g88c2n777ic88gzyccid958ssx1p5l1sklm8bahzyb6221y4110110pge0f9|patternname=unnamed p132|style=raw}},<ref name="post137452" /> are the only oscillators known that hassle or shuttle a U-turner or U-turners.

{{EmbedViewer
|pname = uturner
|position = center
|viewerconfig = #C [[ ZOOM 16 GPS 20 ]]
|caption = [[U-turner]] being hassled 
}}

A [[glider synthesis]] (albeit an extremely inefficient one) was found for this oscillator by [[Dave Greene]] on January 15, {{year|2022}}.<ref name="message932018631238377543" />

==References==
<references>
<ref name="post129552">{{LinkForumThread
|format = ref
|title = Re: Thread for basic questions
|p = 129552
|author = C28
|date = May 4, 2021
}}</ref>
<ref name="post129618">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 129628
|author = David Raucci
|date = May 5, 2021
}}</ref>
<ref name="post130447">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion thread
|p = 130447
|author = David Raucci
|date = May 18, 2021
}}</ref>
<ref name="post137452">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 137452
|author = C28
|date = November 9, 2021
}}</ref>
<ref name="message932018631238377543">{{CiteDiscord
|author = Dave Greene
|date = January 15, 2022
|channel = cgol
|id = 932018631238377543
}}</ref>
</references>

==External links==
{{LinkCatagolue|xp217_ygccy068cd1w1dc86y0cczzyg66y0c26mgwgm62cy066zzyzyk33y333zyl8oo0gya8sm7y9g2qsy3sq2gzwccy3ccya131yrp0ggy3gg0pz088gy3g88yzy5453y3354z6033y33306ysgybccy3ccz3gmey3emg3y9oqe4ya31764zwggy3ggyb1zw11y311zysooy0cgoq2w2qogcy0oozzysccy0o4ccy0cc4oy0cczyzw11w11}}

{{Symmetry|90degree}}
__NOTOC__

Emu

2022-01-16T18:06:30Z

Freywa:

{{Glossary}}
The term '''emu''' refers to [[Herschel loop]]s that do not emit gliders. They are thus flightless, like the bird of the same name. This term was coined by [[David Buckingham]]. Emus have been constructed for [[period]] 52<ref name="post58837" /> and for periods 54 and higher (the first few are [[oscillator]]-assisted).

== Emus as reflectors ==
Emus can be used to reflect gliders in a variety of ways. [[Adam P. Goucher]] (with help from [[Jason Summers]]) exploited this property to construct the first [[Period-59_glider_gun|period-59 gun]]. Unfortunately, that method does not generalise to the remaining emu-only periods, since it uses a special p59+15n reaction based on [[David Buckingham]]'s [[P44_pi-heptomino_hassler|p44 oscillator]].

==Gallery==
<center>
{|
|-
|{{EmbedViewer|pname=p52emu4|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .75 ]]|caption=p52 394×394 emu uses the same mechanism as the [[p13-assisted period-52 glider gun]] }}
|{{EmbedViewer|pname=p57herschelloop1|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .8 ]]|caption=[[p57 Herschel loop 1]], a 334×334 emu }}
|{{EmbedViewer|pname=p59emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 3 ]]|caption=p59 130×90 emu uses [[R49]]s with Herschels<ref name="post137802"/> }}
|-
|{{EmbedViewer|pname=simkinsp60|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 8 ]]|caption=[[Simkin's p60]], 33×31, the smallest known emu }}
|{{EmbedViewer|pname=p61herschelloop2|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 1.3 ]]|caption=[[p61 Herschel loop 2]], a 381×70 emu }}
|{{EmbedViewer|pname=p98emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 6 ]]|caption=p98 46×46 emu made with four copies of the [[R49]] [[conduit]] }}
|-
|{{EmbedViewer|pname=nihonium|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 6 ]]|caption=[[Nihonium]], a p113 58×37 emu where the released gliders annihilate each other }}
|}
</center>

==See also==
*[[Quetzal]]

== External links ==
{{LinkLexicon|lex_e.htm#emu}}

== References ==
<references>

<ref name="post58837">{{LinkForumThread
|format=ref
|title=Re: Oscillator Discussion Thread
|author=Adam P. Goucher
|p=58837
|date=April 13, 2018
}}</ref>

<ref name="post137802">{{LinkForumThread
|format=ref
|title=Re: Execution of Old Guns by Variable-Speed Firing Squad
|author=Matthias Merzenich
|p=137802
|date=November 18, 2021
}}</ref>

</references>

__NOTOC__

Emu

2022-01-16T18:05:38Z

Freywa: a bit more

{{Glossary}}
The term '''emu''' refers to [[Herschel loop]]s that do not emit gliders. They are thus flightless, like the bird of the same name. This term was coined by [[David Buckingham]]. Emus have been constructed for [[period]] 52<ref name="post58837" /> and for periods 54 and higher (the first few are [[oscillator]]-assisted).

== Emus as reflectors ==
Emus can be used to reflect gliders in a variety of ways. [[Adam P. Goucher]] (with help from [[Jason Summers]]) exploited this property to construct the first [[Period-59_glider_gun|period-59 gun]]. Unfortunately, that method does not generalise to the remaining emu-only periods, since it uses a special p59+15n reaction based on [[David Buckingham]]'s [[P44_pi-heptomino_hassler|p44 oscillator]].

==Gallery==
<center>
{|
|-
|{{EmbedViewer|pname=p52emu4|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .75 ]]|caption=p52 394×394 emu uses the same mechanism as the [[p13-assisted period-52 glider gun]] }}
|{{EmbedViewer|pname=p57herschelloop1|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .8 ]]|caption=[[p57 Herschel loop 1]], a 334×334 emu }}
|{{EmbedViewer|pname=p59emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 3 ]]|caption=p59 130×90 emu uses [[R49]]s with Herschels<ref name="post137802"/> }}
|-
|{{EmbedViewer|pname=simkinsp60|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 8 ]]|caption=[[Simkin's p60]], 33×31, the smallest known emu }}
|{{EmbedViewer|pname=p61herschelloop2|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 1.3 ]]|caption=[[p61 Herschel loop 2]], a 381×70 emu }}
|{{EmbedViewer|pname=p98emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 6 ]]|caption=p98 46×46 emu made with four copies of the [[R49]] [[conduit]] }}
|-
|{{EmbedViewer|pname=nihonium|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 6 ]]|caption=[[Nihonium]], a p113 58×37 emu where the released gliders must annihilate each other }}
|}
</center>

==See also==
*[[Quetzal]]

== External links ==
{{LinkLexicon|lex_e.htm#emu}}

== References ==
<references>

<ref name="post58837">{{LinkForumThread
|format=ref
|title=Re: Oscillator Discussion Thread
|author=Adam P. Goucher
|p=58837
|date=April 13, 2018
}}</ref>

<ref name="post137802">{{LinkForumThread
|format=ref
|title=Re: Execution of Old Guns by Variable-Speed Firing Squad
|author=Matthias Merzenich
|p=137802
|date=November 18, 2021
}}</ref>

</references>

__NOTOC__

Emu

2022-01-16T18:04:23Z

Freywa:

{{Glossary}}
The term '''emu''' refers to [[Herschel loop]]s that do not emit gliders. They are thus flightless, like the bird of the same name. This term was coined by [[David Buckingham]]. Emus have been constructed for [[period]] 52<ref name="post58837" /> and for periods 54 and higher (the first few are [[oscillator]]-assisted).

== Emus as reflectors ==
Emus can be used to reflect gliders in a variety of ways. [[Adam P. Goucher]] (with help from [[Jason Summers]]) exploited this property to construct the first [[Period-59_glider_gun|period-59 gun]]. Unfortunately, that method does not generalise to the remaining emu-only periods, since it uses a special p59+15n reaction based on [[David Buckingham]]'s [[P44_pi-heptomino_hassler|p44 oscillator]].

==Gallery==
<center>
{|
|-
|{{EmbedViewer|pname=p52emu4|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .75 ]]|caption=p52 394×394 emu uses the same mechanism as the [[p13-assisted period-52 glider gun]] }}
|{{EmbedViewer|pname=p57herschelloop1|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .8 ]]|caption=[[p57 Herschel loop 1]], a 334×334 emu }}
|{{EmbedViewer|pname=p59emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 3 ]]|caption=p59 130×90 emu uses [[R49]]s with Herschels<ref name="post137802"/> }}
|-
|{{EmbedViewer|pname=simkinsp60|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 8 ]]|caption=[[Simkin's p60]], 33×31, the smallest known emu }}
|{{EmbedViewer|pname=p61herschelloop2|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 1.3 ]]|caption=[[p61 Herschel loop 2]], a 381×70 emu }}
|{{EmbedViewer|pname=p98emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 6 ]]|caption=p98 46×46 emu made with four copies of the [[R49]] [[conduit]] }}
|-
|{{EmbedViewer|pname=nihonium|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 6 ]]|caption=[[Nihonium]], a p113 58×37 emu }}
|}
</center>

==See also==
*[[Quetzal]]

== External links ==
{{LinkLexicon|lex_e.htm#emu}}

== References ==
<references>

<ref name="post58837">{{LinkForumThread
|format=ref
|title=Re: Oscillator Discussion Thread
|author=Adam P. Goucher
|p=58837
|date=April 13, 2018
}}</ref>

<ref name="post137802">{{LinkForumThread
|format=ref
|title=Re: Execution of Old Guns by Variable-Speed Firing Squad
|author=Matthias Merzenich
|p=137802
|date=November 18, 2021
}}</ref>

</references>

__NOTOC__

Emu

2022-01-16T18:03:04Z

Freywa: add nihonium

{{Glossary}}
The term '''emu''' refers to [[Herschel loop]]s that do not emit gliders. They are thus flightless, like the bird of the same name. This term was coined by [[David Buckingham]]. Emus have been constructed for [[period]] 52<ref name="post58837" /> and for periods 54 and higher (the first few are [[oscillator]]-assisted).

== Emus as reflectors ==
Emus can be used to reflect gliders in a variety of ways. [[Adam P. Goucher]] (with help from [[Jason Summers]]) exploited this property to construct the first [[Period-59_glider_gun|period-59 gun]]. Unfortunately, that method does not generalise to the remaining emu-only periods, since it uses a special p59+15n reaction based on [[David Buckingham]]'s [[P44_pi-heptomino_hassler|p44 oscillator]].

==Gallery==
<center>
{|
|-
|{{EmbedViewer|pname=p52emu4|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .75 ]]|caption=p52 394×394 emu uses the same mechanism as the [[p13-assisted period-52 glider gun]] }}
|{{EmbedViewer|pname=p57herschelloop1|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .8 ]]|caption=[[p57 Herschel loop 1]], a 334×334 emu }}
|{{EmbedViewer|pname=p59emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 3 ]]|caption=p59 130×90 emu uses [[R49]]s with Herschels<ref name="post137802"/> }}
|-
|{{EmbedViewer|pname=simkinsp60|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 8 ]]|caption=[[Simkin's p60]], 33×31, the smallest known emu }}
|{{EmbedViewer|pname=p61herschelloop2|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 1.3 ]]|caption=[[p61 Herschel loop 2]], a 381×70 emu }}
|{{EmbedViewer|pname=p98emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 6 ]]|caption=p98 46×46 emu made with four copies of the [[R49]] [[conduit]] }}
|-
|{{EmbedViewer|pname=nihonium|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 6 ]]|caption=[[Nihonium]], a 58×37 emu }}
|}
</center>

==See also==
*[[Quetzal]]

== External links ==
{{LinkLexicon|lex_e.htm#emu}}

== References ==
<references>

<ref name="post58837">{{LinkForumThread
|format=ref
|title=Re: Oscillator Discussion Thread
|author=Adam P. Goucher
|p=58837
|date=April 13, 2018
}}</ref>

<ref name="post137802">{{LinkForumThread
|format=ref
|title=Re: Execution of Old Guns by Variable-Speed Firing Squad
|author=Matthias Merzenich
|p=137802
|date=November 18, 2021
}}</ref>

</references>

__NOTOC__

Emu

2022-01-16T17:39:47Z

Freywa: /* Gallery */ correct dimension

{{Glossary}}
The term '''emu''' refers to [[Herschel loop]]s that do not emit gliders. They are thus flightless, like the bird of the same name. This term was coined by [[David Buckingham]]. Emus have been constructed for [[period]] 52<ref name="post58837" /> and for periods 54 and higher (the first few are [[oscillator]]-assisted).

== Emus as reflectors ==
Emus can be used to reflect gliders in a variety of ways. [[Adam P. Goucher]] (with help from [[Jason Summers]]) exploited this property to construct the first [[Period-59_glider_gun|period-59 gun]]. Unfortunately, that method does not generalise to the remaining emu-only periods, since it uses a special p59+15n reaction based on [[David Buckingham]]'s [[P44_pi-heptomino_hassler|p44 oscillator]].

==Gallery==
<center>
{|
|-
|{{EmbedViewer|pname=p52emu4|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .75 ]]|caption=p52 394×394 emu uses the same mechanism as the [[p13-assisted period-52 glider gun]] }}
|{{EmbedViewer|pname=p57herschelloop1|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM .8 ]]|caption=[[p57 Herschel loop 1]], a 334×334 emu }}
|{{EmbedViewer|pname=p59emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 3 ]]|caption=p59 130×90 emu uses [[R49]]s with Herschels<ref name="post137802"/> }}
|-
|{{EmbedViewer|pname=simkinsp60|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 8 ]]|caption=[[Simkin's p60]], 33×31, the smallest known emu }}
|{{EmbedViewer|pname=p61herschelloop2|position=center|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART ZOOM 1.3 ]]|caption=[[p61 Herschel loop 2]], a 381×70 emu }}
|{{EmbedViewer|pname=p98emu|position=center|viewerconfig= #C [[ AUTOSTART THUMBSIZE 2 ZOOM 6 ]]|caption=p98 46×46 emu made with four copies of the [[R49]] [[conduit]] }}
|}
</center>

==See also==
*[[Quetzal]]

== External links ==
{{LinkLexicon|lex_e.htm#emu}}

== References ==
<references>

<ref name="post58837">{{LinkForumThread
|format=ref
|title=Re: Oscillator Discussion Thread
|author=Adam P. Goucher
|p=58837
|date=April 13, 2018
}}</ref>

<ref name="post137802">{{LinkForumThread
|format=ref
|title=Re: Execution of Old Guns by Variable-Speed Firing Squad
|author=Matthias Merzenich
|p=137802
|date=November 18, 2021
}}</ref>

</references>

__NOTOC__

Oscillator

2022-01-13T20:24:15Z

Freywa: /* Important oscillators by period */ Coe-blocker loop improvements

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period).

[[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
| rowspan="500" style="border: none;" |
! Smallest known
! Minimum # of cells
|-
! {{period|2|brief}}
| [[blinker]]
|[[John Conway]]
| {{year|1970}}
| [[blinker]]
| {{cells|3}}
|-
! {{period|3|brief}}
| [[pulsar]]
|John Conway
| 1970
| [[caterer]]
| {{cells|12}}
|-
! {{period|4|brief}}
| [[pinwheel]]
|[[Simon Norton]]
| 1970
| [[mazing]], [[mold]]
| {{cells|12}}
|-
! {{period|5|brief}}
| [[octagon 2]]
|[[Sol Goodman]], [[Arthur Taber]]
| {{year|1971}}
| [[pseudo-barberpole]]
| {{cells|15}}
|-
! {{period|6|brief}}
| [[$rats]]
|[[David Buckingham]]
| {{year|1972}}
| [[unix]]
| {{cells|16}}
|-
! {{period|7|brief}}
| [[burloaferimeter]]
|David Buckingham
| 1972
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
| {{cells|28}}
|-
! {{period|8|brief}}
| [[figure eight]]
|Simon Norton
| 1970
| [[figure eight]]
| {{cells|12}}
|-
! {{period|9|brief}}
| [[worker bee]]
|David Buckingham
| 1972
| [[29P9]]
| {{cells|29}}
|-
! {{period|10|brief}}
| [[42P10.3]]
|David Buckingham
| ≤{{year|1976}}
| [[24P10]]
| {{cells|24}}
|-
! {{period|11|brief}}
| [[38P11.1]]
|David Buckingham
| {{year|1977}}
| [[rattlesnake]]
| {{cells|33}}
|-
! {{period|12|brief}}
| [[dinner table]]
|[[Robert Wainwright]]
| {{year|1972}}
| [[dinner table]]
| {{cells|33}}
|-
! {{period|13|brief}}
| [[Buckingham's p13]]
|David Buckingham
| 1976
| [[Beluchenko's p13]]
| {{cells|34}}
|-
! {{period|14|brief}}
| [[tumbler]]
|[[George Collins]]
| 1970
| [[tumbler]]
| {{cells|16}}
|-
! {{period|15|brief}}
| [[pentadecathlon]]
|John Conway
| 1970
| [[pentadecathlon]]
| {{cells|12}}
|-
! {{period|16|brief}}
| [[two pre-L hasslers]]
|Robert Wainwright
| {{year|1983}}
| [[Rob's p16]]
| {{cells|21}}
|-
! {{period|17|brief}}
| [[54P17.1]]
|[[Dean Hickerson]]
| {{year|1997}}
| [[honey thieves]]
| {{cells|36}}
|-
! {{period|18|brief}}
| [[117P18]]{{refn|group=note|name=lcm|An oscillator of this period can also be constructed from two [[sparker]]s both of which were known by an earlier date. However, [[LCM oscillator]]s are generally considered "[[boring]]", and thus not listed here despite technically being [[non-trivial]].}}
|David Buckingham
| ≤{{year|1991}}
| [[p18 bi-block hassler]], [[p18 phase shifter]]
| {{cells|43}}
|-
! class="red_td" | 19
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|20|brief}}
| [[145P20]]{{refn|group=note|name=lcm}}
|[[Noam Elkies]]
| {{year|1995}}
| [[mold on fumarole]]
| {{cells|30}}
|-
! {{period|21|brief}}
| [[124P21]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1995
| [[caterer on 28P7.3]]
| {{cells|40}}
|-
! {{period|22|brief}}
| [[168P22.1]]
|Noam Elkies
| 1997
| [[Jason's p22]]
| {{cells|36}}
|-
! {{period|23|brief}}
| [[David Hilbert]]
|[[Luka Okanishi]], [[praosylen]]
| {{year|2019}}
| [[David Hilbert]]
| {{cells|122}}
|-
! {{period|24|brief}}
| [[186P24]]{{refn|group=note|name=lcm}}
|[[Bill Gosper]]
| {{year|1994}}
| [[caterer on figure eight]]
| {{cells|24}}
|-
! {{period|25|brief}}
| [[134P25]]
|Noam Elkies
| 1994
| [[p25 pre-pulsar shuttle]]
| {{cells|83}}
|-
! {{period|26|brief}}
| [[p26 pre-pulsar shuttle]]
|David Buckingham
| 1983
| [[87P26]]
| {{cells|87}}
|-
! {{period|27|brief}}
| [[123P27.1]]
|Noam Elkies
| {{year|2002}}
| [[56P27]]
| {{cells|56}}
|-
! {{period|28|brief}}
| [[newshuttle]]
|David Buckingham
| {{year|1973}}
| [[mold on 34P14 shuttle]]
| {{cells|46}}
|-
! {{period|29|brief}}
| [[p29 pre-pulsar shuttle]]
|David Buckingham
| {{year|1980}}
| [[p29 pre-pulsar shuttle]]
| {{cells|54}}
|-
! {{period|30|brief}}
| [[queen bee shuttle]]
|Bill Gosper
| 1970
| [[queen bee shuttle]]
| {{cells|20}}
|-
! {{period|31|brief}}
| [[Merzenich's p31]]
|[[Matthias Merzenich]]
| {{year|2010}}
| [[Merzenich's p31]]
| {{cells|48}}
|-
! {{period|32|brief}}
| [[gourmet]]
|David Buckingham
| {{year|1978}}
| [[p32 honey farm hassler]]
| {{cells|45}}
|-
! {{period|33|brief}}
| [[258P3 on Achim's p11]]
|Noam Elkies, [[Achim Flammenkamp]]
| 1997
| [[caterer on rattlesnake]]
| {{cells|46}}
|-
! {{period|34|brief}}
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''No non-trivial examples found''
|-
! {{period|35|brief}}
| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
|Dean Hickerson
| 1995
| [[p35 honey farm hassler]]
| {{cells|44}}
|-
! {{period|36|brief}}
| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1984
| [[22P36]]
| {{cells|22}}
|-
! {{period|37|brief}}
| [[Beluchenko's p37]]
|[[Nicolay Beluchenko]]
| {{year|2009}}
| [[Beluchenko's p37]]
| {{cells|124}}
|-
! {{period|38|brief}}
| [[strontium]]
|[[David Raucci]]
| {{year|2022}}
| [[strontium]]
| {{cells|44}}
|-
! {{period|39|brief}}
| [[134P39.1]]
|David Buckingham, Noam Elkies
| {{year|2000}}
| [[caterer on Beluchenko's p13]]
|{{cells|46}}
|-
! {{period|40|brief}}
| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| 1991
| [[Beluchenko's p40]]
| {{cells|26}}
|-
! class="red_td" | 41
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|42|brief}}
| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
|Noam Elkies
| 1994
| [[unix on 34P14 shuttle]]
| {{cells|50}}
|-
! {{period|43|brief}}
| [[p43 Snark loop]]
|[[Mike Playle]]
| {{year|2013}}
| [[p43 Snark loop]]
|{{cells|228}}
|-
! {{period|44|brief}}
| [[p44 pi-heptomino hassler]]
|David Buckingham
| 1992
| [[mold on rattlesnake]]
| {{cells|45}}
|-
! {{period|45|brief}}
| [[pentadecathlon on snacker]]
| [[Mark Niemiec]], John Conway
| ≤1995
| [[pentadecathlon on thumb 1]]
| {{cells|48}}
|-
! {{period|46|brief}}
| [[twin bees shuttle]]
|Bill Gosper
| 1971
| [[twin bees shuttle]]
| {{cells|28}}
|-
! {{period|47|brief}}
| [[p47 pre-pulsar shuttle]]
|David Buckingham
| {{year|1982}}
| [[p47 pre-pulsar shuttle]]
| {{cells|84}}
|-
! {{period|48|brief}}
| [[p48 toad hassler]]
|Bill Gosper
| 1994
| [[unix on Rich's p16]]
| {{cells|52}}
|-
! {{period|49|brief}}
| [[p49 glider shuttle]]
|Noam Elkies
| {{year|1999}}
| [[p49 bumper loop]]
| {{cells|206}}
|-
! {{period|50|brief}}
| [[p50 glider shuttle]]
|Dean Hickerson
| 1992
| [[p50 traffic jam]]
| {{cells|92}}
|-
! {{period|51|brief}}
| [[Beluchenko's p51]]
|Nicolay Beluchenko
| 2009
| [[90P51]]
| {{cells|90}}
|-
! {{period|52|brief}}
| [[Four eaters hassling lumps of muck]]
|David Buckingham
| 1977
| [[four eaters hassling lumps of muck]]
| {{cells|35}}
|-
! {{period|53|brief}}
| [[p53 Snark loop]]
|Mike Playle
| {{year|2013}}
| [[p53 Snark loop]]
|{{cells|228}}
|-
! {{period|54|brief}}
| [[p54 shuttle]]
|David Buckingham
| {{year|1973}}
| [[p54 shuttle]]
| {{cells|48}}
|-
! {{period|55|brief}}
| [[p55 pre-pulsar hassler]]
|David Buckingham
| {{year|1986}}
| [[pseudo-barberpole on rattlesnake]]
| {{cells|49}}
|-
! {{period|56|brief}}
| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| ≤1991
| [[p56 B-heptomino shuttle]]
| {{cells|45}}
|-
! {{period|57|brief}}
| [[p57 Herschel loop 1]]
|[[Dietrich Leithner]]
| 1997
| [[p57 bumper loop]]
|{{cells|152}}
|-
! {{period|58|brief}}
| [[p58 toadsucker]]
|Bill Gosper
| 1994
| [[p58 pre-pulsar shuttle]]
| {{cells|104}}
|-
! {{period|59|brief}}
| [[p59 Herschel loop 1]]
|David Buckingham
| 1997
| [[Adjustable glider loop|p59 Snark loop]]
|{{cells|228}}
|-
! {{period|60|brief}}
| [[p60 glider shuttle]]
|David Buckingham
| ≤ 1971
| [[mold on pentadecathlon]]
| {{cells|24}}
|-
! {{period|61|brief}}
| [[p61 Herschel loop 1]]
|David Buckingham
| {{year|1996}}
| [[Adjustable glider loop|p61 Snark loop]]
|{{cells|228}}
|-
! {{period|62|brief}}
| ?
| ?
| ?
| [[66P62]]
| {{cells|66}}
|-
! {{period|63|brief}}
| ?
| ?
| ?
| [[snacker on 38P7.2]]
| {{cells|78}}
|-
! {{period|64|brief}}
| ?
| ?
| ?
| [[Merzenich's p64]]
| {{cells|34}}
|-
! {{period|65|brief}}
| ?
| ?
| ?
| [[fumarole on Beluchenko's p13]]
| {{cells|52}}
|-
! {{period|66|brief}}
| ?
| ?
| ?
| [[caterer on Jason's p22]]
| {{cells|48}}
|-
! {{period|67|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p67 Snark loop]]
|{{cells|228}}
|-
! {{period|68|brief}}
| ?
| ?
| ?
| [[72P68]]
|{{cells|72}}
|-
! {{period|69|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p69 bumper loop]]
|{{cells|152}}
|-
! {{period|70|brief}}
| ?
| ?
| ?
| [[fumarole on 34P14 shuttle]]
| {{cells|52}}
|-
! {{period|71|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p71 Snark loop]]
|{{cells|228}}
|-
! {{period|72|brief}}
| [[two blockers hassling R-pentomino]]
|Robert Wainwright
| 1990
| [[figure eight on 22P36]]
| {{cells|36}}
|-
! {{period|73|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p73 Snark loop]]
|{{cells|228}}
|-
! {{period|74|brief}}
| p74 Herschel loop
|David Buckingham
| 1996
| [[Raucci's p74]]
| {{cells|84}}
|-
! {{period|75|brief}}
| ?
| ?
| ?
| [[6 bits]]
|{{cells|49}}
|-
! {{period|76|brief}}
| ?
| ?
| ?
| [[mold on strontium]]
| {{cells|56}}
|-
! {{period|77|brief}}
| ?
| ?
| ?
| [[77P77]]
|{{cells|77}}
|-
! {{period|78|brief}}
| ?
| ?
| ?
| [[p6 thumb on Beluchenko's p13]]
|{{cells|61}}
|-
! {{period|79|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p79 Snark loop]]
|{{cells|228}}
|-
! {{period|80|brief}}
| ?
| ?
| ?
| [[fumarole on Rob's p16]]
| {{cells|39}}
|-
! {{period|81|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p81 bumper loop]]
|{{cells|152}}
|-
! {{period|82|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p82 Snark loop]]
|{{cells|208}}
|-
! {{period|83|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p83 Snark loop]]
|{{cells|228}}
|-
! {{period|84|brief}}
| ?
| ?
| ?
| [[52P84]]
| {{cells|52}}
|-
! {{period|85|brief}}
| ?
| ?
| ?
| [[74P85]]
|{{cells|74}}
|-
! {{period|86|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p86 Snark loop]]
|{{cells|208}}
|-
! {{period|87|brief}}
| ?
| ?
| ?
| [[84P87]]
| {{cells|84}}
|-
! {{period|88|brief}}
| p88 glider loop
|David Buckingham
| 1992
| [[figure eight on rattlesnake]]
| {{cells|45}}
|-
! {{period|89|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p89 Snark loop]]
|{{cells|228}}
|-
! {{period|90|brief}}
| ?
| ?
| ?
| [[thumb 1 on queen bee shuttle]]
| {{cells|56}}
|-
! {{period|91|brief}}
| ?
| ?
| ?
| [[44P7 on Beluchenko's p13]]
|{{cells|78}}
|-
! {{period|92|brief}}
| ?
| ?
| ?
| [[50P92.1]], [[twin bees shuttle on 22P4.3]]
| {{cells|50}}
|-
! {{period|93|brief}}
| ?
| ?
| ?
| [[caterer on Merzenich's p31]]
|{{cells|60}}
|-
! {{period|94|brief}}
| capped [[AK-47 reaction|AK-47]] gun
|Dean Hickerson
| 1990
| {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]]
| {{cells|110}}
|-
! {{period|95|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p95 Snark loop]]
|{{cells|228}}
|-
! {{period|96|brief}}
| ?
| ?
| ?
| [[period-48 glider gun]] {{LinkCatagolue|xp96_0178cy766zy44koy6m640ooe4a4z0gs26x11xoy1oo022440ezo8go|patternname=with boat-bit|style=raw}}
| {{cells|59}}
|-
! {{period|97|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p97 Snark loop]]
|{{cells|228}}
|-
! {{period|98|brief}}
| ?
| ?
| ?
| [[Gallus]]
| {{cells|105}}
|-
! {{period|99|brief}}
| ?
| ?
| ?
| [[48P9 on rattlesnake]]
|{{cells|82}}
|-
! {{period|100|brief}}
| [[centinal]]
|Bill Gosper
| ≤{{year|1987}}
| [[centinal]]
| {{cells|70}}
|-
! {{period|101|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p101 Snark loop]]
|{{cells|228}}
|-
! {{period|102|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp102_yzy2ca230oomewcczyzx33y3cczzyu42ey3o4ozyygs26x1zyzy3ca8zzzy54kczycoge2zy7696y3sg8zzy1ccy3ggzccwsq660ggkc011zy51|patternname=p102 unix loop|style=raw}}
| {{cells|96}}
|-
! {{period|103|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p103 Snark loop]]
|{{cells|228}}
|-
! {{period|104|brief}}
| ?
| ?
| ?
| [[figure eight on Beluchenko's p13]]
| {{cells|46}}
|-
! {{period|105|brief}}
| ?
| ?
| ?
| [[pentadecathlon on 37P7.1]]
|{{cells|49}}
|-
! {{period|106|brief}}
| ?
| ?
| ?
| [[rectifier|p106 rectifier loop]]
|{{cells|169}}
|-
! {{period|107|brief}}
| ?
| ?
| ?
| [[rectifier|p107 rectifier loop]]
|{{cells|136}}
|-
! {{period|108|brief}}
| ?
| ?
| ?
| [[22P4.3 on 56P27]]
|{{cells|78}}
|-
! {{period|109|brief}}
| ?
| ?
| ?
| [[rectifier|p109 rectifier loop]]
|{{cells|156}}
|-
! {{period|110|brief}}
| [[p110 traffic jam]]
|Bill Gosper
| 1994
| [[pseudo-barberpole on Jason's p22]]
|{{cells|51}}
|-
! {{period|111|brief}}
| ?
| ?
| ?
| [[rectifier|p111 rectifier loop]]
|{{cells|136}}
|-
! {{period|112|brief}}
| ?
| ?
| ?
| [[tumbler on Rich's p16]]
|{{cells|50}}
|-
! {{period|113|brief}}
| ?
| ?
| ?
| [[nihonium]]
| {{cells|106}}
|-
! {{period|114|brief}}
| ?
| ?
| ?
| [[caterer on strontium]]
|{{cells|57}}
|-
! {{period|115|brief}}
| ?
| ?
| ?
| [[rectifier|p115 rectifier loop]]
|{{cells|136}}
|-
! {{period|116|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=102P116|style=raw}}
|{{cells|102}}
|-
! {{period|117|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp117_y1o44mhar0rahm44ozwg8p7870167876107871zq6hcbagy1szg9gf99gfy26a8oz56o3t5zx1|patternname=117P117|style=raw}}
| {{cells|117}}
|-
! {{period|118|brief}}
| ?
| ?
| ?
| [[rectifier|p118 rectifier loop]]
|{{cells|154}}
|-
! {{period|119|brief}}
| ?
| ?
| ?
| [[rectifier|p119 rectifier loop]]
|{{cells|136}}
|-
! {{period|120|brief}}
| ?
| ?
| ?
| [[figure eight on pentadecathlon]]
| {{cells|24}}
|-
! {{period|121|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|122|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|123|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|124|brief}}
| [[p124 lumps of muck hassler]]
|Dean Hickerson
| 1994
| [[mold on Merzenich's p31]]
| {{cells|60}}
|-
! {{period|125|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|126|brief}}
| ?
| ?
| ?
| [[snacker on 34P14 shuttle]]
| {{cells|74}}
|-
! {{period|127|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|128|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp128_y3ca73oswcczyqg88gzy1ggyh6bbcxca4z8ko010onmcy04eewuscy26dt30g0352z4a6x6qqcyh11zy01221zyh66w73osa6|patternname=p128 wing hassler|style=raw}}, {{LinkCatagolue|xp128_ytokgyb6664abw66zyz8kk8y9ccwgc8gzyvggkcya33y473666zooogoy4ggyaca23w1zx134c2wcc011y64aa4zy3oowkk8oooyb2a6zy71|patternname=p128 Coe-blocker loop|style=raw}}
|{{cells|108}}
|-
! {{period|129|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p129 bumper loop]]
|{{cells|152}}
|-
! {{period|130|brief}}
| ?
| ?
| ?
| [[55P10 on Beluchenko's p13]]
| {{cells|89}}
|-
! {{period|131|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|132|brief}}
| p132 glider loop
|David Buckingham
| 1992
| [[mold on Jason's p33]]
| {{cells|72}}
|-
! {{period|133|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|134|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|135|brief}}
| [[106P135]]
|Bill Gosper
| {{year|1989}}
| [[pentadecathlon on 56P27]]
|{{cells|68}}
|-
! {{period|136|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp136_y3ca73oswcczy2ggwooy98m113czccwe192y166y7220o8zyq113y0oggzyz23088y7ccy18igew66zyz6oggd2y933w11zyzya66w73osa6|patternname=p136 Coe-blocker loop|style=raw}}
| {{cells|108}}
|-
! {{period|137|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|138|brief}}
| ?
| ?
| ?
| [[Gabriel's p138]]
| {{cells|36}}
|-
! {{period|139|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|140|brief}}
| p140 traffic jam
|Bill Gosper
| 1994
| [[34P14 shuttle on dockyard]]
| {{cells|82}}
|-
! {{period|141|brief}}
| ?
| ?
| ?
| [[p47 pre-pulsar shuttle phase-shifting 28P7.1]]
| {{cells|114}}
|-
! {{period|142|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|143|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|144|brief}}
| capped p144 [[gunstar]]
|David Buckingham
| 1990
| [[Achim's p144]]
| {{cells|42}}
|-
! {{period|150|brief}}
| ?
| ?
| ?
| [[buckaroo|p150 buckaroo shuttle]]
| {{cells|51}}
|-
! {{period|152|brief}}
| ?
| ?
| ?
| [[figure eight on strontium]]
| {{cells|60}}
|-
! {{period|156|brief}}
| p156 [[traffic jam]] oscillator
|Bill Gosper
| 1994
| {{LinkCatagolue|xp156_ccc4ak8g032aczy1efy2gcgzy933zy7o4ozy81x62sgzzymggzyn346wg8gzys121zyqgcszyr3y2gfnzyt354cw1252333|patternname=p156 unix loop|style=raw}}
| {{cells|86}}
|-
! {{period|165|brief}}
| ?
| ?
| ?
| [[rattlesnake on pentadecathlon]]
| {{cells|45}}
|-
! {{period|168|brief}}
| ?
| ?
| ?
| [[figure eight on p21 honey farm hassler]]
| {{cells|72}}
|-
! {{period|177|brief}}
| ?
| ?
| ?
| [[Karel's p177]]
| {{cells|104}}
|-
! {{period|184|brief}}
| ?
| ?
| ?
| [[figure eight on twin bees shuttle]]
| {{cells|40}}
|-
! {{period|186|brief}}
| ?
| ?
| ?
| [[unix on Merzenich's p31]]
| {{cells|64}}
|-
! {{period|188|brief}}
| ?
| ?
| ?
| [[AK-94]] {{LinkCatagolue|xp188_x696o8b9czy065x33xc871wbdzoozwgg04ahhha4y5c871z4701yfoozxggy0ggzx56w4701xmmggo5jzya146w343|patternname=with boat-bits|style=raw}}
| {{cells|108}}
|-
! {{period|196|brief}}
| ?
| ?
| ?
| [[p196 pi-heptomino hassler]]
| {{cells|66}}
|-
! {{period|200|brief}}
| p200 glider loop
|Bill Gosper
| ≤{{year|1987}}
| [[figure eight on centinal]]
|{{cells|82}}
|-
! {{period|226|brief}}
| ?
| ?
| ?
| [[nihonium*]]
| {{cells|107}}
|-
! {{period|230|brief}}
| ?
| ?
| ?
| [[fumarole on twin bees shuttle]]
|{{cells|46}}
|-
! {{period|232|brief}}
| ?
| ?
| ?
| [[figure eight on p29 pre-pulsar shuttle]]
|{{cells|66}}
|-
! {{period|240|brief}}
| ?
| ?
| ?
| [[pentadecathlon on Rob's p16]]
| {{cells|33}}
|-
! {{period|246|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp246_ya32acydg8k8ooozyu1utzzzybcirrd6y4cc4zy1ggy61zggwg9g89z14w61ye354c|patternname=relative|style=raw}}
| {{cells|68}}
|-
! {{period|256|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp256_ytokgyb6664abw66zyz8kk8y9ccwgc8gzyvggkcya33y473666zooogoy4ggyaca23w1zx134c2wcc011y64aa4zy3oowkk8ooozy71|patternname=p256 Coe-blocker loop|style=raw}}
| {{cells|103}}
|-
! {{period|276|brief}}
| ?
| ?
| ?
| [[caterer on 50P92.1]]
| {{cells|62}}
|-
! {{period|300|brief}}
| ?
| ?
| ?
| [[pentadecathlon on centinal]]
| {{cells|88}}
|-
! {{period|312|brief}}
| ?
| ?
| ?
| [[60P312]]
| {{cells|60}}
|-
! {{period|320|brief}}
| ?
| ?
| ?
| [[fumarole on Merzenich's p64]]
| {{cells|52}}
|-
! {{period|360|brief}}
| ?
| ?
| ?
| [[thumb 1 on Beluchenko's p40]]
| {{cells|62}}
|-
! {{period|368|brief}}
| ?
| ?
| ?
| [[period-184 glider gun]] {{LinkCatagolue|xp368_y0gy632aczy01156zzggyp62sgz56yc65134w16zync4ozy8o8goy911|patternname=with boat-bits|style=raw}}
| {{cells|50}}
|-
! {{period|460|brief}}
| ?
| ?
| ?
| [[pseudo-barberpole on 50P92.1]]
| {{cells|65}}
|-
! {{period|492|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp492_y0o4qa344ozx118f0dc3z8oyago0ab2sycc871z0123y9126e431zy8ooz0mqzyt66w7bcczyy66|patternname=with boat-bit|style=raw}}
| {{cells|87}}
|-
! {{period|496|brief}}
| ?
| ?
| ?
| [[Rob's p16 on Merzenich's p31]]
| {{cells|69}}
|-
! {{period|512|brief}}
| ?
| ?
| ?
| [[period-256 glider gun]] {{LinkCatagolue|xp512_yr33y166z0ggy033y16426ye33y0ccz011w66yuggz66yz56zzzy2mqyz66zygckgk2a21ya66woozy133y0ccye6426y1cczy566y1cc|patternname=with boat-bits|style=raw}}
| {{cells|100}}
|-
! {{period|856|brief}}
| [[period-856 glider gun]]
| [[David Buckingham]]
| 1991
| {{LinkCatagolue|xp856_yzyzyrca8ya66wd52666zyzyzyw8kk8y9cccoszyzyzysggkcya33y11261w66zyzyzys1zzzzzzzzzzzzzzzooogoy4ggyaca23zx134c2wcc011y64aa4zy3oowkk8ooozy71|patternname=p856 Coe-blocker loop|style=raw}}
|{{cells|103}}
|}

==Flipper==
A '''flipper''' is any [[oscillator]] that forms its mirror image halfway through its [[period]].

==Notes==
<references group=note />

==See also==
*[[List of common oscillators]]
*[[:Category:Flipping oscillators|List of flipping oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
*[[Table of oscillators by period]]
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]

==External links==
{{LinkWikipedia|Oscillator_(cellular_automaton)}}
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkLexicon|lex_f.htm#flipper|name=Flipper}}

===Forum threads===
{{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
{{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
{{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}

__NOTOC__

Mold on strontium

2022-01-13T18:36:09Z

Freywa: first of the strontium-based LCMs

{{Oscillator
|name = Mold on strontium
|pname = moldonstrontium
|c = 56
|bx = 46
|by = 13
|p = 76
|m = 76
|h = 59.79
|v = 0.94
|sv = 0.01
|rulemin = B3/S23
|rulemax = B3/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B36i7c/S234c6i8
|plaintext = true
|rle = true
|viewerconfig = #C [[ LOOP 76 THUMBSIZE 2 GPS 19 ZOOM 10 ]]
|apgcode = xp76_o4an7y1ca23yi32acz0110888xooxoa6ya6aoxoox888zy47ys7
}}
'''Mold on strontium''' is a {{period|76}} [[oscillator]] that is composed of a [[mold]] and [[strontium]]. Although it is composed of two oscillators of smaller periods ({{period|4|brief}} and {{period|38|brief}} respectively), it is considered non-trivial because it contains three [[cell]]s that oscillate at the full period. In terms of its {{cells|56}} cells, it is the smallest known non-trivial period 76 oscillator.

==External links==
{{LinkCatagolue|xp76_o4an7y1ca23yi32acz0110888xooxoa6ya6aoxoox888zy47ys7}}

[[Category:Least-common-multiple oscillators]]

RLE:Moldonstrontium

2022-01-13T18:32:32Z

Freywa: RLE

x = 45, y = 12, rule = B3/S23
4bo8bo22bo$2b2obo5b3o22b3o$bo8bo28bo$obo2bo4b2o26b2o$o2bo$b2o$16b2o14b
2o$5bo11bo14bo11bo$5bo4b2o4bo16bo4b2o4bo$5bo5bo2b2o18b2o2bo5bo2$7b3o
30b3o!

Oscillator

2022-01-13T12:14:13Z

Freywa: SKOP504 has exactly the same mechanism as the SKOP102

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period).

[[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
| rowspan="500" style="border: none;" |
! Smallest known
! Minimum # of cells
|-
! {{period|2|brief}}
| [[blinker]]
|[[John Conway]]
| {{year|1970}}
| [[blinker]]
| {{cells|3}}
|-
! {{period|3|brief}}
| [[pulsar]]
|John Conway
| 1970
| [[caterer]]
| {{cells|12}}
|-
! {{period|4|brief}}
| [[pinwheel]]
|[[Simon Norton]]
| 1970
| [[mazing]], [[mold]]
| {{cells|12}}
|-
! {{period|5|brief}}
| [[octagon 2]]
|[[Sol Goodman]], [[Arthur Taber]]
| {{year|1971}}
| [[pseudo-barberpole]]
| {{cells|15}}
|-
! {{period|6|brief}}
| [[$rats]]
|[[David Buckingham]]
| {{year|1972}}
| [[unix]]
| {{cells|16}}
|-
! {{period|7|brief}}
| [[burloaferimeter]]
|David Buckingham
| 1972
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
| {{cells|28}}
|-
! {{period|8|brief}}
| [[figure eight]]
|Simon Norton
| 1970
| [[figure eight]]
| {{cells|12}}
|-
! {{period|9|brief}}
| [[worker bee]]
|David Buckingham
| 1972
| [[29P9]]
| {{cells|29}}
|-
! {{period|10|brief}}
| [[42P10.3]]
|David Buckingham
| ≤{{year|1976}}
| [[24P10]]
| {{cells|24}}
|-
! {{period|11|brief}}
| [[38P11.1]]
|David Buckingham
| {{year|1977}}
| [[rattlesnake]]
| {{cells|33}}
|-
! {{period|12|brief}}
| [[dinner table]]
|[[Robert Wainwright]]
| {{year|1972}}
| [[dinner table]]
| {{cells|33}}
|-
! {{period|13|brief}}
| [[Buckingham's p13]]
|David Buckingham
| 1976
| [[Beluchenko's p13]]
| {{cells|34}}
|-
! {{period|14|brief}}
| [[tumbler]]
|[[George Collins]]
| 1970
| [[tumbler]]
| {{cells|16}}
|-
! {{period|15|brief}}
| [[pentadecathlon]]
|John Conway
| 1970
| [[pentadecathlon]]
| {{cells|12}}
|-
! {{period|16|brief}}
| [[two pre-L hasslers]]
|Robert Wainwright
| {{year|1983}}
| [[Rob's p16]]
| {{cells|21}}
|-
! {{period|17|brief}}
| [[54P17.1]]
|[[Dean Hickerson]]
| {{year|1997}}
| [[honey thieves]]
| {{cells|36}}
|-
! {{period|18|brief}}
| [[117P18]]{{refn|group=note|name=lcm|An oscillator of this period can also be constructed from two [[sparker]]s both of which were known by an earlier date. However, [[LCM oscillator]]s are generally considered "[[boring]]", and thus not listed here despite technically being [[non-trivial]].}}
|David Buckingham
| ≤{{year|1991}}
| [[p18 bi-block hassler]], [[p18 phase shifter]]
| {{cells|43}}
|-
! class="red_td" | 19
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|20|brief}}
| [[145P20]]{{refn|group=note|name=lcm}}
|[[Noam Elkies]]
| {{year|1995}}
| [[mold on fumarole]]
| {{cells|30}}
|-
! {{period|21|brief}}
| [[124P21]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1995
| [[caterer on 28P7.3]]
| {{cells|40}}
|-
! {{period|22|brief}}
| [[168P22.1]]
|Noam Elkies
| 1997
| [[Jason's p22]]
| {{cells|36}}
|-
! {{period|23|brief}}
| [[David Hilbert]]
|[[Luka Okanishi]], [[praosylen]]
| {{year|2019}}
| [[David Hilbert]]
| {{cells|122}}
|-
! {{period|24|brief}}
| [[186P24]]{{refn|group=note|name=lcm}}
|[[Bill Gosper]]
| {{year|1994}}
| [[caterer on figure eight]]
| {{cells|24}}
|-
! {{period|25|brief}}
| [[134P25]]
|Noam Elkies
| 1994
| [[p25 pre-pulsar shuttle]]
| {{cells|83}}
|-
! {{period|26|brief}}
| [[p26 pre-pulsar shuttle]]
|David Buckingham
| 1983
| [[87P26]]
| {{cells|87}}
|-
! {{period|27|brief}}
| [[123P27.1]]
|Noam Elkies
| {{year|2002}}
| [[56P27]]
| {{cells|56}}
|-
! {{period|28|brief}}
| [[newshuttle]]
|David Buckingham
| {{year|1973}}
| [[mold on 34P14 shuttle]]
| {{cells|46}}
|-
! {{period|29|brief}}
| [[p29 pre-pulsar shuttle]]
|David Buckingham
| {{year|1980}}
| [[p29 pre-pulsar shuttle]]
| {{cells|54}}
|-
! {{period|30|brief}}
| [[queen bee shuttle]]
|Bill Gosper
| 1970
| [[queen bee shuttle]]
| {{cells|20}}
|-
! {{period|31|brief}}
| [[Merzenich's p31]]
|[[Matthias Merzenich]]
| {{year|2010}}
| [[Merzenich's p31]]
| {{cells|48}}
|-
! {{period|32|brief}}
| [[gourmet]]
|David Buckingham
| {{year|1978}}
| [[p32 honey farm hassler]]
| {{cells|45}}
|-
! {{period|33|brief}}
| [[258P3 on Achim's p11]]
|Noam Elkies, [[Achim Flammenkamp]]
| 1997
| [[caterer on rattlesnake]]
| {{cells|46}}
|-
! {{period|34|brief}}
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''No non-trivial examples found''
|-
! {{period|35|brief}}
| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
|Dean Hickerson
| 1995
| [[p35 honey farm hassler]]
| {{cells|44}}
|-
! {{period|36|brief}}
| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1984
| [[22P36]]
| {{cells|22}}
|-
! {{period|37|brief}}
| [[Beluchenko's p37]]
|[[Nicolay Beluchenko]]
| {{year|2009}}
| [[Beluchenko's p37]]
| {{cells|124}}
|-
! {{period|38|brief}}
| [[strontium]]
|[[David Raucci]]
| {{year|2022}}
| [[strontium]]
| {{cells|44}}
|-
! {{period|39|brief}}
| [[134P39.1]]
|David Buckingham, Noam Elkies
| {{year|2000}}
| [[caterer on Beluchenko's p13]]
|{{cells|46}}
|-
! {{period|40|brief}}
| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| 1991
| [[Beluchenko's p40]]
| {{cells|26}}
|-
! class="red_td" | 41
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|42|brief}}
| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
|Noam Elkies
| 1994
| [[unix on 34P14 shuttle]]
| {{cells|50}}
|-
! {{period|43|brief}}
| [[p43 Snark loop]]
|[[Mike Playle]]
| {{year|2013}}
| [[p43 Snark loop]]
|{{cells|228}}
|-
! {{period|44|brief}}
| [[p44 pi-heptomino hassler]]
|David Buckingham
| 1992
| [[mold on rattlesnake]]
| {{cells|45}}
|-
! {{period|45|brief}}
| [[pentadecathlon on snacker]]
| [[Mark Niemiec]], John Conway
| ≤1995
| [[pentadecathlon on thumb 1]]
| {{cells|48}}
|-
! {{period|46|brief}}
| [[twin bees shuttle]]
|Bill Gosper
| 1971
| [[twin bees shuttle]]
| {{cells|28}}
|-
! {{period|47|brief}}
| [[p47 pre-pulsar shuttle]]
|David Buckingham
| {{year|1982}}
| [[p47 pre-pulsar shuttle]]
| {{cells|84}}
|-
! {{period|48|brief}}
| [[p48 toad hassler]]
|Bill Gosper
| 1994
| [[unix on Rich's p16]]
| {{cells|52}}
|-
! {{period|49|brief}}
| [[p49 glider shuttle]]
|Noam Elkies
| {{year|1999}}
| [[p49 bumper loop]]
| {{cells|206}}
|-
! {{period|50|brief}}
| [[p50 glider shuttle]]
|Dean Hickerson
| 1992
| [[p50 traffic jam]]
| {{cells|92}}
|-
! {{period|51|brief}}
| [[Beluchenko's p51]]
|Nicolay Beluchenko
| 2009
| [[90P51]]
| {{cells|90}}
|-
! {{period|52|brief}}
| [[Four eaters hassling lumps of muck]]
|David Buckingham
| 1977
| [[four eaters hassling lumps of muck]]
| {{cells|35}}
|-
! {{period|53|brief}}
| [[p53 Snark loop]]
|Mike Playle
| {{year|2013}}
| [[p53 Snark loop]]
|{{cells|228}}
|-
! {{period|54|brief}}
| [[p54 shuttle]]
|David Buckingham
| {{year|1973}}
| [[p54 shuttle]]
| {{cells|48}}
|-
! {{period|55|brief}}
| [[p55 pre-pulsar hassler]]
|David Buckingham
| {{year|1986}}
| [[pseudo-barberpole on rattlesnake]]
| {{cells|49}}
|-
! {{period|56|brief}}
| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| ≤1991
| [[p56 B-heptomino shuttle]]
| {{cells|45}}
|-
! {{period|57|brief}}
| [[p57 Herschel loop 1]]
|[[Dietrich Leithner]]
| 1997
| [[p57 bumper loop]]
|{{cells|152}}
|-
! {{period|58|brief}}
| [[p58 toadsucker]]
|Bill Gosper
| 1994
| [[p58 pre-pulsar shuttle]]
| {{cells|104}}
|-
! {{period|59|brief}}
| [[p59 Herschel loop 1]]
|David Buckingham
| 1997
| [[Adjustable glider loop|p59 Snark loop]]
|{{cells|228}}
|-
! {{period|60|brief}}
| [[p60 glider shuttle]]
|David Buckingham
| ≤ 1971
| [[mold on pentadecathlon]]
| {{cells|24}}
|-
! {{period|61|brief}}
| [[p61 Herschel loop 1]]
|David Buckingham
| {{year|1996}}
| [[Adjustable glider loop|p61 Snark loop]]
|{{cells|228}}
|-
! {{period|62|brief}}
| ?
| ?
| ?
| [[66P62]]
| {{cells|66}}
|-
! {{period|63|brief}}
| ?
| ?
| ?
| [[snacker on 38P7.2]]
| {{cells|78}}
|-
! {{period|64|brief}}
| ?
| ?
| ?
| [[Merzenich's p64]]
| {{cells|34}}
|-
! {{period|65|brief}}
| ?
| ?
| ?
| [[fumarole on Beluchenko's p13]]
| {{cells|52}}
|-
! {{period|66|brief}}
| ?
| ?
| ?
| [[caterer on Jason's p22]]
| {{cells|48}}
|-
! {{period|67|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p67 Snark loop]]
|{{cells|228}}
|-
! {{period|68|brief}}
| ?
| ?
| ?
| [[72P68]]
|{{cells|72}}
|-
! {{period|69|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p69 bumper loop]]
|{{cells|152}}
|-
! {{period|70|brief}}
| ?
| ?
| ?
| [[fumarole on 34P14 shuttle]]
| {{cells|52}}
|-
! {{period|71|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p71 Snark loop]]
|{{cells|228}}
|-
! {{period|72|brief}}
| [[two blockers hassling R-pentomino]]
|Robert Wainwright
| 1990
| [[figure eight on 22P36]]
| {{cells|36}}
|-
! {{period|73|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p73 Snark loop]]
|{{cells|228}}
|-
! {{period|74|brief}}
| p74 Herschel loop
|David Buckingham
| 1996
| [[Raucci's p74]]
| {{cells|84}}
|-
! {{period|75|brief}}
| ?
| ?
| ?
| [[6 bits]]
|{{cells|49}}
|-
! {{period|76|brief}}
| ?
| ?
| ?
| [[mold on strontium]]
| {{cells|56}}
|-
! {{period|77|brief}}
| ?
| ?
| ?
| [[77P77]]
|{{cells|77}}
|-
! {{period|78|brief}}
| ?
| ?
| ?
| [[p6 thumb on Beluchenko's p13]]
|{{cells|61}}
|-
! {{period|79|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p79 Snark loop]]
|{{cells|228}}
|-
! {{period|80|brief}}
| ?
| ?
| ?
| [[fumarole on Rob's p16]]
| {{cells|39}}
|-
! {{period|81|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p81 bumper loop]]
|{{cells|152}}
|-
! {{period|82|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p82 Snark loop]]
|{{cells|208}}
|-
! {{period|83|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p83 Snark loop]]
|{{cells|228}}
|-
! {{period|84|brief}}
| ?
| ?
| ?
| [[52P84]]
| {{cells|52}}
|-
! {{period|85|brief}}
| ?
| ?
| ?
| [[74P85]]
|{{cells|74}}
|-
! {{period|86|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p86 Snark loop]]
|{{cells|208}}
|-
! {{period|87|brief}}
| ?
| ?
| ?
| [[84P87]]
| {{cells|84}}
|-
! {{period|88|brief}}
| p88 glider loop
|David Buckingham
| 1992
| [[figure eight on rattlesnake]]
| {{cells|45}}
|-
! {{period|89|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p89 Snark loop]]
|{{cells|228}}
|-
! {{period|90|brief}}
| ?
| ?
| ?
| [[thumb 1 on queen bee shuttle]]
| {{cells|56}}
|-
! {{period|91|brief}}
| ?
| ?
| ?
| [[44P7 on Beluchenko's p13]]
|{{cells|78}}
|-
! {{period|92|brief}}
| ?
| ?
| ?
| [[50P92.1]], [[twin bees shuttle on 22P4.3]]
| {{cells|50}}
|-
! {{period|93|brief}}
| ?
| ?
| ?
| [[caterer on Merzenich's p31]]
|{{cells|60}}
|-
! {{period|94|brief}}
| capped [[AK-47 reaction|AK-47]] gun
|Dean Hickerson
| 1990
| {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]]
| {{cells|110}}
|-
! {{period|95|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p95 Snark loop]]
|{{cells|228}}
|-
! {{period|96|brief}}
| ?
| ?
| ?
| [[period-48 glider gun]] {{LinkCatagolue|xp96_0178cy766zy44koy6m640ooe4a4z0gs26x11xoy1oo022440ezo8go|patternname=with boat-bit|style=raw}}
| {{cells|59}}
|-
! {{period|97|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p97 Snark loop]]
|{{cells|228}}
|-
! {{period|98|brief}}
| ?
| ?
| ?
| [[Gallus]]
| {{cells|105}}
|-
! {{period|99|brief}}
| ?
| ?
| ?
| [[48P9 on rattlesnake]]
|{{cells|82}}
|-
! {{period|100|brief}}
| [[centinal]]
|Bill Gosper
| ≤{{year|1987}}
| [[centinal]]
| {{cells|70}}
|-
! {{period|101|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p101 Snark loop]]
|{{cells|228}}
|-
! {{period|102|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp102_yzy2ca230oomewcczyzx33y3cczzyu42ey3o4ozyygs26x1zyzy3ca8zzzy54kczycoge2zy7696y3sg8zzy1ccy3ggzccwsq660ggkc011zy51|patternname=p102 unix loop|style=raw}}
| {{cells|96}}
|-
! {{period|103|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p103 Snark loop]]
|{{cells|228}}
|-
! {{period|104|brief}}
| ?
| ?
| ?
| [[figure eight on Beluchenko's p13]]
| {{cells|46}}
|-
! {{period|105|brief}}
| ?
| ?
| ?
| [[pentadecathlon on 37P7.1]]
|{{cells|49}}
|-
! {{period|106|brief}}
| ?
| ?
| ?
| [[rectifier|p106 rectifier loop]]
|{{cells|169}}
|-
! {{period|107|brief}}
| ?
| ?
| ?
| [[rectifier|p107 rectifier loop]]
|{{cells|136}}
|-
! {{period|108|brief}}
| ?
| ?
| ?
| [[22P4.3 on 56P27]]
|{{cells|78}}
|-
! {{period|109|brief}}
| ?
| ?
| ?
| [[rectifier|p109 rectifier loop]]
|{{cells|156}}
|-
! {{period|110|brief}}
| [[p110 traffic jam]]
|Bill Gosper
| 1994
| [[pseudo-barberpole on Jason's p22]]
|{{cells|51}}
|-
! {{period|111|brief}}
| ?
| ?
| ?
| [[rectifier|p111 rectifier loop]]
|{{cells|136}}
|-
! {{period|112|brief}}
| ?
| ?
| ?
| [[tumbler on Rich's p16]]
|{{cells|50}}
|-
! {{period|113|brief}}
| ?
| ?
| ?
| [[nihonium]]
| {{cells|106}}
|-
! {{period|114|brief}}
| ?
| ?
| ?
| [[caterer on strontium]]
|{{cells|57}}
|-
! {{period|115|brief}}
| ?
| ?
| ?
| [[rectifier|p115 rectifier loop]]
|{{cells|136}}
|-
! {{period|116|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=102P116|style=raw}}
|{{cells|102}}
|-
! {{period|117|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp117_y1o44mhar0rahm44ozwg8p7870167876107871zq6hcbagy1szg9gf99gfy26a8oz56o3t5zx1|patternname=117P117|style=raw}}
| {{cells|117}}
|-
! {{period|118|brief}}
| ?
| ?
| ?
| [[rectifier|p118 rectifier loop]]
|{{cells|154}}
|-
! {{period|119|brief}}
| ?
| ?
| ?
| [[rectifier|p119 rectifier loop]]
|{{cells|136}}
|-
! {{period|120|brief}}
| ?
| ?
| ?
| [[figure eight on pentadecathlon]]
| {{cells|24}}
|-
! {{period|121|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|122|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|123|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|124|brief}}
| [[p124 lumps of muck hassler]]
|Dean Hickerson
| 1994
| [[mold on Merzenich's p31]]
| {{cells|60}}
|-
! {{period|125|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|126|brief}}
| ?
| ?
| ?
| [[snacker on 34P14 shuttle]]
| {{cells|74}}
|-
! {{period|127|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|128|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp128_y3ca73oswcczyqg88gzy1ggyh6bbcxca4z8ko010onmcy04eewuscy26dt30g0352z4a6x6qqcyh11zy01221zyh66w73osa6|patternname=p128 wing hassler|style=raw}}
|{{cells|108}}
|-
! {{period|129|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p129 bumper loop]]
|{{cells|152}}
|-
! {{period|130|brief}}
| ?
| ?
| ?
| [[55P10 on Beluchenko's p13]]
| {{cells|89}}
|-
! {{period|131|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|132|brief}}
| p132 glider loop
|David Buckingham
| 1992
| [[mold on Jason's p33]]
| {{cells|72}}
|-
! {{period|133|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|134|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|135|brief}}
| [[106P135]]
|Bill Gosper
| {{year|1989}}
| [[pentadecathlon on 56P27]]
|{{cells|68}}
|-
! {{period|136|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|137|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|138|brief}}
| ?
| ?
| ?
| [[Gabriel's p138]]
| {{cells|36}}
|-
! {{period|139|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|140|brief}}
| p140 traffic jam
|Bill Gosper
| 1994
| [[34P14 shuttle on dockyard]]
| {{cells|82}}
|-
! {{period|141|brief}}
| ?
| ?
| ?
| [[p47 pre-pulsar shuttle phase-shifting 28P7.1]]
| {{cells|114}}
|-
! {{period|142|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|143|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|144|brief}}
| capped p144 [[gunstar]]
|David Buckingham
| 1990
| [[Achim's p144]]
| {{cells|42}}
|-
! {{period|150|brief}}
| ?
| ?
| ?
| [[buckaroo|p150 buckaroo shuttle]]
| {{cells|51}}
|-
! {{period|152|brief}}
| ?
| ?
| ?
| [[figure eight on strontium]]
| {{cells|60}}
|-
! {{period|156|brief}}
| p156 [[traffic jam]] oscillator
|Bill Gosper
| 1994
| {{LinkCatagolue|xp156_ccc4ak8g032aczy1efy2gcgzy933zy7o4ozy81x62sgzzymggzyn346wg8gzys121zyqgcszyr3y2gfnzyt354cw1252333|patternname=p156 unix loop|style=raw}}
| {{cells|86}}
|-
! {{period|165|brief}}
| ?
| ?
| ?
| [[rattlesnake on pentadecathlon]]
| {{cells|45}}
|-
! {{period|168|brief}}
| ?
| ?
| ?
| [[figure eight on p21 honey farm hassler]]
| {{cells|72}}
|-
! {{period|177|brief}}
| ?
| ?
| ?
| [[Karel's p177]]
| {{cells|104}}
|-
! {{period|184|brief}}
| ?
| ?
| ?
| [[figure eight on twin bees shuttle]]
| {{cells|40}}
|-
! {{period|186|brief}}
| ?
| ?
| ?
| [[unix on Merzenich's p31]]
| {{cells|64}}
|-
! {{period|188|brief}}
| ?
| ?
| ?
| [[AK-94]] {{LinkCatagolue|xp188_x696o8b9czy065x33xc871wbdzoozwgg04ahhha4y5c871z4701yfoozxggy0ggzx56w4701xmmggo5jzya146w343|patternname=with boat-bits|style=raw}}
| {{cells|108}}
|-
! {{period|196|brief}}
| ?
| ?
| ?
| [[p196 pi-heptomino hassler]]
| {{cells|66}}
|-
! {{period|200|brief}}
| p200 glider loop
|Bill Gosper
| ≤{{year|1987}}
| [[figure eight on centinal]]
|{{cells|82}}
|-
! {{period|226|brief}}
| ?
| ?
| ?
| [[nihonium*]]
| {{cells|107}}
|-
! {{period|230|brief}}
| ?
| ?
| ?
| [[fumarole on twin bees shuttle]]
|{{cells|46}}
|-
! {{period|232|brief}}
| ?
| ?
| ?
| [[figure eight on p29 pre-pulsar shuttle]]
|{{cells|66}}
|-
! {{period|240|brief}}
| ?
| ?
| ?
| [[pentadecathlon on Rob's p16]]
| {{cells|33}}
|-
! {{period|246|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp246_ya32acydg8k8ooozyu1utzzzybcirrd6y4cc4zy1ggy61zggwg9g89z14w61ye354c|patternname=relative|style=raw}}
| {{cells|68}}
|-
! {{period|256|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp256_yr33y166z0ggy033y4178cyb33y0ccz011w66z66yyg88czy4699voyn11zy38ox61zy1311yz66zyzx66woozy133y0ccyb31e8y4cczy566y1cc|patternname=capped|style=raw}} [[period-256 glider gun]]
| {{cells|104}}
|-
! {{period|276|brief}}
| ?
| ?
| ?
| [[caterer on 50P92.1]]
| {{cells|62}}
|-
! {{period|300|brief}}
| ?
| ?
| ?
| [[pentadecathlon on centinal]]
| {{cells|88}}
|-
! {{period|312|brief}}
| ?
| ?
| ?
| [[60P312]]
| {{cells|60}}
|-
! {{period|320|brief}}
| ?
| ?
| ?
| [[fumarole on Merzenich's p64]]
| {{cells|52}}
|-
! {{period|360|brief}}
| ?
| ?
| ?
| [[thumb 1 on Beluchenko's p40]]
| {{cells|62}}
|-
! {{period|368|brief}}
| ?
| ?
| ?
| [[period-184 glider gun]] {{LinkCatagolue|xp368_y0gy632aczy01156zzggyp62sgz56yc65134w16zync4ozy8o8goy911|patternname=with boat-bits|style=raw}}
| {{cells|50}}
|-
! {{period|460|brief}}
| ?
| ?
| ?
| [[pseudo-barberpole on 50P92.1]]
| {{cells|65}}
|-
! {{period|492|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp492_y0o4qa344ozx118f0dc3z8oyago0ab2sycc871z0123y9126e431zy8ooz0mqzyt66w7bcczyy66|patternname=with boat-bit|style=raw}}
| {{cells|87}}
|-
! {{period|496|brief}}
| ?
| ?
| ?
| [[Rob's p16 on Merzenich's p31]]
| {{cells|69}}
|-
! {{period|512|brief}}
| ?
| ?
| ?
| [[period-256 glider gun]] {{LinkCatagolue|xp512_yr33y166z0ggy033y16426ye33y0ccz011w66yuggz66yz56zzzy2mqyz66zygckgk2a21ya66woozy133y0ccye6426y1cczy566y1cc|patternname=with boat-bits|style=raw}}
| {{cells|100}}
|-
! {{period|856|brief}}
| [[period-856 glider gun]]
| [[David Buckingham]]
| 1991
| {{LinkCatagolue|xp856_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzzzzzzzzzzyzyzyl844oxccy1vv03333rrzyzyzyl6603x66y1ddcccc0ffzyzyzym33|patternname=p856 glider shuttle|style=raw}}
|{{cells|109}}
|}

==Flipper==
A '''flipper''' is any [[oscillator]] that forms its mirror image halfway through its [[period]].

==Notes==
<references group=note />

==See also==
*[[List of common oscillators]]
*[[:Category:Flipping oscillators|List of flipping oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
*[[Table of oscillators by period]]
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]

==External links==
{{LinkWikipedia|Oscillator_(cellular_automaton)}}
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkLexicon|lex_f.htm#flipper|name=Flipper}}

===Forum threads===
{{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
{{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
{{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}

__NOTOC__

Oscillator

2022-01-13T12:09:11Z

Freywa: Jason's p156 no longer SKOP156 (all 6n periods need to be checked now!)

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period).

[[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
| rowspan="500" style="border: none;" |
! Smallest known
! Minimum # of cells
|-
! {{period|2|brief}}
| [[blinker]]
|[[John Conway]]
| {{year|1970}}
| [[blinker]]
| {{cells|3}}
|-
! {{period|3|brief}}
| [[pulsar]]
|John Conway
| 1970
| [[caterer]]
| {{cells|12}}
|-
! {{period|4|brief}}
| [[pinwheel]]
|[[Simon Norton]]
| 1970
| [[mazing]], [[mold]]
| {{cells|12}}
|-
! {{period|5|brief}}
| [[octagon 2]]
|[[Sol Goodman]], [[Arthur Taber]]
| {{year|1971}}
| [[pseudo-barberpole]]
| {{cells|15}}
|-
! {{period|6|brief}}
| [[$rats]]
|[[David Buckingham]]
| {{year|1972}}
| [[unix]]
| {{cells|16}}
|-
! {{period|7|brief}}
| [[burloaferimeter]]
|David Buckingham
| 1972
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
| {{cells|28}}
|-
! {{period|8|brief}}
| [[figure eight]]
|Simon Norton
| 1970
| [[figure eight]]
| {{cells|12}}
|-
! {{period|9|brief}}
| [[worker bee]]
|David Buckingham
| 1972
| [[29P9]]
| {{cells|29}}
|-
! {{period|10|brief}}
| [[42P10.3]]
|David Buckingham
| ≤{{year|1976}}
| [[24P10]]
| {{cells|24}}
|-
! {{period|11|brief}}
| [[38P11.1]]
|David Buckingham
| {{year|1977}}
| [[rattlesnake]]
| {{cells|33}}
|-
! {{period|12|brief}}
| [[dinner table]]
|[[Robert Wainwright]]
| {{year|1972}}
| [[dinner table]]
| {{cells|33}}
|-
! {{period|13|brief}}
| [[Buckingham's p13]]
|David Buckingham
| 1976
| [[Beluchenko's p13]]
| {{cells|34}}
|-
! {{period|14|brief}}
| [[tumbler]]
|[[George Collins]]
| 1970
| [[tumbler]]
| {{cells|16}}
|-
! {{period|15|brief}}
| [[pentadecathlon]]
|John Conway
| 1970
| [[pentadecathlon]]
| {{cells|12}}
|-
! {{period|16|brief}}
| [[two pre-L hasslers]]
|Robert Wainwright
| {{year|1983}}
| [[Rob's p16]]
| {{cells|21}}
|-
! {{period|17|brief}}
| [[54P17.1]]
|[[Dean Hickerson]]
| {{year|1997}}
| [[honey thieves]]
| {{cells|36}}
|-
! {{period|18|brief}}
| [[117P18]]{{refn|group=note|name=lcm|An oscillator of this period can also be constructed from two [[sparker]]s both of which were known by an earlier date. However, [[LCM oscillator]]s are generally considered "[[boring]]", and thus not listed here despite technically being [[non-trivial]].}}
|David Buckingham
| ≤{{year|1991}}
| [[p18 bi-block hassler]], [[p18 phase shifter]]
| {{cells|43}}
|-
! class="red_td" | 19
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|20|brief}}
| [[145P20]]{{refn|group=note|name=lcm}}
|[[Noam Elkies]]
| {{year|1995}}
| [[mold on fumarole]]
| {{cells|30}}
|-
! {{period|21|brief}}
| [[124P21]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1995
| [[caterer on 28P7.3]]
| {{cells|40}}
|-
! {{period|22|brief}}
| [[168P22.1]]
|Noam Elkies
| 1997
| [[Jason's p22]]
| {{cells|36}}
|-
! {{period|23|brief}}
| [[David Hilbert]]
|[[Luka Okanishi]], [[praosylen]]
| {{year|2019}}
| [[David Hilbert]]
| {{cells|122}}
|-
! {{period|24|brief}}
| [[186P24]]{{refn|group=note|name=lcm}}
|[[Bill Gosper]]
| {{year|1994}}
| [[caterer on figure eight]]
| {{cells|24}}
|-
! {{period|25|brief}}
| [[134P25]]
|Noam Elkies
| 1994
| [[p25 pre-pulsar shuttle]]
| {{cells|83}}
|-
! {{period|26|brief}}
| [[p26 pre-pulsar shuttle]]
|David Buckingham
| 1983
| [[87P26]]
| {{cells|87}}
|-
! {{period|27|brief}}
| [[123P27.1]]
|Noam Elkies
| {{year|2002}}
| [[56P27]]
| {{cells|56}}
|-
! {{period|28|brief}}
| [[newshuttle]]
|David Buckingham
| {{year|1973}}
| [[mold on 34P14 shuttle]]
| {{cells|46}}
|-
! {{period|29|brief}}
| [[p29 pre-pulsar shuttle]]
|David Buckingham
| {{year|1980}}
| [[p29 pre-pulsar shuttle]]
| {{cells|54}}
|-
! {{period|30|brief}}
| [[queen bee shuttle]]
|Bill Gosper
| 1970
| [[queen bee shuttle]]
| {{cells|20}}
|-
! {{period|31|brief}}
| [[Merzenich's p31]]
|[[Matthias Merzenich]]
| {{year|2010}}
| [[Merzenich's p31]]
| {{cells|48}}
|-
! {{period|32|brief}}
| [[gourmet]]
|David Buckingham
| {{year|1978}}
| [[p32 honey farm hassler]]
| {{cells|45}}
|-
! {{period|33|brief}}
| [[258P3 on Achim's p11]]
|Noam Elkies, [[Achim Flammenkamp]]
| 1997
| [[caterer on rattlesnake]]
| {{cells|46}}
|-
! {{period|34|brief}}
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''No non-trivial examples found''
|-
! {{period|35|brief}}
| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
|Dean Hickerson
| 1995
| [[p35 honey farm hassler]]
| {{cells|44}}
|-
! {{period|36|brief}}
| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1984
| [[22P36]]
| {{cells|22}}
|-
! {{period|37|brief}}
| [[Beluchenko's p37]]
|[[Nicolay Beluchenko]]
| {{year|2009}}
| [[Beluchenko's p37]]
| {{cells|124}}
|-
! {{period|38|brief}}
| [[strontium]]
|[[David Raucci]]
| {{year|2022}}
| [[strontium]]
| {{cells|44}}
|-
! {{period|39|brief}}
| [[134P39.1]]
|David Buckingham, Noam Elkies
| {{year|2000}}
| [[caterer on Beluchenko's p13]]
|{{cells|46}}
|-
! {{period|40|brief}}
| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| 1991
| [[Beluchenko's p40]]
| {{cells|26}}
|-
! class="red_td" | 41
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|42|brief}}
| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
|Noam Elkies
| 1994
| [[unix on 34P14 shuttle]]
| {{cells|50}}
|-
! {{period|43|brief}}
| [[p43 Snark loop]]
|[[Mike Playle]]
| {{year|2013}}
| [[p43 Snark loop]]
|{{cells|228}}
|-
! {{period|44|brief}}
| [[p44 pi-heptomino hassler]]
|David Buckingham
| 1992
| [[mold on rattlesnake]]
| {{cells|45}}
|-
! {{period|45|brief}}
| [[pentadecathlon on snacker]]
| [[Mark Niemiec]], John Conway
| ≤1995
| [[pentadecathlon on thumb 1]]
| {{cells|48}}
|-
! {{period|46|brief}}
| [[twin bees shuttle]]
|Bill Gosper
| 1971
| [[twin bees shuttle]]
| {{cells|28}}
|-
! {{period|47|brief}}
| [[p47 pre-pulsar shuttle]]
|David Buckingham
| {{year|1982}}
| [[p47 pre-pulsar shuttle]]
| {{cells|84}}
|-
! {{period|48|brief}}
| [[p48 toad hassler]]
|Bill Gosper
| 1994
| [[unix on Rich's p16]]
| {{cells|52}}
|-
! {{period|49|brief}}
| [[p49 glider shuttle]]
|Noam Elkies
| {{year|1999}}
| [[p49 bumper loop]]
| {{cells|206}}
|-
! {{period|50|brief}}
| [[p50 glider shuttle]]
|Dean Hickerson
| 1992
| [[p50 traffic jam]]
| {{cells|92}}
|-
! {{period|51|brief}}
| [[Beluchenko's p51]]
|Nicolay Beluchenko
| 2009
| [[90P51]]
| {{cells|90}}
|-
! {{period|52|brief}}
| [[Four eaters hassling lumps of muck]]
|David Buckingham
| 1977
| [[four eaters hassling lumps of muck]]
| {{cells|35}}
|-
! {{period|53|brief}}
| [[p53 Snark loop]]
|Mike Playle
| {{year|2013}}
| [[p53 Snark loop]]
|{{cells|228}}
|-
! {{period|54|brief}}
| [[p54 shuttle]]
|David Buckingham
| {{year|1973}}
| [[p54 shuttle]]
| {{cells|48}}
|-
! {{period|55|brief}}
| [[p55 pre-pulsar hassler]]
|David Buckingham
| {{year|1986}}
| [[pseudo-barberpole on rattlesnake]]
| {{cells|49}}
|-
! {{period|56|brief}}
| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| ≤1991
| [[p56 B-heptomino shuttle]]
| {{cells|45}}
|-
! {{period|57|brief}}
| [[p57 Herschel loop 1]]
|[[Dietrich Leithner]]
| 1997
| [[p57 bumper loop]]
|{{cells|152}}
|-
! {{period|58|brief}}
| [[p58 toadsucker]]
|Bill Gosper
| 1994
| [[p58 pre-pulsar shuttle]]
| {{cells|104}}
|-
! {{period|59|brief}}
| [[p59 Herschel loop 1]]
|David Buckingham
| 1997
| [[Adjustable glider loop|p59 Snark loop]]
|{{cells|228}}
|-
! {{period|60|brief}}
| [[p60 glider shuttle]]
|David Buckingham
| ≤ 1971
| [[mold on pentadecathlon]]
| {{cells|24}}
|-
! {{period|61|brief}}
| [[p61 Herschel loop 1]]
|David Buckingham
| {{year|1996}}
| [[Adjustable glider loop|p61 Snark loop]]
|{{cells|228}}
|-
! {{period|62|brief}}
| ?
| ?
| ?
| [[66P62]]
| {{cells|66}}
|-
! {{period|63|brief}}
| ?
| ?
| ?
| [[snacker on 38P7.2]]
| {{cells|78}}
|-
! {{period|64|brief}}
| ?
| ?
| ?
| [[Merzenich's p64]]
| {{cells|34}}
|-
! {{period|65|brief}}
| ?
| ?
| ?
| [[fumarole on Beluchenko's p13]]
| {{cells|52}}
|-
! {{period|66|brief}}
| ?
| ?
| ?
| [[caterer on Jason's p22]]
| {{cells|48}}
|-
! {{period|67|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p67 Snark loop]]
|{{cells|228}}
|-
! {{period|68|brief}}
| ?
| ?
| ?
| [[72P68]]
|{{cells|72}}
|-
! {{period|69|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p69 bumper loop]]
|{{cells|152}}
|-
! {{period|70|brief}}
| ?
| ?
| ?
| [[fumarole on 34P14 shuttle]]
| {{cells|52}}
|-
! {{period|71|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p71 Snark loop]]
|{{cells|228}}
|-
! {{period|72|brief}}
| [[two blockers hassling R-pentomino]]
|Robert Wainwright
| 1990
| [[figure eight on 22P36]]
| {{cells|36}}
|-
! {{period|73|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p73 Snark loop]]
|{{cells|228}}
|-
! {{period|74|brief}}
| p74 Herschel loop
|David Buckingham
| 1996
| [[Raucci's p74]]
| {{cells|84}}
|-
! {{period|75|brief}}
| ?
| ?
| ?
| [[6 bits]]
|{{cells|49}}
|-
! {{period|76|brief}}
| ?
| ?
| ?
| [[mold on strontium]]
| {{cells|56}}
|-
! {{period|77|brief}}
| ?
| ?
| ?
| [[77P77]]
|{{cells|77}}
|-
! {{period|78|brief}}
| ?
| ?
| ?
| [[p6 thumb on Beluchenko's p13]]
|{{cells|61}}
|-
! {{period|79|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p79 Snark loop]]
|{{cells|228}}
|-
! {{period|80|brief}}
| ?
| ?
| ?
| [[fumarole on Rob's p16]]
| {{cells|39}}
|-
! {{period|81|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p81 bumper loop]]
|{{cells|152}}
|-
! {{period|82|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p82 Snark loop]]
|{{cells|208}}
|-
! {{period|83|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p83 Snark loop]]
|{{cells|228}}
|-
! {{period|84|brief}}
| ?
| ?
| ?
| [[52P84]]
| {{cells|52}}
|-
! {{period|85|brief}}
| ?
| ?
| ?
| [[74P85]]
|{{cells|74}}
|-
! {{period|86|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p86 Snark loop]]
|{{cells|208}}
|-
! {{period|87|brief}}
| ?
| ?
| ?
| [[84P87]]
| {{cells|84}}
|-
! {{period|88|brief}}
| p88 glider loop
|David Buckingham
| 1992
| [[figure eight on rattlesnake]]
| {{cells|45}}
|-
! {{period|89|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p89 Snark loop]]
|{{cells|228}}
|-
! {{period|90|brief}}
| ?
| ?
| ?
| [[thumb 1 on queen bee shuttle]]
| {{cells|56}}
|-
! {{period|91|brief}}
| ?
| ?
| ?
| [[44P7 on Beluchenko's p13]]
|{{cells|78}}
|-
! {{period|92|brief}}
| ?
| ?
| ?
| [[50P92.1]], [[twin bees shuttle on 22P4.3]]
| {{cells|50}}
|-
! {{period|93|brief}}
| ?
| ?
| ?
| [[caterer on Merzenich's p31]]
|{{cells|60}}
|-
! {{period|94|brief}}
| capped [[AK-47 reaction|AK-47]] gun
|Dean Hickerson
| 1990
| {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]]
| {{cells|110}}
|-
! {{period|95|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p95 Snark loop]]
|{{cells|228}}
|-
! {{period|96|brief}}
| ?
| ?
| ?
| [[period-48 glider gun]] {{LinkCatagolue|xp96_0178cy766zy44koy6m640ooe4a4z0gs26x11xoy1oo022440ezo8go|patternname=with boat-bit|style=raw}}
| {{cells|59}}
|-
! {{period|97|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p97 Snark loop]]
|{{cells|228}}
|-
! {{period|98|brief}}
| ?
| ?
| ?
| [[Gallus]]
| {{cells|105}}
|-
! {{period|99|brief}}
| ?
| ?
| ?
| [[48P9 on rattlesnake]]
|{{cells|82}}
|-
! {{period|100|brief}}
| [[centinal]]
|Bill Gosper
| ≤{{year|1987}}
| [[centinal]]
| {{cells|70}}
|-
! {{period|101|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p101 Snark loop]]
|{{cells|228}}
|-
! {{period|102|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp102_yzy2ca230oomewcczyzx33y3cczzyu42ey3o4ozyygs26x1zyzy3ca8zzzy54kczycoge2zy7696y3sg8zzy1ccy3ggzccwsq660ggkc011zy51|patternname=p102 unix loop|style=raw}}
| {{cells|96}}
|-
! {{period|103|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p103 Snark loop]]
|{{cells|228}}
|-
! {{period|104|brief}}
| ?
| ?
| ?
| [[figure eight on Beluchenko's p13]]
| {{cells|46}}
|-
! {{period|105|brief}}
| ?
| ?
| ?
| [[pentadecathlon on 37P7.1]]
|{{cells|49}}
|-
! {{period|106|brief}}
| ?
| ?
| ?
| [[rectifier|p106 rectifier loop]]
|{{cells|169}}
|-
! {{period|107|brief}}
| ?
| ?
| ?
| [[rectifier|p107 rectifier loop]]
|{{cells|136}}
|-
! {{period|108|brief}}
| ?
| ?
| ?
| [[22P4.3 on 56P27]]
|{{cells|78}}
|-
! {{period|109|brief}}
| ?
| ?
| ?
| [[rectifier|p109 rectifier loop]]
|{{cells|156}}
|-
! {{period|110|brief}}
| [[p110 traffic jam]]
|Bill Gosper
| 1994
| [[pseudo-barberpole on Jason's p22]]
|{{cells|51}}
|-
! {{period|111|brief}}
| ?
| ?
| ?
| [[rectifier|p111 rectifier loop]]
|{{cells|136}}
|-
! {{period|112|brief}}
| ?
| ?
| ?
| [[tumbler on Rich's p16]]
|{{cells|50}}
|-
! {{period|113|brief}}
| ?
| ?
| ?
| [[nihonium]]
| {{cells|106}}
|-
! {{period|114|brief}}
| ?
| ?
| ?
| [[caterer on strontium]]
|{{cells|57}}
|-
! {{period|115|brief}}
| ?
| ?
| ?
| [[rectifier|p115 rectifier loop]]
|{{cells|136}}
|-
! {{period|116|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=102P116|style=raw}}
|{{cells|102}}
|-
! {{period|117|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp117_y1o44mhar0rahm44ozwg8p7870167876107871zq6hcbagy1szg9gf99gfy26a8oz56o3t5zx1|patternname=117P117|style=raw}}
| {{cells|117}}
|-
! {{period|118|brief}}
| ?
| ?
| ?
| [[rectifier|p118 rectifier loop]]
|{{cells|154}}
|-
! {{period|119|brief}}
| ?
| ?
| ?
| [[rectifier|p119 rectifier loop]]
|{{cells|136}}
|-
! {{period|120|brief}}
| ?
| ?
| ?
| [[figure eight on pentadecathlon]]
| {{cells|24}}
|-
! {{period|121|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|122|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|123|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|124|brief}}
| [[p124 lumps of muck hassler]]
|Dean Hickerson
| 1994
| [[mold on Merzenich's p31]]
| {{cells|60}}
|-
! {{period|125|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|126|brief}}
| ?
| ?
| ?
| [[snacker on 34P14 shuttle]]
| {{cells|74}}
|-
! {{period|127|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|128|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp128_y3ca73oswcczyqg88gzy1ggyh6bbcxca4z8ko010onmcy04eewuscy26dt30g0352z4a6x6qqcyh11zy01221zyh66w73osa6|patternname=p128 wing hassler|style=raw}}
|{{cells|108}}
|-
! {{period|129|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p129 bumper loop]]
|{{cells|152}}
|-
! {{period|130|brief}}
| ?
| ?
| ?
| [[55P10 on Beluchenko's p13]]
| {{cells|89}}
|-
! {{period|131|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|132|brief}}
| p132 glider loop
|David Buckingham
| 1992
| [[mold on Jason's p33]]
| {{cells|72}}
|-
! {{period|133|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|134|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|135|brief}}
| [[106P135]]
|Bill Gosper
| {{year|1989}}
| [[pentadecathlon on 56P27]]
|{{cells|68}}
|-
! {{period|136|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|137|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|138|brief}}
| ?
| ?
| ?
| [[Gabriel's p138]]
| {{cells|36}}
|-
! {{period|139|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|140|brief}}
| p140 traffic jam
|Bill Gosper
| 1994
| [[34P14 shuttle on dockyard]]
| {{cells|82}}
|-
! {{period|141|brief}}
| ?
| ?
| ?
| [[p47 pre-pulsar shuttle phase-shifting 28P7.1]]
| {{cells|114}}
|-
! {{period|142|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|143|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|144|brief}}
| capped p144 [[gunstar]]
|David Buckingham
| 1990
| [[Achim's p144]]
| {{cells|42}}
|-
! {{period|150|brief}}
| ?
| ?
| ?
| [[buckaroo|p150 buckaroo shuttle]]
| {{cells|51}}
|-
! {{period|152|brief}}
| ?
| ?
| ?
| [[figure eight on strontium]]
| {{cells|60}}
|-
! {{period|156|brief}}
| p156 [[traffic jam]] oscillator
|Bill Gosper
| 1994
| {{LinkCatagolue|xp156_ccc4ak8g032aczy1efy2gcgzy933zy7o4ozy81x62sgzzymggzyn346wg8gzys121zyqgcszyr3y2gfnzyt354cw1252333|patternname=p156 unix loop|style=raw}}
| {{cells|86}}
|-
! {{period|165|brief}}
| ?
| ?
| ?
| [[rattlesnake on pentadecathlon]]
| {{cells|45}}
|-
! {{period|168|brief}}
| ?
| ?
| ?
| [[figure eight on p21 honey farm hassler]]
| {{cells|72}}
|-
! {{period|177|brief}}
| ?
| ?
| ?
| [[Karel's p177]]
| {{cells|104}}
|-
! {{period|184|brief}}
| ?
| ?
| ?
| [[figure eight on twin bees shuttle]]
| {{cells|40}}
|-
! {{period|186|brief}}
| ?
| ?
| ?
| [[unix on Merzenich's p31]]
| {{cells|64}}
|-
! {{period|188|brief}}
| ?
| ?
| ?
| [[AK-94]] {{LinkCatagolue|xp188_x696o8b9czy065x33xc871wbdzoozwgg04ahhha4y5c871z4701yfoozxggy0ggzx56w4701xmmggo5jzya146w343|patternname=with boat-bits|style=raw}}
| {{cells|108}}
|-
! {{period|196|brief}}
| ?
| ?
| ?
| [[p196 pi-heptomino hassler]]
| {{cells|66}}
|-
! {{period|200|brief}}
| p200 glider loop
|Bill Gosper
| ≤{{year|1987}}
| [[figure eight on centinal]]
|{{cells|82}}
|-
! {{period|226|brief}}
| ?
| ?
| ?
| [[nihonium*]]
| {{cells|107}}
|-
! {{period|230|brief}}
| ?
| ?
| ?
| [[fumarole on twin bees shuttle]]
|{{cells|46}}
|-
! {{period|232|brief}}
| ?
| ?
| ?
| [[figure eight on p29 pre-pulsar shuttle]]
|{{cells|66}}
|-
! {{period|240|brief}}
| ?
| ?
| ?
| [[pentadecathlon on Rob's p16]]
| {{cells|33}}
|-
! {{period|246|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp246_ya32acydg8k8ooozyu1utzzzybcirrd6y4cc4zy1ggy61zggwg9g89z14w61ye354c|patternname=relative|style=raw}}
| {{cells|68}}
|-
! {{period|256|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp256_yr33y166z0ggy033y4178cyb33y0ccz011w66z66yyg88czy4699voyn11zy38ox61zy1311yz66zyzx66woozy133y0ccyb31e8y4cczy566y1cc|patternname=capped|style=raw}} [[period-256 glider gun]]
| {{cells|104}}
|-
! {{period|276|brief}}
| ?
| ?
| ?
| [[caterer on 50P92.1]]
| {{cells|62}}
|-
! {{period|300|brief}}
| ?
| ?
| ?
| [[pentadecathlon on centinal]]
| {{cells|88}}
|-
! {{period|312|brief}}
| ?
| ?
| ?
| [[60P312]]
| {{cells|60}}
|-
! {{period|320|brief}}
| ?
| ?
| ?
| [[fumarole on Merzenich's p64]]
| {{cells|52}}
|-
! {{period|360|brief}}
| ?
| ?
| ?
| [[thumb 1 on Beluchenko's p40]]
| {{cells|62}}
|-
! {{period|368|brief}}
| ?
| ?
| ?
| [[period-184 glider gun]] {{LinkCatagolue|xp368_y0gy632aczy01156zzggyp62sgz56yc65134w16zync4ozy8o8goy911|patternname=with boat-bits|style=raw}}
| {{cells|50}}
|-
! {{period|460|brief}}
| ?
| ?
| ?
| [[pseudo-barberpole on 50P92.1]]
| {{cells|65}}
|-
! {{period|492|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp492_y0o4qa344ozx118f0dc3z8oyago0ab2sycc871z0123y9126e431zy8ooz0mqzyt66w7bcczyy66|patternname=with boat-bit|style=raw}}
| {{cells|87}}
|-
! {{period|496|brief}}
| ?
| ?
| ?
| [[Rob's p16 on Merzenich's p31]]
| {{cells|69}}
|-
! {{period|504|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp504_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzyzygg88gxooy1uu06666mmzyzygcc07xccy1rroooo0vvzyzyh66|patternname=p504 glider shuttle|style=raw}}
| {{cells|109}}
|-
! {{period|512|brief}}
| ?
| ?
| ?
| [[period-256 glider gun]] {{LinkCatagolue|xp512_yr33y166z0ggy033y16426ye33y0ccz011w66yuggz66yz56zzzy2mqyz66zygckgk2a21ya66woozy133y0ccye6426y1cczy566y1cc|patternname=with boat-bits|style=raw}}
| {{cells|100}}
|-
! {{period|856|brief}}
| [[period-856 glider gun]]
| [[David Buckingham]]
| 1991
| {{LinkCatagolue|xp856_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzzzzzzzzzzyzyzyl844oxccy1vv03333rrzyzyzyl6603x66y1ddcccc0ffzyzyzym33|patternname=p856 glider shuttle|style=raw}}
|{{cells|109}}
|}

==Flipper==
A '''flipper''' is any [[oscillator]] that forms its mirror image halfway through its [[period]].

==Notes==
<references group=note />

==See also==
*[[List of common oscillators]]
*[[:Category:Flipping oscillators|List of flipping oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
*[[Table of oscillators by period]]
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]

==External links==
{{LinkWikipedia|Oscillator_(cellular_automaton)}}
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkLexicon|lex_f.htm#flipper|name=Flipper}}

===Forum threads===
{{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
{{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
{{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}

__NOTOC__

Oscillator

2022-01-12T20:57:04Z

Freywa:

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period).

[[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
| rowspan="500" style="border: none;" |
! Smallest known
! Minimum # of cells
|-
! {{period|2|brief}}
| [[blinker]]
|[[John Conway]]
| {{year|1970}}
| [[blinker]]
| {{cells|3}}
|-
! {{period|3|brief}}
| [[pulsar]]
|John Conway
| 1970
| [[caterer]]
| {{cells|12}}
|-
! {{period|4|brief}}
| [[pinwheel]]
|[[Simon Norton]]
| 1970
| [[mazing]], [[mold]]
| {{cells|12}}
|-
! {{period|5|brief}}
| [[octagon 2]]
|[[Sol Goodman]], [[Arthur Taber]]
| {{year|1971}}
| [[pseudo-barberpole]]
| {{cells|15}}
|-
! {{period|6|brief}}
| [[$rats]]
|[[David Buckingham]]
| {{year|1972}}
| [[unix]]
| {{cells|16}}
|-
! {{period|7|brief}}
| [[burloaferimeter]]
|David Buckingham
| 1972
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
| {{cells|28}}
|-
! {{period|8|brief}}
| [[figure eight]]
|Simon Norton
| 1970
| [[figure eight]]
| {{cells|12}}
|-
! {{period|9|brief}}
| [[worker bee]]
|David Buckingham
| 1972
| [[29P9]]
| {{cells|29}}
|-
! {{period|10|brief}}
| [[42P10.3]]
|David Buckingham
| ≤{{year|1976}}
| [[24P10]]
| {{cells|24}}
|-
! {{period|11|brief}}
| [[38P11.1]]
|David Buckingham
| {{year|1977}}
| [[rattlesnake]]
| {{cells|33}}
|-
! {{period|12|brief}}
| [[dinner table]]
|[[Robert Wainwright]]
| {{year|1972}}
| [[dinner table]]
| {{cells|33}}
|-
! {{period|13|brief}}
| [[Buckingham's p13]]
|David Buckingham
| 1976
| [[Beluchenko's p13]]
| {{cells|34}}
|-
! {{period|14|brief}}
| [[tumbler]]
|[[George Collins]]
| 1970
| [[tumbler]]
| {{cells|16}}
|-
! {{period|15|brief}}
| [[pentadecathlon]]
|John Conway
| 1970
| [[pentadecathlon]]
| {{cells|12}}
|-
! {{period|16|brief}}
| [[two pre-L hasslers]]
|Robert Wainwright
| {{year|1983}}
| [[Rob's p16]]
| {{cells|21}}
|-
! {{period|17|brief}}
| [[54P17.1]]
|[[Dean Hickerson]]
| {{year|1997}}
| [[honey thieves]]
| {{cells|36}}
|-
! {{period|18|brief}}
| [[117P18]]{{refn|group=note|name=lcm|An oscillator of this period can also be constructed from two [[sparker]]s both of which were known by an earlier date. However, [[LCM oscillator]]s are generally considered "[[boring]]", and thus not listed here despite technically being [[non-trivial]].}}
|David Buckingham
| ≤{{year|1991}}
| [[p18 bi-block hassler]], [[p18 phase shifter]]
| {{cells|43}}
|-
! class="red_td" | 19
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|20|brief}}
| [[145P20]]{{refn|group=note|name=lcm}}
|[[Noam Elkies]]
| {{year|1995}}
| [[mold on fumarole]]
| {{cells|30}}
|-
! {{period|21|brief}}
| [[124P21]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1995
| [[caterer on 28P7.3]]
| {{cells|40}}
|-
! {{period|22|brief}}
| [[168P22.1]]
|Noam Elkies
| 1997
| [[Jason's p22]]
| {{cells|36}}
|-
! {{period|23|brief}}
| [[David Hilbert]]
|[[Luka Okanishi]], [[praosylen]]
| {{year|2019}}
| [[David Hilbert]]
| {{cells|122}}
|-
! {{period|24|brief}}
| [[186P24]]{{refn|group=note|name=lcm}}
|[[Bill Gosper]]
| {{year|1994}}
| [[caterer on figure eight]]
| {{cells|24}}
|-
! {{period|25|brief}}
| [[134P25]]
|Noam Elkies
| 1994
| [[p25 pre-pulsar shuttle]]
| {{cells|83}}
|-
! {{period|26|brief}}
| [[p26 pre-pulsar shuttle]]
|David Buckingham
| 1983
| [[87P26]]
| {{cells|87}}
|-
! {{period|27|brief}}
| [[123P27.1]]
|Noam Elkies
| {{year|2002}}
| [[56P27]]
| {{cells|56}}
|-
! {{period|28|brief}}
| [[newshuttle]]
|David Buckingham
| {{year|1973}}
| [[mold on 34P14 shuttle]]
| {{cells|46}}
|-
! {{period|29|brief}}
| [[p29 pre-pulsar shuttle]]
|David Buckingham
| {{year|1980}}
| [[p29 pre-pulsar shuttle]]
| {{cells|54}}
|-
! {{period|30|brief}}
| [[queen bee shuttle]]
|Bill Gosper
| 1970
| [[queen bee shuttle]]
| {{cells|20}}
|-
! {{period|31|brief}}
| [[Merzenich's p31]]
|[[Matthias Merzenich]]
| {{year|2010}}
| [[Merzenich's p31]]
| {{cells|48}}
|-
! {{period|32|brief}}
| [[gourmet]]
|David Buckingham
| {{year|1978}}
| [[p32 honey farm hassler]]
| {{cells|45}}
|-
! {{period|33|brief}}
| [[258P3 on Achim's p11]]
|Noam Elkies, [[Achim Flammenkamp]]
| 1997
| [[caterer on rattlesnake]]
| {{cells|46}}
|-
! {{period|34|brief}}
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''No non-trivial examples found''
|-
! {{period|35|brief}}
| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
|Dean Hickerson
| 1995
| [[p35 honey farm hassler]]
| {{cells|44}}
|-
! {{period|36|brief}}
| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1984
| [[22P36]]
| {{cells|22}}
|-
! {{period|37|brief}}
| [[Beluchenko's p37]]
|[[Nicolay Beluchenko]]
| {{year|2009}}
| [[Beluchenko's p37]]
| {{cells|124}}
|-
! {{period|38|brief}}
| [[strontium]]
|[[David Raucci]]
| {{year|2022}}
| [[strontium]]
| {{cells|44}}
|-
! {{period|39|brief}}
| [[134P39.1]]
|David Buckingham, Noam Elkies
| {{year|2000}}
| [[caterer on Beluchenko's p13]]
|{{cells|46}}
|-
! {{period|40|brief}}
| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| 1991
| [[Beluchenko's p40]]
| {{cells|26}}
|-
! class="red_td" | 41
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|42|brief}}
| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
|Noam Elkies
| 1994
| [[unix on 34P14 shuttle]]
| {{cells|50}}
|-
! {{period|43|brief}}
| [[p43 Snark loop]]
|[[Mike Playle]]
| {{year|2013}}
| [[p43 Snark loop]]
|{{cells|228}}
|-
! {{period|44|brief}}
| [[p44 pi-heptomino hassler]]
|David Buckingham
| 1992
| [[mold on rattlesnake]]
| {{cells|45}}
|-
! {{period|45|brief}}
| [[pentadecathlon on snacker]]
| [[Mark Niemiec]], John Conway
| ≤1995
| [[pentadecathlon on thumb 1]]
| {{cells|48}}
|-
! {{period|46|brief}}
| [[twin bees shuttle]]
|Bill Gosper
| 1971
| [[twin bees shuttle]]
| {{cells|28}}
|-
! {{period|47|brief}}
| [[p47 pre-pulsar shuttle]]
|David Buckingham
| {{year|1982}}
| [[p47 pre-pulsar shuttle]]
| {{cells|84}}
|-
! {{period|48|brief}}
| [[p48 toad hassler]]
|Bill Gosper
| 1994
| [[unix on Rich's p16]]
| {{cells|52}}
|-
! {{period|49|brief}}
| [[p49 glider shuttle]]
|Noam Elkies
| {{year|1999}}
| [[p49 bumper loop]]
| {{cells|206}}
|-
! {{period|50|brief}}
| [[p50 glider shuttle]]
|Dean Hickerson
| 1992
| [[p50 traffic jam]]
| {{cells|92}}
|-
! {{period|51|brief}}
| [[Beluchenko's p51]]
|Nicolay Beluchenko
| 2009
| [[90P51]]
| {{cells|90}}
|-
! {{period|52|brief}}
| [[Four eaters hassling lumps of muck]]
|David Buckingham
| 1977
| [[four eaters hassling lumps of muck]]
| {{cells|35}}
|-
! {{period|53|brief}}
| [[p53 Snark loop]]
|Mike Playle
| {{year|2013}}
| [[p53 Snark loop]]
|{{cells|228}}
|-
! {{period|54|brief}}
| [[p54 shuttle]]
|David Buckingham
| {{year|1973}}
| [[p54 shuttle]]
| {{cells|48}}
|-
! {{period|55|brief}}
| [[p55 pre-pulsar hassler]]
|David Buckingham
| {{year|1986}}
| [[pseudo-barberpole on rattlesnake]]
| {{cells|49}}
|-
! {{period|56|brief}}
| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| ≤1991
| [[p56 B-heptomino shuttle]]
| {{cells|45}}
|-
! {{period|57|brief}}
| [[p57 Herschel loop 1]]
|[[Dietrich Leithner]]
| 1997
| [[p57 bumper loop]]
|{{cells|152}}
|-
! {{period|58|brief}}
| [[p58 toadsucker]]
|Bill Gosper
| 1994
| [[p58 pre-pulsar shuttle]]
| {{cells|104}}
|-
! {{period|59|brief}}
| [[p59 Herschel loop 1]]
|David Buckingham
| 1997
| [[Adjustable glider loop|p59 Snark loop]]
|{{cells|228}}
|-
! {{period|60|brief}}
| [[p60 glider shuttle]]
|David Buckingham
| ≤ 1971
| [[mold on pentadecathlon]]
| {{cells|24}}
|-
! {{period|61|brief}}
| [[p61 Herschel loop 1]]
|David Buckingham
| {{year|1996}}
| [[Adjustable glider loop|p61 Snark loop]]
|{{cells|228}}
|-
! {{period|62|brief}}
| ?
| ?
| ?
| [[66P62]]
| {{cells|66}}
|-
! {{period|63|brief}}
| ?
| ?
| ?
| [[snacker on 38P7.2]]
| {{cells|78}}
|-
! {{period|64|brief}}
| ?
| ?
| ?
| [[Merzenich's p64]]
| {{cells|34}}
|-
! {{period|65|brief}}
| ?
| ?
| ?
| [[fumarole on Beluchenko's p13]]
| {{cells|52}}
|-
! {{period|66|brief}}
| ?
| ?
| ?
| [[caterer on Jason's p22]]
| {{cells|48}}
|-
! {{period|67|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p67 Snark loop]]
|{{cells|228}}
|-
! {{period|68|brief}}
| ?
| ?
| ?
| [[72P68]]
|{{cells|72}}
|-
! {{period|69|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p69 bumper loop]]
|{{cells|152}}
|-
! {{period|70|brief}}
| ?
| ?
| ?
| [[fumarole on 34P14 shuttle]]
| {{cells|52}}
|-
! {{period|71|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p71 Snark loop]]
|{{cells|228}}
|-
! {{period|72|brief}}
| [[two blockers hassling R-pentomino]]
|Robert Wainwright
| 1990
| [[figure eight on 22P36]]
| {{cells|36}}
|-
! {{period|73|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p73 Snark loop]]
|{{cells|228}}
|-
! {{period|74|brief}}
| p74 Herschel loop
|David Buckingham
| 1996
| [[Raucci's p74]]
| {{cells|84}}
|-
! {{period|75|brief}}
| ?
| ?
| ?
| [[6 bits]]
|{{cells|49}}
|-
! {{period|76|brief}}
| ?
| ?
| ?
| [[mold on strontium]]
| {{cells|56}}
|-
! {{period|77|brief}}
| ?
| ?
| ?
| [[77P77]]
|{{cells|77}}
|-
! {{period|78|brief}}
| ?
| ?
| ?
| [[p6 thumb on Beluchenko's p13]]
|{{cells|61}}
|-
! {{period|79|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p79 Snark loop]]
|{{cells|228}}
|-
! {{period|80|brief}}
| ?
| ?
| ?
| [[fumarole on Rob's p16]]
| {{cells|39}}
|-
! {{period|81|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p81 bumper loop]]
|{{cells|152}}
|-
! {{period|82|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p82 Snark loop]]
|{{cells|208}}
|-
! {{period|83|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p83 Snark loop]]
|{{cells|228}}
|-
! {{period|84|brief}}
| ?
| ?
| ?
| [[52P84]]
| {{cells|52}}
|-
! {{period|85|brief}}
| ?
| ?
| ?
| [[74P85]]
|{{cells|74}}
|-
! {{period|86|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p86 Snark loop]]
|{{cells|208}}
|-
! {{period|87|brief}}
| ?
| ?
| ?
| [[84P87]]
| {{cells|84}}
|-
! {{period|88|brief}}
| p88 glider loop
|David Buckingham
| 1992
| [[figure eight on rattlesnake]]
| {{cells|45}}
|-
! {{period|89|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p89 Snark loop]]
|{{cells|228}}
|-
! {{period|90|brief}}
| ?
| ?
| ?
| [[thumb 1 on queen bee shuttle]]
| {{cells|56}}
|-
! {{period|91|brief}}
| ?
| ?
| ?
| [[44P7 on Beluchenko's p13]]
|{{cells|78}}
|-
! {{period|92|brief}}
| ?
| ?
| ?
| [[50P92.1]], [[twin bees shuttle on 22P4.3]]
| {{cells|50}}
|-
! {{period|93|brief}}
| ?
| ?
| ?
| [[caterer on Merzenich's p31]]
|{{cells|60}}
|-
! {{period|94|brief}}
| capped [[AK-47 reaction|AK-47]] gun
|Dean Hickerson
| 1990
| {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]]
| {{cells|110}}
|-
! {{period|95|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p95 Snark loop]]
|{{cells|228}}
|-
! {{period|96|brief}}
| ?
| ?
| ?
| [[period-48 glider gun]] {{LinkCatagolue|xp96_0178cy766zy44koy6m640ooe4a4z0gs26x11xoy1oo022440ezo8go|patternname=with boat-bit|style=raw}}
| {{cells|59}}
|-
! {{period|97|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p97 Snark loop]]
|{{cells|228}}
|-
! {{period|98|brief}}
| ?
| ?
| ?
| [[Gallus]]
| {{cells|105}}
|-
! {{period|99|brief}}
| ?
| ?
| ?
| [[48P9 on rattlesnake]]
|{{cells|82}}
|-
! {{period|100|brief}}
| [[centinal]]
|Bill Gosper
| ≤{{year|1987}}
| [[centinal]]
| {{cells|70}}
|-
! {{period|101|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p101 Snark loop]]
|{{cells|228}}
|-
! {{period|102|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp102_yzy2ca230oomewcczyzx33y3cczzyu42ey3o4ozyygs26x1zyzy3ca8zzzy54kczycoge2zy7696y3sg8zzy1ccy3ggzccwsq660ggkc011zy51|patternname=p102 unix shuttle loop|style=raw}}
| {{cells|96}}
|-
! {{period|103|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p103 Snark loop]]
|{{cells|228}}
|-
! {{period|104|brief}}
| ?
| ?
| ?
| [[figure eight on Beluchenko's p13]]
| {{cells|46}}
|-
! {{period|105|brief}}
| ?
| ?
| ?
| [[pentadecathlon on 37P7.1]]
|{{cells|49}}
|-
! {{period|106|brief}}
| ?
| ?
| ?
| [[rectifier|p106 rectifier loop]]
|{{cells|169}}
|-
! {{period|107|brief}}
| ?
| ?
| ?
| [[rectifier|p107 rectifier loop]]
|{{cells|136}}
|-
! {{period|108|brief}}
| ?
| ?
| ?
| [[22P4.3 on 56P27]]
|{{cells|78}}
|-
! {{period|109|brief}}
| ?
| ?
| ?
| [[rectifier|p109 rectifier loop]]
|{{cells|156}}
|-
! {{period|110|brief}}
| [[p110 traffic jam]]
|Bill Gosper
| 1994
| [[pseudo-barberpole on Jason's p22]]
|{{cells|51}}
|-
! {{period|111|brief}}
| ?
| ?
| ?
| [[rectifier|p111 rectifier loop]]
|{{cells|136}}
|-
! {{period|112|brief}}
| ?
| ?
| ?
| [[tumbler on Rich's p16]]
|{{cells|50}}
|-
! {{period|113|brief}}
| ?
| ?
| ?
| [[nihonium]]
| {{cells|106}}
|-
! {{period|114|brief}}
| ?
| ?
| ?
| [[caterer on strontium]]
|{{cells|57}}
|-
! {{period|115|brief}}
| ?
| ?
| ?
| [[rectifier|p115 rectifier loop]]
|{{cells|136}}
|-
! {{period|116|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=102P116|style=raw}}
|{{cells|102}}
|-
! {{period|117|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp117_y1o44mhar0rahm44ozwg8p7870167876107871zq6hcbagy1szg9gf99gfy26a8oz56o3t5zx1|patternname=117P117|style=raw}}
| {{cells|117}}
|-
! {{period|118|brief}}
| ?
| ?
| ?
| [[rectifier|p118 rectifier loop]]
|{{cells|154}}
|-
! {{period|119|brief}}
| ?
| ?
| ?
| [[rectifier|p119 rectifier loop]]
|{{cells|136}}
|-
! {{period|120|brief}}
| ?
| ?
| ?
| [[figure eight on pentadecathlon]]
| {{cells|24}}
|-
! {{period|121|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|122|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|123|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|124|brief}}
| [[p124 lumps of muck hassler]]
|Dean Hickerson
| 1994
| [[mold on Merzenich's p31]]
| {{cells|60}}
|-
! {{period|125|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|126|brief}}
| ?
| ?
| ?
| [[snacker on 34P14 shuttle]]
| {{cells|74}}
|-
! {{period|127|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|128|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp128_y3ca73oswcczyqg88gzy1ggyh6bbcxca4z8ko010onmcy04eewuscy26dt30g0352z4a6x6qqcyh11zy01221zyh66w73osa6|patternname=p128 wing hassler|style=raw}}
|{{cells|108}}
|-
! {{period|129|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p129 bumper loop]]
|{{cells|152}}
|-
! {{period|130|brief}}
| ?
| ?
| ?
| [[55P10 on Beluchenko's p13]]
| {{cells|89}}
|-
! {{period|131|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|132|brief}}
| p132 glider loop
|David Buckingham
| 1992
| [[mold on Jason's p33]]
| {{cells|72}}
|-
! {{period|133|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|134|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|135|brief}}
| [[106P135]]
|Bill Gosper
| {{year|1989}}
| [[pentadecathlon on 56P27]]
|{{cells|68}}
|-
! {{period|136|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|137|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|138|brief}}
| ?
| ?
| ?
| [[Gabriel's p138]]
| {{cells|36}}
|-
! {{period|139|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|140|brief}}
| p140 traffic jam
|Bill Gosper
| 1994
| [[34P14 shuttle on dockyard]]
| {{cells|82}}
|-
! {{period|141|brief}}
| ?
| ?
| ?
| [[p47 pre-pulsar shuttle phase-shifting 28P7.1]]
| {{cells|114}}
|-
! {{period|142|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|143|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|144|brief}}
| capped p144 [[gunstar]]
|David Buckingham
| 1990
| [[Achim's p144]]
| {{cells|42}}
|-
! {{period|150|brief}}
| ?
| ?
| ?
| [[buckaroo|p150 buckaroo shuttle]]
| {{cells|51}}
|-
! {{period|152|brief}}
| ?
| ?
| ?
| [[figure eight on strontium]]
| {{cells|60}}
|-
! {{period|156|brief}}
| p156 [[traffic jam]] oscillator
|Bill Gosper
| 1994
| [[Jason's p156]]
| {{cells|92}}
|-
! {{period|165|brief}}
| ?
| ?
| ?
| [[rattlesnake on pentadecathlon]]
| {{cells|45}}
|-
! {{period|168|brief}}
| ?
| ?
| ?
| [[figure eight on p21 honey farm hassler]]
| {{cells|72}}
|-
! {{period|177|brief}}
| ?
| ?
| ?
| [[Karel's p177]]
| {{cells|104}}
|-
! {{period|184|brief}}
| ?
| ?
| ?
| [[figure eight on twin bees shuttle]]
| {{cells|40}}
|-
! {{period|186|brief}}
| ?
| ?
| ?
| [[unix on Merzenich's p31]]
| {{cells|64}}
|-
! {{period|188|brief}}
| ?
| ?
| ?
| [[AK-94]] {{LinkCatagolue|xp188_x696o8b9czy065x33xc871wbdzoozwgg04ahhha4y5c871z4701yfoozxggy0ggzx56w4701xmmggo5jzya146w343|patternname=with boat-bits|style=raw}}
| {{cells|108}}
|-
! {{period|196|brief}}
| ?
| ?
| ?
| [[p196 pi-heptomino hassler]]
| {{cells|66}}
|-
! {{period|200|brief}}
| p200 glider loop
|Bill Gosper
| ≤{{year|1987}}
| [[figure eight on centinal]]
|{{cells|82}}
|-
! {{period|226|brief}}
| ?
| ?
| ?
| [[nihonium*]]
| {{cells|107}}
|-
! {{period|230|brief}}
| ?
| ?
| ?
| [[fumarole on twin bees shuttle]]
|{{cells|46}}
|-
! {{period|232|brief}}
| ?
| ?
| ?
| [[figure eight on p29 pre-pulsar shuttle]]
|{{cells|66}}
|-
! {{period|240|brief}}
| ?
| ?
| ?
| [[pentadecathlon on Rob's p16]]
| {{cells|33}}
|-
! {{period|246|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp246_ya32acydg8k8ooozyu1utzzzybcirrd6y4cc4zy1ggy61zggwg9g89z14w61ye354c|patternname=relative|style=raw}}
| {{cells|68}}
|-
! {{period|256|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp256_yr33y166z0ggy033y4178cyb33y0ccz011w66z66yyg88czy4699voyn11zy38ox61zy1311yz66zyzx66woozy133y0ccyb31e8y4cczy566y1cc|patternname=capped|style=raw}} [[period-256 glider gun]]
| {{cells|104}}
|-
! {{period|276|brief}}
| ?
| ?
| ?
| [[caterer on 50P92.1]]
| {{cells|62}}
|-
! {{period|300|brief}}
| ?
| ?
| ?
| [[pentadecathlon on centinal]]
| {{cells|88}}
|-
! {{period|312|brief}}
| ?
| ?
| ?
| [[60P312]]
| {{cells|60}}
|-
! {{period|320|brief}}
| ?
| ?
| ?
| [[fumarole on Merzenich's p64]]
| {{cells|52}}
|-
! {{period|360|brief}}
| ?
| ?
| ?
| [[thumb 1 on Beluchenko's p40]]
| {{cells|62}}
|-
! {{period|368|brief}}
| ?
| ?
| ?
| [[period-184 glider gun]] {{LinkCatagolue|xp368_y0gy632aczy01156zzggyp62sgz56yc65134w16zync4ozy8o8goy911|patternname=with boat-bits|style=raw}}
| {{cells|50}}
|-
! {{period|460|brief}}
| ?
| ?
| ?
| [[pseudo-barberpole on 50P92.1]]
| {{cells|65}}
|-
! {{period|492|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp492_y0o4qa344ozx118f0dc3z8oyago0ab2sycc871z0123y9126e431zy8ooz0mqzyt66w7bcczyy66|patternname=with boat-bit|style=raw}}
| {{cells|87}}
|-
! {{period|496|brief}}
| ?
| ?
| ?
| [[Rob's p16 on Merzenich's p31]]
| {{cells|69}}
|-
! {{period|504|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp504_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzyzygg88gxooy1uu06666mmzyzygcc07xccy1rroooo0vvzyzyh66|patternname=p504 glider shuttle|style=raw}}
| {{cells|109}}
|-
! {{period|512|brief}}
| ?
| ?
| ?
| [[period-256 glider gun]] {{LinkCatagolue|xp512_yr33y166z0ggy033y16426ye33y0ccz011w66yuggz66yz56zzzy2mqyz66zygckgk2a21ya66woozy133y0ccye6426y1cczy566y1cc|patternname=with boat-bits|style=raw}}
| {{cells|100}}
|-
! {{period|856|brief}}
| [[period-856 glider gun]]
| [[David Buckingham]]
| 1991
| {{LinkCatagolue|xp856_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzzzzzzzzzzyzyzyl844oxccy1vv03333rrzyzyzyl6603x66y1ddcccc0ffzyzyzym33|patternname=p856 glider shuttle|style=raw}}
|{{cells|109}}
|-
! {{period|1008|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp1008_y48oyc356zy432yi696y9o8gozyjc871zzy12552yg2bq4y4o8zca6y3oggyp113y3ca6zy823ys8kk8zzyogs26zx3123y9cicyi8ozymckoyc32|patternname=R126 loop with boat-bits|style=raw}}
| {{cells|107}}
|}

==Flipper==
A '''flipper''' is any [[oscillator]] that forms its mirror image halfway through its [[period]].

==Notes==
<references group=note />

==See also==
*[[List of common oscillators]]
*[[:Category:Flipping oscillators|List of flipping oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
*[[Table of oscillators by period]]
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]

==External links==
{{LinkWikipedia|Oscillator_(cellular_automaton)}}
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkLexicon|lex_f.htm#flipper|name=Flipper}}

===Forum threads===
{{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
{{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
{{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}

__NOTOC__

Oscillator

2022-01-12T20:51:08Z

Freywa: new SKOP102

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period).

[[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
| rowspan="500" style="border: none;" |
! Smallest known
! Minimum # of cells
|-
! {{period|2|brief}}
| [[blinker]]
|[[John Conway]]
| {{year|1970}}
| [[blinker]]
| {{cells|3}}
|-
! {{period|3|brief}}
| [[pulsar]]
|John Conway
| 1970
| [[caterer]]
| {{cells|12}}
|-
! {{period|4|brief}}
| [[pinwheel]]
|[[Simon Norton]]
| 1970
| [[mazing]], [[mold]]
| {{cells|12}}
|-
! {{period|5|brief}}
| [[octagon 2]]
|[[Sol Goodman]], [[Arthur Taber]]
| {{year|1971}}
| [[pseudo-barberpole]]
| {{cells|15}}
|-
! {{period|6|brief}}
| [[$rats]]
|[[David Buckingham]]
| {{year|1972}}
| [[unix]]
| {{cells|16}}
|-
! {{period|7|brief}}
| [[burloaferimeter]]
|David Buckingham
| 1972
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
| {{cells|28}}
|-
! {{period|8|brief}}
| [[figure eight]]
|Simon Norton
| 1970
| [[figure eight]]
| {{cells|12}}
|-
! {{period|9|brief}}
| [[worker bee]]
|David Buckingham
| 1972
| [[29P9]]
| {{cells|29}}
|-
! {{period|10|brief}}
| [[42P10.3]]
|David Buckingham
| ≤{{year|1976}}
| [[24P10]]
| {{cells|24}}
|-
! {{period|11|brief}}
| [[38P11.1]]
|David Buckingham
| {{year|1977}}
| [[rattlesnake]]
| {{cells|33}}
|-
! {{period|12|brief}}
| [[dinner table]]
|[[Robert Wainwright]]
| {{year|1972}}
| [[dinner table]]
| {{cells|33}}
|-
! {{period|13|brief}}
| [[Buckingham's p13]]
|David Buckingham
| 1976
| [[Beluchenko's p13]]
| {{cells|34}}
|-
! {{period|14|brief}}
| [[tumbler]]
|[[George Collins]]
| 1970
| [[tumbler]]
| {{cells|16}}
|-
! {{period|15|brief}}
| [[pentadecathlon]]
|John Conway
| 1970
| [[pentadecathlon]]
| {{cells|12}}
|-
! {{period|16|brief}}
| [[two pre-L hasslers]]
|Robert Wainwright
| {{year|1983}}
| [[Rob's p16]]
| {{cells|21}}
|-
! {{period|17|brief}}
| [[54P17.1]]
|[[Dean Hickerson]]
| {{year|1997}}
| [[honey thieves]]
| {{cells|36}}
|-
! {{period|18|brief}}
| [[117P18]]{{refn|group=note|name=lcm|An oscillator of this period can also be constructed from two [[sparker]]s both of which were known by an earlier date. However, [[LCM oscillator]]s are generally considered "[[boring]]", and thus not listed here despite technically being [[non-trivial]].}}
|David Buckingham
| ≤{{year|1991}}
| [[p18 bi-block hassler]], [[p18 phase shifter]]
| {{cells|43}}
|-
! class="red_td" | 19
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|20|brief}}
| [[145P20]]{{refn|group=note|name=lcm}}
|[[Noam Elkies]]
| {{year|1995}}
| [[mold on fumarole]]
| {{cells|30}}
|-
! {{period|21|brief}}
| [[124P21]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1995
| [[caterer on 28P7.3]]
| {{cells|40}}
|-
! {{period|22|brief}}
| [[168P22.1]]
|Noam Elkies
| 1997
| [[Jason's p22]]
| {{cells|36}}
|-
! {{period|23|brief}}
| [[David Hilbert]]
|[[Luka Okanishi]], [[praosylen]]
| {{year|2019}}
| [[David Hilbert]]
| {{cells|122}}
|-
! {{period|24|brief}}
| [[186P24]]{{refn|group=note|name=lcm}}
|[[Bill Gosper]]
| {{year|1994}}
| [[caterer on figure eight]]
| {{cells|24}}
|-
! {{period|25|brief}}
| [[134P25]]
|Noam Elkies
| 1994
| [[p25 pre-pulsar shuttle]]
| {{cells|83}}
|-
! {{period|26|brief}}
| [[p26 pre-pulsar shuttle]]
|David Buckingham
| 1983
| [[87P26]]
| {{cells|87}}
|-
! {{period|27|brief}}
| [[123P27.1]]
|Noam Elkies
| {{year|2002}}
| [[56P27]]
| {{cells|56}}
|-
! {{period|28|brief}}
| [[newshuttle]]
|David Buckingham
| {{year|1973}}
| [[mold on 34P14 shuttle]]
| {{cells|46}}
|-
! {{period|29|brief}}
| [[p29 pre-pulsar shuttle]]
|David Buckingham
| {{year|1980}}
| [[p29 pre-pulsar shuttle]]
| {{cells|54}}
|-
! {{period|30|brief}}
| [[queen bee shuttle]]
|Bill Gosper
| 1970
| [[queen bee shuttle]]
| {{cells|20}}
|-
! {{period|31|brief}}
| [[Merzenich's p31]]
|[[Matthias Merzenich]]
| {{year|2010}}
| [[Merzenich's p31]]
| {{cells|48}}
|-
! {{period|32|brief}}
| [[gourmet]]
|David Buckingham
| {{year|1978}}
| [[p32 honey farm hassler]]
| {{cells|45}}
|-
! {{period|33|brief}}
| [[258P3 on Achim's p11]]
|Noam Elkies, [[Achim Flammenkamp]]
| 1997
| [[caterer on rattlesnake]]
| {{cells|46}}
|-
! {{period|34|brief}}
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''No non-trivial examples found''
|-
! {{period|35|brief}}
| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
|Dean Hickerson
| 1995
| [[p35 honey farm hassler]]
| {{cells|44}}
|-
! {{period|36|brief}}
| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1984
| [[22P36]]
| {{cells|22}}
|-
! {{period|37|brief}}
| [[Beluchenko's p37]]
|[[Nicolay Beluchenko]]
| {{year|2009}}
| [[Beluchenko's p37]]
| {{cells|124}}
|-
! {{period|38|brief}}
| [[strontium]]
|[[David Raucci]]
| {{year|2022}}
| [[strontium]]
| {{cells|44}}
|-
! {{period|39|brief}}
| [[134P39.1]]
|David Buckingham, Noam Elkies
| {{year|2000}}
| [[caterer on Beluchenko's p13]]
|{{cells|46}}
|-
! {{period|40|brief}}
| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| 1991
| [[Beluchenko's p40]]
| {{cells|26}}
|-
! class="red_td" | 41
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|42|brief}}
| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
|Noam Elkies
| 1994
| [[unix on 34P14 shuttle]]
| {{cells|50}}
|-
! {{period|43|brief}}
| [[p43 Snark loop]]
|[[Mike Playle]]
| {{year|2013}}
| [[p43 Snark loop]]
|{{cells|228}}
|-
! {{period|44|brief}}
| [[p44 pi-heptomino hassler]]
|David Buckingham
| 1992
| [[mold on rattlesnake]]
| {{cells|45}}
|-
! {{period|45|brief}}
| [[pentadecathlon on snacker]]
| [[Mark Niemiec]], John Conway
| ≤1995
| [[pentadecathlon on thumb 1]]
| {{cells|48}}
|-
! {{period|46|brief}}
| [[twin bees shuttle]]
|Bill Gosper
| 1971
| [[twin bees shuttle]]
| {{cells|28}}
|-
! {{period|47|brief}}
| [[p47 pre-pulsar shuttle]]
|David Buckingham
| {{year|1982}}
| [[p47 pre-pulsar shuttle]]
| {{cells|84}}
|-
! {{period|48|brief}}
| [[p48 toad hassler]]
|Bill Gosper
| 1994
| [[unix on Rich's p16]]
| {{cells|52}}
|-
! {{period|49|brief}}
| [[p49 glider shuttle]]
|Noam Elkies
| {{year|1999}}
| [[p49 bumper loop]]
| {{cells|206}}
|-
! {{period|50|brief}}
| [[p50 glider shuttle]]
|Dean Hickerson
| 1992
| [[p50 traffic jam]]
| {{cells|92}}
|-
! {{period|51|brief}}
| [[Beluchenko's p51]]
|Nicolay Beluchenko
| 2009
| [[90P51]]
| {{cells|90}}
|-
! {{period|52|brief}}
| [[Four eaters hassling lumps of muck]]
|David Buckingham
| 1977
| [[four eaters hassling lumps of muck]]
| {{cells|35}}
|-
! {{period|53|brief}}
| [[p53 Snark loop]]
|Mike Playle
| {{year|2013}}
| [[p53 Snark loop]]
|{{cells|228}}
|-
! {{period|54|brief}}
| [[p54 shuttle]]
|David Buckingham
| {{year|1973}}
| [[p54 shuttle]]
| {{cells|48}}
|-
! {{period|55|brief}}
| [[p55 pre-pulsar hassler]]
|David Buckingham
| {{year|1986}}
| [[pseudo-barberpole on rattlesnake]]
| {{cells|49}}
|-
! {{period|56|brief}}
| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| ≤1991
| [[p56 B-heptomino shuttle]]
| {{cells|45}}
|-
! {{period|57|brief}}
| [[p57 Herschel loop 1]]
|[[Dietrich Leithner]]
| 1997
| [[p57 bumper loop]]
|{{cells|152}}
|-
! {{period|58|brief}}
| [[p58 toadsucker]]
|Bill Gosper
| 1994
| [[p58 pre-pulsar shuttle]]
| {{cells|104}}
|-
! {{period|59|brief}}
| [[p59 Herschel loop 1]]
|David Buckingham
| 1997
| [[Adjustable glider loop|p59 Snark loop]]
|{{cells|228}}
|-
! {{period|60|brief}}
| [[p60 glider shuttle]]
|David Buckingham
| ≤ 1971
| [[mold on pentadecathlon]]
| {{cells|24}}
|-
! {{period|61|brief}}
| [[p61 Herschel loop 1]]
|David Buckingham
| {{year|1996}}
| [[Adjustable glider loop|p61 Snark loop]]
|{{cells|228}}
|-
! {{period|62|brief}}
| ?
| ?
| ?
| [[66P62]]
| {{cells|66}}
|-
! {{period|63|brief}}
| ?
| ?
| ?
| [[snacker on 38P7.2]]
| {{cells|78}}
|-
! {{period|64|brief}}
| ?
| ?
| ?
| [[Merzenich's p64]]
| {{cells|34}}
|-
! {{period|65|brief}}
| ?
| ?
| ?
| [[fumarole on Beluchenko's p13]]
| {{cells|52}}
|-
! {{period|66|brief}}
| ?
| ?
| ?
| [[caterer on Jason's p22]]
| {{cells|48}}
|-
! {{period|67|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p67 Snark loop]]
|{{cells|228}}
|-
! {{period|68|brief}}
| ?
| ?
| ?
| [[72P68]]
|{{cells|72}}
|-
! {{period|69|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p69 bumper loop]]
|{{cells|152}}
|-
! {{period|70|brief}}
| ?
| ?
| ?
| [[fumarole on 34P14 shuttle]]
| {{cells|52}}
|-
! {{period|71|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p71 Snark loop]]
|{{cells|228}}
|-
! {{period|72|brief}}
| [[two blockers hassling R-pentomino]]
|Robert Wainwright
| 1990
| [[figure eight on 22P36]]
| {{cells|36}}
|-
! {{period|73|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p73 Snark loop]]
|{{cells|228}}
|-
! {{period|74|brief}}
| p74 Herschel loop
|David Buckingham
| 1996
| [[Raucci's p74]]
| {{cells|84}}
|-
! {{period|75|brief}}
| ?
| ?
| ?
| [[6 bits]]
|{{cells|49}}
|-
! {{period|76|brief}}
| ?
| ?
| ?
| [[mold on 44P38]]
| {{cells|56}}
|-
! {{period|77|brief}}
| ?
| ?
| ?
| [[77P77]]
|{{cells|77}}
|-
! {{period|78|brief}}
| ?
| ?
| ?
| [[p6 thumb on Beluchenko's p13]]
|{{cells|61}}
|-
! {{period|79|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p79 Snark loop]]
|{{cells|228}}
|-
! {{period|80|brief}}
| ?
| ?
| ?
| [[fumarole on Rob's p16]]
| {{cells|39}}
|-
! {{period|81|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p81 bumper loop]]
|{{cells|152}}
|-
! {{period|82|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p82 Snark loop]]
|{{cells|208}}
|-
! {{period|83|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p83 Snark loop]]
|{{cells|228}}
|-
! {{period|84|brief}}
| ?
| ?
| ?
| [[52P84]]
| {{cells|52}}
|-
! {{period|85|brief}}
| ?
| ?
| ?
| [[74P85]]
|{{cells|74}}
|-
! {{period|86|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p86 Snark loop]]
|{{cells|208}}
|-
! {{period|87|brief}}
| ?
| ?
| ?
| [[84P87]]
| {{cells|84}}
|-
! {{period|88|brief}}
| p88 glider loop
|David Buckingham
| 1992
| [[figure eight on rattlesnake]]
| {{cells|45}}
|-
! {{period|89|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p89 Snark loop]]
|{{cells|228}}
|-
! {{period|90|brief}}
| ?
| ?
| ?
| [[thumb 1 on queen bee shuttle]]
| {{cells|56}}
|-
! {{period|91|brief}}
| ?
| ?
| ?
| [[44P7 on Beluchenko's p13]]
|{{cells|78}}
|-
! {{period|92|brief}}
| ?
| ?
| ?
| [[50P92.1]], [[twin bees shuttle on 22P4.3]]
| {{cells|50}}
|-
! {{period|93|brief}}
| ?
| ?
| ?
| [[caterer on Merzenich's p31]]
|{{cells|60}}
|-
! {{period|94|brief}}
| capped [[AK-47 reaction|AK-47]] gun
|Dean Hickerson
| 1990
| {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]]
| {{cells|110}}
|-
! {{period|95|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p95 Snark loop]]
|{{cells|228}}
|-
! {{period|96|brief}}
| ?
| ?
| ?
| [[period-48 glider gun]] {{LinkCatagolue|xp96_0178cy766zy44koy6m640ooe4a4z0gs26x11xoy1oo022440ezo8go|patternname=with boat-bit|style=raw}}
| {{cells|59}}
|-
! {{period|97|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p97 Snark loop]]
|{{cells|228}}
|-
! {{period|98|brief}}
| ?
| ?
| ?
| [[Gallus]]
| {{cells|105}}
|-
! {{period|99|brief}}
| ?
| ?
| ?
| [[48P9 on rattlesnake]]
|{{cells|82}}
|-
! {{period|100|brief}}
| [[centinal]]
|Bill Gosper
| ≤{{year|1987}}
| [[centinal]]
| {{cells|70}}
|-
! {{period|101|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p101 Snark loop]]
|{{cells|228}}
|-
! {{period|102|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp102_yzy2ca230oomewcczyzx33y3cczzyu42ey3o4ozyygs26x1zyzy3ca8zzzy54kczycoge2zy7696y3sg8zzy1ccy3ggzccwsq660ggkc011zy51|patternname=Sandbar|style=raw}}
| {{cells|96}}
|-
! {{period|103|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p103 Snark loop]]
|{{cells|228}}
|-
! {{period|104|brief}}
| ?
| ?
| ?
| [[figure eight on Beluchenko's p13]]
| {{cells|46}}
|-
! {{period|105|brief}}
| ?
| ?
| ?
| [[pentadecathlon on 37P7.1]]
|{{cells|49}}
|-
! {{period|106|brief}}
| ?
| ?
| ?
| [[rectifier|p106 rectifier loop]]
|{{cells|169}}
|-
! {{period|107|brief}}
| ?
| ?
| ?
| [[rectifier|p107 rectifier loop]]
|{{cells|136}}
|-
! {{period|108|brief}}
| ?
| ?
| ?
| [[22P4.3 on 56P27]]
|{{cells|78}}
|-
! {{period|109|brief}}
| ?
| ?
| ?
| [[rectifier|p109 rectifier loop]]
|{{cells|156}}
|-
! {{period|110|brief}}
| [[p110 traffic jam]]
|Bill Gosper
| 1994
| [[pseudo-barberpole on Jason's p22]]
|{{cells|51}}
|-
! {{period|111|brief}}
| ?
| ?
| ?
| [[rectifier|p111 rectifier loop]]
|{{cells|136}}
|-
! {{period|112|brief}}
| ?
| ?
| ?
| [[tumbler on Rich's p16]]
|{{cells|50}}
|-
! {{period|113|brief}}
| ?
| ?
| ?
| [[nihonium]]
| {{cells|106}}
|-
! {{period|114|brief}}
| ?
| ?
| ?
| [[caterer on strontium]]
|{{cells|57}}
|-
! {{period|115|brief}}
| ?
| ?
| ?
| [[rectifier|p115 rectifier loop]]
|{{cells|136}}
|-
! {{period|116|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=102P116|style=raw}}
|{{cells|102}}
|-
! {{period|117|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp117_y1o44mhar0rahm44ozwg8p7870167876107871zq6hcbagy1szg9gf99gfy26a8oz56o3t5zx1|patternname=117P117|style=raw}}
| {{cells|117}}
|-
! {{period|118|brief}}
| ?
| ?
| ?
| [[rectifier|p118 rectifier loop]]
|{{cells|154}}
|-
! {{period|119|brief}}
| ?
| ?
| ?
| [[rectifier|p119 rectifier loop]]
|{{cells|136}}
|-
! {{period|120|brief}}
| ?
| ?
| ?
| [[figure eight on pentadecathlon]]
| {{cells|24}}
|-
! {{period|121|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|122|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|123|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|124|brief}}
| [[p124 lumps of muck hassler]]
|Dean Hickerson
| 1994
| [[mold on Merzenich's p31]]
| {{cells|60}}
|-
! {{period|125|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|126|brief}}
| ?
| ?
| ?
| [[snacker on 34P14 shuttle]]
| {{cells|74}}
|-
! {{period|127|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|128|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp128_y3ca73oswcczyqg88gzy1ggyh6bbcxca4z8ko010onmcy04eewuscy26dt30g0352z4a6x6qqcyh11zy01221zyh66w73osa6|patternname=p128 wing hassler|style=raw}}
|{{cells|108}}
|-
! {{period|129|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p129 bumper loop]]
|{{cells|152}}
|-
! {{period|130|brief}}
| ?
| ?
| ?
| [[55P10 on Beluchenko's p13]]
| {{cells|89}}
|-
! {{period|131|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|132|brief}}
| p132 glider loop
|David Buckingham
| 1992
| [[mold on Jason's p33]]
| {{cells|72}}
|-
! {{period|133|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|134|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|135|brief}}
| [[106P135]]
|Bill Gosper
| {{year|1989}}
| [[pentadecathlon on 56P27]]
|{{cells|68}}
|-
! {{period|136|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|137|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|138|brief}}
| ?
| ?
| ?
| [[Gabriel's p138]]
| {{cells|36}}
|-
! {{period|139|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|140|brief}}
| p140 traffic jam
|Bill Gosper
| 1994
| [[34P14 shuttle on dockyard]]
| {{cells|82}}
|-
! {{period|141|brief}}
| ?
| ?
| ?
| [[p47 pre-pulsar shuttle phase-shifting 28P7.1]]
| {{cells|114}}
|-
! {{period|142|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|143|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|144|brief}}
| capped p144 [[gunstar]]
|David Buckingham
| 1990
| [[Achim's p144]]
| {{cells|42}}
|-
! {{period|150|brief}}
| ?
| ?
| ?
| [[buckaroo|p150 buckaroo shuttle]]
| {{cells|51}}
|-
! {{period|152|brief}}
| ?
| ?
| ?
| [[figure eight on 44P38]]
| {{cells|60}}
|-
! {{period|156|brief}}
| p156 [[traffic jam]] oscillator
|Bill Gosper
| 1994
| [[Jason's p156]]
| {{cells|92}}
|-
! {{period|165|brief}}
| ?
| ?
| ?
| [[rattlesnake on pentadecathlon]]
| {{cells|45}}
|-
! {{period|168|brief}}
| ?
| ?
| ?
| [[figure eight on p21 honey farm hassler]]
| {{cells|72}}
|-
! {{period|177|brief}}
| ?
| ?
| ?
| [[Karel's p177]]
| {{cells|104}}
|-
! {{period|184|brief}}
| ?
| ?
| ?
| [[figure eight on twin bees shuttle]]
| {{cells|40}}
|-
! {{period|186|brief}}
| ?
| ?
| ?
| [[unix on Merzenich's p31]]
| {{cells|64}}
|-
! {{period|188|brief}}
| ?
| ?
| ?
| [[AK-94]] {{LinkCatagolue|xp188_x696o8b9czy065x33xc871wbdzoozwgg04ahhha4y5c871z4701yfoozxggy0ggzx56w4701xmmggo5jzya146w343|patternname=with boat-bits|style=raw}}
| {{cells|108}}
|-
! {{period|196|brief}}
| ?
| ?
| ?
| [[p196 pi-heptomino hassler]]
| {{cells|66}}
|-
! {{period|200|brief}}
| p200 glider loop
|Bill Gosper
| ≤{{year|1987}}
| [[figure eight on centinal]]
|{{cells|82}}
|-
! {{period|226|brief}}
| ?
| ?
| ?
| [[nihonium*]]
| {{cells|107}}
|-
! {{period|230|brief}}
| ?
| ?
| ?
| [[fumarole on twin bees shuttle]]
|{{cells|46}}
|-
! {{period|232|brief}}
| ?
| ?
| ?
| [[figure eight on p29 pre-pulsar shuttle]]
|{{cells|66}}
|-
! {{period|240|brief}}
| ?
| ?
| ?
| [[pentadecathlon on Rob's p16]]
| {{cells|33}}
|-
! {{period|246|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp246_ya32acydg8k8ooozyu1utzzzybcirrd6y4cc4zy1ggy61zggwg9g89z14w61ye354c|patternname=relative|style=raw}}
| {{cells|68}}
|-
! {{period|256|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp256_yr33y166z0ggy033y4178cyb33y0ccz011w66z66yyg88czy4699voyn11zy38ox61zy1311yz66zyzx66woozy133y0ccyb31e8y4cczy566y1cc|patternname=capped|style=raw}} [[period-256 glider gun]]
| {{cells|104}}
|-
! {{period|276|brief}}
| ?
| ?
| ?
| [[caterer on 50P92.1]]
| {{cells|62}}
|-
! {{period|300|brief}}
| ?
| ?
| ?
| [[pentadecathlon on centinal]]
| {{cells|88}}
|-
! {{period|312|brief}}
| ?
| ?
| ?
| [[60P312]]
| {{cells|60}}
|-
! {{period|320|brief}}
| ?
| ?
| ?
| [[fumarole on Merzenich's p64]]
| {{cells|52}}
|-
! {{period|360|brief}}
| ?
| ?
| ?
| [[thumb 1 on Beluchenko's p40]]
| {{cells|62}}
|-
! {{period|368|brief}}
| ?
| ?
| ?
| [[period-184 glider gun]] {{LinkCatagolue|xp368_y0gy632aczy01156zzggyp62sgz56yc65134w16zync4ozy8o8goy911|patternname=with boat-bits|style=raw}}
| {{cells|50}}
|-
! {{period|460|brief}}
| ?
| ?
| ?
| [[pseudo-barberpole on 50P92.1]]
| {{cells|65}}
|-
! {{period|492|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp492_y0o4qa344ozx118f0dc3z8oyago0ab2sycc871z0123y9126e431zy8ooz0mqzyt66w7bcczyy66|patternname=with boat-bit|style=raw}}
| {{cells|87}}
|-
! {{period|496|brief}}
| ?
| ?
| ?
| [[Rob's p16 on Merzenich's p31]]
| {{cells|69}}
|-
! {{period|504|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp504_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzyzygg88gxooy1uu06666mmzyzygcc07xccy1rroooo0vvzyzyh66|patternname=p504 glider shuttle|style=raw}}
| {{cells|109}}
|-
! {{period|512|brief}}
| ?
| ?
| ?
| [[period-256 glider gun]] {{LinkCatagolue|xp512_yr33y166z0ggy033y16426ye33y0ccz011w66yuggz66yz56zzzy2mqyz66zygckgk2a21ya66woozy133y0ccye6426y1cczy566y1cc|patternname=with boat-bits|style=raw}}
| {{cells|100}}
|-
! {{period|856|brief}}
| [[period-856 glider gun]]
| [[David Buckingham]]
| 1991
| {{LinkCatagolue|xp856_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzzzzzzzzzzyzyzyl844oxccy1vv03333rrzyzyzyl6603x66y1ddcccc0ffzyzyzym33|patternname=p856 glider shuttle|style=raw}}
|{{cells|109}}
|-
! {{period|1008|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp1008_y48oyc356zy432yi696y9o8gozyjc871zzy12552yg2bq4y4o8zca6y3oggyp113y3ca6zy823ys8kk8zzyogs26zx3123y9cicyi8ozymckoyc32|patternname=R126 loop with boat-bits|style=raw}}
| {{cells|107}}
|}

==Flipper==
A '''flipper''' is any [[oscillator]] that forms its mirror image halfway through its [[period]].

==Notes==
<references group=note />

==See also==
*[[List of common oscillators]]
*[[:Category:Flipping oscillators|List of flipping oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
*[[Table of oscillators by period]]
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]

==External links==
{{LinkWikipedia|Oscillator_(cellular_automaton)}}
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkLexicon|lex_f.htm#flipper|name=Flipper}}

===Forum threads===
{{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
{{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
{{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}

__NOTOC__

Oscillator

2022-01-12T18:35:52Z

Freywa: shuffle names around

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period).

[[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
| rowspan="500" style="border: none;" |
! Smallest known
! Minimum # of cells
|-
! {{period|2|brief}}
| [[blinker]]
|[[John Conway]]
| {{year|1970}}
| [[blinker]]
| {{cells|3}}
|-
! {{period|3|brief}}
| [[pulsar]]
|John Conway
| 1970
| [[caterer]]
| {{cells|12}}
|-
! {{period|4|brief}}
| [[pinwheel]]
|[[Simon Norton]]
| 1970
| [[mazing]], [[mold]]
| {{cells|12}}
|-
! {{period|5|brief}}
| [[octagon 2]]
|[[Sol Goodman]], [[Arthur Taber]]
| {{year|1971}}
| [[pseudo-barberpole]]
| {{cells|15}}
|-
! {{period|6|brief}}
| [[$rats]]
|[[David Buckingham]]
| {{year|1972}}
| [[unix]]
| {{cells|16}}
|-
! {{period|7|brief}}
| [[burloaferimeter]]
|David Buckingham
| 1972
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
| {{cells|28}}
|-
! {{period|8|brief}}
| [[figure eight]]
|Simon Norton
| 1970
| [[figure eight]]
| {{cells|12}}
|-
! {{period|9|brief}}
| [[worker bee]]
|David Buckingham
| 1972
| [[29P9]]
| {{cells|29}}
|-
! {{period|10|brief}}
| [[42P10.3]]
|David Buckingham
| ≤{{year|1976}}
| [[24P10]]
| {{cells|24}}
|-
! {{period|11|brief}}
| [[38P11.1]]
|David Buckingham
| {{year|1977}}
| [[rattlesnake]]
| {{cells|33}}
|-
! {{period|12|brief}}
| [[dinner table]]
|[[Robert Wainwright]]
| {{year|1972}}
| [[dinner table]]
| {{cells|33}}
|-
! {{period|13|brief}}
| [[Buckingham's p13]]
|David Buckingham
| 1976
| [[Beluchenko's p13]]
| {{cells|34}}
|-
! {{period|14|brief}}
| [[tumbler]]
|[[George Collins]]
| 1970
| [[tumbler]]
| {{cells|16}}
|-
! {{period|15|brief}}
| [[pentadecathlon]]
|John Conway
| 1970
| [[pentadecathlon]]
| {{cells|12}}
|-
! {{period|16|brief}}
| [[two pre-L hasslers]]
|Robert Wainwright
| {{year|1983}}
| [[Rob's p16]]
| {{cells|21}}
|-
! {{period|17|brief}}
| [[54P17.1]]
|[[Dean Hickerson]]
| {{year|1997}}
| [[honey thieves]]
| {{cells|36}}
|-
! {{period|18|brief}}
| [[117P18]]{{refn|group=note|name=lcm|An oscillator of this period can also be constructed from two [[sparker]]s both of which were known by an earlier date. However, [[LCM oscillator]]s are generally considered "[[boring]]", and thus not listed here despite technically being [[non-trivial]].}}
|David Buckingham
| ≤{{year|1991}}
| [[p18 bi-block hassler]], [[p18 phase shifter]]
| {{cells|43}}
|-
! class="red_td" | 19
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|20|brief}}
| [[145P20]]{{refn|group=note|name=lcm}}
|[[Noam Elkies]]
| {{year|1995}}
| [[mold on fumarole]]
| {{cells|30}}
|-
! {{period|21|brief}}
| [[124P21]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1995
| [[caterer on 28P7.3]]
| {{cells|40}}
|-
! {{period|22|brief}}
| [[168P22.1]]
|Noam Elkies
| 1997
| [[Jason's p22]]
| {{cells|36}}
|-
! {{period|23|brief}}
| [[David Hilbert]]
|[[Luka Okanishi]], [[praosylen]]
| {{year|2019}}
| [[David Hilbert]]
| {{cells|122}}
|-
! {{period|24|brief}}
| [[186P24]]{{refn|group=note|name=lcm}}
|[[Bill Gosper]]
| {{year|1994}}
| [[caterer on figure eight]]
| {{cells|24}}
|-
! {{period|25|brief}}
| [[134P25]]
|Noam Elkies
| 1994
| [[p25 pre-pulsar shuttle]]
| {{cells|83}}
|-
! {{period|26|brief}}
| [[p26 pre-pulsar shuttle]]
|David Buckingham
| 1983
| [[87P26]]
| {{cells|87}}
|-
! {{period|27|brief}}
| [[123P27.1]]
|Noam Elkies
| {{year|2002}}
| [[56P27]]
| {{cells|56}}
|-
! {{period|28|brief}}
| [[newshuttle]]
|David Buckingham
| {{year|1973}}
| [[mold on 34P14 shuttle]]
| {{cells|46}}
|-
! {{period|29|brief}}
| [[p29 pre-pulsar shuttle]]
|David Buckingham
| {{year|1980}}
| [[p29 pre-pulsar shuttle]]
| {{cells|54}}
|-
! {{period|30|brief}}
| [[queen bee shuttle]]
|Bill Gosper
| 1970
| [[queen bee shuttle]]
| {{cells|20}}
|-
! {{period|31|brief}}
| [[Merzenich's p31]]
|[[Matthias Merzenich]]
| {{year|2010}}
| [[Merzenich's p31]]
| {{cells|48}}
|-
! {{period|32|brief}}
| [[gourmet]]
|David Buckingham
| {{year|1978}}
| [[p32 honey farm hassler]]
| {{cells|45}}
|-
! {{period|33|brief}}
| [[258P3 on Achim's p11]]
|Noam Elkies, [[Achim Flammenkamp]]
| 1997
| [[caterer on rattlesnake]]
| {{cells|46}}
|-
! {{period|34|brief}}
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''No non-trivial examples found''
|-
! {{period|35|brief}}
| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
|Dean Hickerson
| 1995
| [[p35 honey farm hassler]]
| {{cells|44}}
|-
! {{period|36|brief}}
| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1984
| [[22P36]]
| {{cells|22}}
|-
! {{period|37|brief}}
| [[Beluchenko's p37]]
|[[Nicolay Beluchenko]]
| {{year|2009}}
| [[Beluchenko's p37]]
| {{cells|124}}
|-
! {{period|38|brief}}
| [[44P38]]
|[[David Raucci]]
| {{year|2022}}
| [[44P38]]
| {{cells|44}}
|-
! {{period|39|brief}}
| [[134P39.1]]
|David Buckingham, Noam Elkies
| {{year|2000}}
| [[caterer on Beluchenko's p13]]
|{{cells|46}}
|-
! {{period|40|brief}}
| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| 1991
| [[Beluchenko's p40]]
| {{cells|26}}
|-
! class="red_td" | 41
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|42|brief}}
| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
|Noam Elkies
| 1994
| [[unix on 34P14 shuttle]]
| {{cells|50}}
|-
! {{period|43|brief}}
| [[p43 Snark loop]]
|[[Mike Playle]]
| {{year|2013}}
| [[p43 Snark loop]]
|{{cells|228}}
|-
! {{period|44|brief}}
| [[p44 pi-heptomino hassler]]
|David Buckingham
| 1992
| [[mold on rattlesnake]]
| {{cells|45}}
|-
! {{period|45|brief}}
| [[pentadecathlon on snacker]]
| [[Mark Niemiec]], John Conway
| ≤1995
| [[pentadecathlon on thumb 1]]
| {{cells|48}}
|-
! {{period|46|brief}}
| [[twin bees shuttle]]
|Bill Gosper
| 1971
| [[twin bees shuttle]]
| {{cells|28}}
|-
! {{period|47|brief}}
| [[p47 pre-pulsar shuttle]]
|David Buckingham
| {{year|1982}}
| [[p47 pre-pulsar shuttle]]
| {{cells|84}}
|-
! {{period|48|brief}}
| [[p48 toad hassler]]
|Bill Gosper
| 1994
| [[unix on Rich's p16]]
| {{cells|52}}
|-
! {{period|49|brief}}
| [[p49 glider shuttle]]
|Noam Elkies
| {{year|1999}}
| [[p49 bumper loop]]
| {{cells|206}}
|-
! {{period|50|brief}}
| [[p50 glider shuttle]]
|Dean Hickerson
| 1992
| [[p50 traffic jam]]
| {{cells|92}}
|-
! {{period|51|brief}}
| [[Beluchenko's p51]]
|Nicolay Beluchenko
| 2009
| [[90P51]]
| {{cells|90}}
|-
! {{period|52|brief}}
| [[Four eaters hassling lumps of muck]]
|David Buckingham
| 1977
| [[four eaters hassling lumps of muck]]
| {{cells|35}}
|-
! {{period|53|brief}}
| [[p53 Snark loop]]
|Mike Playle
| {{year|2013}}
| [[p53 Snark loop]]
|{{cells|228}}
|-
! {{period|54|brief}}
| [[p54 shuttle]]
|David Buckingham
| {{year|1973}}
| [[p54 shuttle]]
| {{cells|48}}
|-
! {{period|55|brief}}
| [[p55 pre-pulsar hassler]]
|David Buckingham
| {{year|1986}}
| [[pseudo-barberpole on rattlesnake]]
| {{cells|49}}
|-
! {{period|56|brief}}
| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| ≤1991
| [[p56 B-heptomino shuttle]]
| {{cells|45}}
|-
! {{period|57|brief}}
| [[p57 Herschel loop 1]]
|[[Dietrich Leithner]]
| 1997
| [[p57 bumper loop]]
|{{cells|152}}
|-
! {{period|58|brief}}
| [[p58 toadsucker]]
|Bill Gosper
| 1994
| [[p58 pre-pulsar shuttle]]
| {{cells|104}}
|-
! {{period|59|brief}}
| [[p59 Herschel loop 1]]
|David Buckingham
| 1997
| [[Adjustable glider loop|p59 Snark loop]]
|{{cells|228}}
|-
! {{period|60|brief}}
| [[p60 glider shuttle]]
|David Buckingham
| ≤ 1971
| [[mold on pentadecathlon]]
| {{cells|24}}
|-
! {{period|61|brief}}
| [[p61 Herschel loop 1]]
|David Buckingham
| {{year|1996}}
| [[Adjustable glider loop|p61 Snark loop]]
|{{cells|228}}
|-
! {{period|62|brief}}
| ?
| ?
| ?
| [[66P62]]
| {{cells|66}}
|-
! {{period|63|brief}}
| ?
| ?
| ?
| [[snacker on 38P7.2]]
| {{cells|78}}
|-
! {{period|64|brief}}
| ?
| ?
| ?
| [[Merzenich's p64]]
| {{cells|34}}
|-
! {{period|65|brief}}
| ?
| ?
| ?
| [[fumarole on Beluchenko's p13]]
| {{cells|52}}
|-
! {{period|66|brief}}
| ?
| ?
| ?
| [[caterer on Jason's p22]]
| {{cells|48}}
|-
! {{period|67|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p67 Snark loop]]
|{{cells|228}}
|-
! {{period|68|brief}}
| ?
| ?
| ?
| [[72P68]]
|{{cells|72}}
|-
! {{period|69|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p69 bumper loop]]
|{{cells|152}}
|-
! {{period|70|brief}}
| ?
| ?
| ?
| [[fumarole on 34P14 shuttle]]
| {{cells|52}}
|-
! {{period|71|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p71 Snark loop]]
|{{cells|228}}
|-
! {{period|72|brief}}
| [[two blockers hassling R-pentomino]]
|Robert Wainwright
| 1990
| [[figure eight on 22P36]]
| {{cells|36}}
|-
! {{period|73|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p73 Snark loop]]
|{{cells|228}}
|-
! {{period|74|brief}}
| p74 Herschel loop
|David Buckingham
| 1996
| [[Raucci's p74]]
| {{cells|84}}
|-
! {{period|75|brief}}
| ?
| ?
| ?
| [[6 bits]]
|{{cells|49}}
|-
! {{period|76|brief}}
| ?
| ?
| ?
| [[p76 pi-heptomino hassler]]
| {{cells|57}}
|-
! {{period|77|brief}}
| ?
| ?
| ?
| [[77P77]]
|{{cells|77}}
|-
! {{period|78|brief}}
| ?
| ?
| ?
| [[p6 thumb on Beluchenko's p13]]
|{{cells|61}}
|-
! {{period|79|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p79 Snark loop]]
|{{cells|228}}
|-
! {{period|80|brief}}
| ?
| ?
| ?
| [[fumarole on Rob's p16]]
| {{cells|39}}
|-
! {{period|81|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p81 bumper loop]]
|{{cells|152}}
|-
! {{period|82|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p82 Snark loop]]
|{{cells|208}}
|-
! {{period|83|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p83 Snark loop]]
|{{cells|228}}
|-
! {{period|84|brief}}
| ?
| ?
| ?
| [[52P84]]
| {{cells|52}}
|-
! {{period|85|brief}}
| ?
| ?
| ?
| [[74P85]]
|{{cells|74}}
|-
! {{period|86|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p86 Snark loop]]
|{{cells|208}}
|-
! {{period|87|brief}}
| ?
| ?
| ?
| [[84P87]]
| {{cells|84}}
|-
! {{period|88|brief}}
| p88 glider loop
|David Buckingham
| 1992
| [[figure eight on rattlesnake]]
| {{cells|45}}
|-
! {{period|89|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p89 Snark loop]]
|{{cells|228}}
|-
! {{period|90|brief}}
| ?
| ?
| ?
| [[thumb 1 on queen bee shuttle]]
| {{cells|56}}
|-
! {{period|91|brief}}
| ?
| ?
| ?
| [[44P7 on Beluchenko's p13]]
|{{cells|78}}
|-
! {{period|92|brief}}
| ?
| ?
| ?
| [[50P92.1]], [[twin bees shuttle on 22P4.3]]
| {{cells|50}}
|-
! {{period|93|brief}}
| ?
| ?
| ?
| [[caterer on Merzenich's p31]]
|{{cells|60}}
|-
! {{period|94|brief}}
| capped [[AK-47 reaction|AK-47]] gun
|Dean Hickerson
| 1990
| {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]]
| {{cells|110}}
|-
! {{period|95|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p95 Snark loop]]
|{{cells|228}}
|-
! {{period|96|brief}}
| ?
| ?
| ?
| [[period-48 glider gun]] {{LinkCatagolue|xp96_0178cy766zy44koy6m640ooe4a4z0gs26x11xoy1oo022440ezo8go|patternname=with boat-bit|style=raw}}
| {{cells|59}}
|-
! {{period|97|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p97 Snark loop]]
|{{cells|228}}
|-
! {{period|98|brief}}
| ?
| ?
| ?
| [[Gallus]]
| {{cells|105}}
|-
! {{period|99|brief}}
| ?
| ?
| ?
| [[48P9 on rattlesnake]]
|{{cells|82}}
|-
! {{period|100|brief}}
| [[centinal]]
|Bill Gosper
| ≤{{year|1987}}
| [[centinal]]
| {{cells|70}}
|-
! {{period|101|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p101 Snark loop]]
|{{cells|228}}
|-
! {{period|102|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp102_w660259gcy5ca23z8oy166y06msz0123wggyqcczy11243ykccwsq66zoomewccykg8gz0ccyp12210ggzyleqoy0oox1074zyeggkcy5c248g0oozye1ya11|patternname=p102 bumper loop|style=raw}}
| {{cells|122}}
|-
! {{period|103|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p103 Snark loop]]
|{{cells|228}}
|-
! {{period|104|brief}}
| ?
| ?
| ?
| [[figure eight on Beluchenko's p13]]
| {{cells|46}}
|-
! {{period|105|brief}}
| ?
| ?
| ?
| [[pentadecathlon on 37P7.1]]
|{{cells|49}}
|-
! {{period|106|brief}}
| ?
| ?
| ?
| [[rectifier|p106 rectifier loop]]
|{{cells|169}}
|-
! {{period|107|brief}}
| ?
| ?
| ?
| [[rectifier|p107 rectifier loop]]
|{{cells|136}}
|-
! {{period|108|brief}}
| ?
| ?
| ?
| [[22P4.3 on 56P27]]
|{{cells|78}}
|-
! {{period|109|brief}}
| ?
| ?
| ?
| [[rectifier|p109 rectifier loop]]
|{{cells|156}}
|-
! {{period|110|brief}}
| [[p110 traffic jam]]
|Bill Gosper
| 1994
| [[pseudo-barberpole on Jason's p22]]
|{{cells|51}}
|-
! {{period|111|brief}}
| ?
| ?
| ?
| [[rectifier|p111 rectifier loop]]
|{{cells|136}}
|-
! {{period|112|brief}}
| ?
| ?
| ?
| [[tumbler on Rich's p16]]
|{{cells|50}}
|-
! {{period|113|brief}}
| ?
| ?
| ?
| [[nihonium]]
| {{cells|106}}
|-
! {{period|114|brief}}
| ?
| ?
| ?
| [[Ocellus]]
|{{cells|92}}
|-
! {{period|115|brief}}
| ?
| ?
| ?
| [[rectifier|p115 rectifier loop]]
|{{cells|136}}
|-
! {{period|116|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=102P116|style=raw}}
|{{cells|102}}
|-
! {{period|117|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp117_y1o44mhar0rahm44ozwg8p7870167876107871zq6hcbagy1szg9gf99gfy26a8oz56o3t5zx1|patternname=117P117|style=raw}}
| {{cells|117}}
|-
! {{period|118|brief}}
| ?
| ?
| ?
| [[rectifier|p118 rectifier loop]]
|{{cells|154}}
|-
! {{period|119|brief}}
| ?
| ?
| ?
| [[rectifier|p119 rectifier loop]]
|{{cells|136}}
|-
! {{period|120|brief}}
| ?
| ?
| ?
| [[figure eight on pentadecathlon]]
| {{cells|24}}
|-
! {{period|121|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|122|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|123|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|124|brief}}
| [[p124 lumps of muck hassler]]
|Dean Hickerson
| 1994
| [[mold on Merzenich's p31]]
| {{cells|60}}
|-
! {{period|125|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|126|brief}}
| ?
| ?
| ?
| [[snacker on 34P14 shuttle]]
| {{cells|74}}
|-
! {{period|127|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|128|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp128_y3ca73oswcczyqg88gzy1ggyh6bbcxca4z8ko010onmcy04eewuscy26dt30g0352z4a6x6qqcyh11zy01221zyh66w73osa6|patternname=p128 wing hassler|style=raw}}
|{{cells|108}}
|-
! {{period|129|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p129 bumper loop]]
|{{cells|152}}
|-
! {{period|130|brief}}
| ?
| ?
| ?
| [[55P10 on Beluchenko's p13]]
| {{cells|89}}
|-
! {{period|131|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|132|brief}}
| p132 glider loop
|David Buckingham
| 1992
| [[mold on Jason's p33]]
| {{cells|72}}
|-
! {{period|133|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|134|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|135|brief}}
| [[106P135]]
|Bill Gosper
| {{year|1989}}
| [[pentadecathlon on 56P27]]
|{{cells|68}}
|-
! {{period|136|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|137|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|138|brief}}
| ?
| ?
| ?
| [[Gabriel's p138]]
| {{cells|36}}
|-
! {{period|139|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|140|brief}}
| p140 traffic jam
|Bill Gosper
| 1994
| [[34P14 shuttle on dockyard]]
| {{cells|82}}
|-
! {{period|141|brief}}
| ?
| ?
| ?
| [[p47 pre-pulsar shuttle phase-shifting 28P7.1]]
| {{cells|114}}
|-
! {{period|142|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|143|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|144|brief}}
| capped p144 [[gunstar]]
|David Buckingham
| 1990
| [[Achim's p144]]
| {{cells|42}}
|-
! {{period|150|brief}}
| ?
| ?
| ?
| [[buckaroo|p150 buckaroo shuttle]]
| {{cells|51}}
|-
! {{period|152|brief}}
| ?
| ?
| ?
| [[figure eight on p76 pi-heptomino hassler]]
| {{cells|94}}
|-
! {{period|156|brief}}
| p156 [[traffic jam]] oscillator
|Bill Gosper
| 1994
| [[Jason's p156]]
| {{cells|92}}
|-
! {{period|165|brief}}
| ?
| ?
| ?
| [[rattlesnake on pentadecathlon]]
| {{cells|45}}
|-
! {{period|168|brief}}
| ?
| ?
| ?
| [[figure eight on p21 honey farm hassler]]
| {{cells|72}}
|-
! {{period|177|brief}}
| ?
| ?
| ?
| [[Karel's p177]]
| {{cells|104}}
|-
! {{period|184|brief}}
| ?
| ?
| ?
| [[figure eight on twin bees shuttle]]
| {{cells|40}}
|-
! {{period|186|brief}}
| ?
| ?
| ?
| [[unix on Merzenich's p31]]
| {{cells|64}}
|-
! {{period|188|brief}}
| ?
| ?
| ?
| [[AK-94]] {{LinkCatagolue|xp188_x696o8b9czy065x33xc871wbdzoozwgg04ahhha4y5c871z4701yfoozxggy0ggzx56w4701xmmggo5jzya146w343|patternname=with boat-bits|style=raw}}
| {{cells|108}}
|-
! {{period|196|brief}}
| ?
| ?
| ?
| [[p196 pi-heptomino hassler]]
| {{cells|66}}
|-
! {{period|200|brief}}
| p200 glider loop
|Bill Gosper
| ≤{{year|1987}}
| [[figure eight on centinal]]
|{{cells|82}}
|-
! {{period|226|brief}}
| ?
| ?
| ?
| [[nihonium*]]
| {{cells|107}}
|-
! {{period|230|brief}}
| ?
| ?
| ?
| [[fumarole on twin bees shuttle]]
|{{cells|46}}
|-
! {{period|232|brief}}
| ?
| ?
| ?
| [[figure eight on p29 pre-pulsar shuttle]]
|{{cells|66}}
|-
! {{period|240|brief}}
| ?
| ?
| ?
| [[pentadecathlon on Rob's p16]]
| {{cells|33}}
|-
! {{period|246|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp246_ya32acydg8k8ooozyu1utzzzybcirrd6y4cc4zy1ggy61zggwg9g89z14w61ye354c|patternname=relative|style=raw}}
| {{cells|68}}
|-
! {{period|256|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp256_yr33y166z0ggy033y4178cyb33y0ccz011w66z66yyg88czy4699voyn11zy38ox61zy1311yz66zyzx66woozy133y0ccyb31e8y4cczy566y1cc|patternname=capped|style=raw}} [[period-256 glider gun]]
| {{cells|104}}
|-
! {{period|276|brief}}
| ?
| ?
| ?
| [[caterer on 50P92.1]]
| {{cells|62}}
|-
! {{period|300|brief}}
| ?
| ?
| ?
| [[pentadecathlon on centinal]]
| {{cells|88}}
|-
! {{period|312|brief}}
| ?
| ?
| ?
| [[60P312]]
| {{cells|60}}
|-
! {{period|320|brief}}
| ?
| ?
| ?
| [[fumarole on Merzenich's p64]]
| {{cells|52}}
|-
! {{period|360|brief}}
| ?
| ?
| ?
| [[thumb 1 on Beluchenko's p40]]
| {{cells|62}}
|-
! {{period|368|brief}}
| ?
| ?
| ?
| [[period-184 glider gun]] {{LinkCatagolue|xp368_y0gy632aczy01156zzggyp62sgz56yc65134w16zync4ozy8o8goy911|patternname=with boat-bits|style=raw}}
| {{cells|50}}
|-
! {{period|460|brief}}
| ?
| ?
| ?
| [[pseudo-barberpole on 50P92.1]]
| {{cells|65}}
|-
! {{period|492|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp492_y0o4qa344ozx118f0dc3z8oyago0ab2sycc871z0123y9126e431zy8ooz0mqzyt66w7bcczyy66|patternname=with boat-bit|style=raw}}
| {{cells|87}}
|-
! {{period|496|brief}}
| ?
| ?
| ?
| [[Rob's p16 on Merzenich's p31]]
| {{cells|69}}
|-
! {{period|504|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp504_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzyzygg88gxooy1uu06666mmzyzygcc07xccy1rroooo0vvzyzyh66|patternname=p504 glider shuttle|style=raw}}
| {{cells|109}}
|-
! {{period|512|brief}}
| ?
| ?
| ?
| [[period-256 glider gun]] {{LinkCatagolue|xp512_yr33y166z0ggy033y16426ye33y0ccz011w66yuggz66yz56zzzy2mqyz66zygckgk2a21ya66woozy133y0ccye6426y1cczy566y1cc|patternname=with boat-bits|style=raw}}
| {{cells|100}}
|-
! {{period|856|brief}}
| [[period-856 glider gun]]
| [[David Buckingham]]
| 1991
| {{LinkCatagolue|xp856_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzzzzzzzzzzyzyzyl844oxccy1vv03333rrzyzyzyl6603x66y1ddcccc0ffzyzyzym33|patternname=p856 glider shuttle|style=raw}}
|{{cells|109}}
|-
! {{period|1008|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp1008_y48oyc356zy432yi696y9o8gozyjc871zzy12552yg2bq4y4o8zca6y3oggyp113y3ca6zy823ys8kk8zzyogs26zx3123y9cicyi8ozymckoyc32|patternname=R126 loop with boat-bits|style=raw}}
| {{cells|107}}
|}

==Flipper==
A '''flipper''' is any [[oscillator]] that forms its mirror image halfway through its [[period]].

==Notes==
<references group=note />

==See also==
*[[List of common oscillators]]
*[[:Category:Flipping oscillators|List of flipping oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
*[[Table of oscillators by period]]
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]

==External links==
{{LinkWikipedia|Oscillator_(cellular_automaton)}}
{{LinkLexicon|lex_o.htm#oscillator}}
{{LinkLexicon|lex_f.htm#flipper|name=Flipper}}

===Forum threads===
{{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
{{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
{{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}

__NOTOC__

Kinetic symmetry

2022-01-12T12:08:37Z

Freywa: /* Oscillators */ the rest of them

A '''kinetic symmetry''' (contrast [[static symmetry]]) describes the spatial and temporal symmetries of a periodic pattern such as a [[still life]], [[oscillator]] or [[spaceship]]. It combines a pattern's spatial (rotational and reflectional) symmetries from the more general [[static symmetry]] with symmetrical transformations of said pattern arising from its evolution.<ref name="post138823" />

== On a square grid ==
There are a total of 43 different kinetic symmetries possible on a usual [[square grid]], comprised of the 16 static symmetries (D8_2 is excluded) with 27 possible time transformations.

Oscillators have a much wider range of possible kinetic symmetries than still lifes. It is very easy to see that the 27 time transformations cannot apply to still lifes by definition, as they require the pattern to have distinct phases which can be compared to each other, and therefore for the pattern to evolve, which still lifes do not. As such, oscillators can only have 16 of the possible 43 kinetic symmetry types, which therefore corresponds with the 16 different static symmetry types. The symmetry class is the symmetry class of the oscillator in a single generation followed by the symmetry class of the union of the generation and its congruent successors.<ref>{{CiteHickersonOscillators|accessdate=December 13, 2021}}</ref>

Both still lifes and oscillators can exhibit a wider range than spaceships can, at least as far as isotropic rules are concerned. Many higher kinetic symmetries, notably those involving rotation or with reflection happening on more than one axis, would forbid the pattern from having a nonzero displacement, as the symmetry would either force it to move in two directly opposing directions or redirect it back to its starting point. Many spaceships can have glide symmetry, which oscillators cannot have due to having no overall displacement, however glide symmetry very closely resembles certain mirror symmetries which oscillators do exhibit.

The ratio of a pattern's [[mod]] to its [[period]], for rules on a square grid, can only be 1, 2 or 4.

=== Kinetic symmetry naming system ===
[[Dean Hickerson]] invented a compact naming system for kinetic symmetries.

For still lifes, as well as oscillators and spaceships which have identical mods to periods, an initial symbol stand for a kind of transformation, and a symbol following it refers to the type of region where said transformation is centered.

Oscillators and spaceships of unequal period and mod will follow this string with another string detailing how the pattern is transformed after cycling through its mod.

Hickerson's naming scheme initially used "c" for the center of a cell and "k" for the vertex of a cell - these have been revised to "f" for the face of a cell and "v" for the vertex of a cell to clarify things and reduce any confusion that may arise due to homophones.

==== Symbols ====
{| class="wikitable"
! Hickerson name
! Wiki name
! Meaning
|-
! colspan="2" | n
| No symmetry
|-
! colspan="2" | -
| One line of orthogonal mirror symmetry
|-
! colspan="2" | /
| One line of diagonal mirror symmetry
|-
! colspan="2" | +
| Two lines of orthogonal mirror symmetry
|-
! colspan="2" | x
| Two lines of diagonal mirror symmetry
|-
! colspan="2" | *
| Two lines each of orthogonal and diagonal mirror symmetry
|-
! colspan="2" | r
| 90-degree rotational symmetry
|-
! colspan="2" | .
| 180-degree rotational symmetry
|-
! c
! f
| Transformation is centered on the center of a cell
|-
! colspan="2" | e
| Transformation is centered on the edge of a cell
|-
! k
! v
| Transformation is centered on the vertex of a cell
|}

=== List ===
==== Still lifes ====
These are equivalent to static symmetries (excluding D8_2). The corresponding static symmetries are detailed in the table for each type.

{| class="wikitable"
! Equivalent static symmetry
! Hickerson name
! Wiki name
! Description
! Example
! Image
|-
! C1
! colspan="2" | n
| No symmetry
| [[Eater 1]]
| [[File:Symmetry C1.png|33px]]
|-
! D2_+1
! -c
! -f
| One line of orthogonal mirror symmetry Line passes through cell centers and edges
| [[Hat]]
| [[File:Symmetry D2_+1.png|33px]]
|-
! D2_+2
! colspan="2" | -e
| One line of orthogonal mirror symmetry Line passes through cell edges and vertices
| [[Cap and table]]
| [[File:Symmetry D2_+2.png|33px]]
|-
! D2_x
! colspan="2" | /
| One line of diagonal mirror symmetry
| [[Boat]]
| [[File:Symmetry D2_x.png|33px]]
|-
! C2_1
! .c
! .f
| 180-degree rotation Rotation is centered on the center of a cell
| [[Long snake]]
| [[File:Symmetry C2_1.png|33px]]
|-
! C2_2
! colspan="2" | .e
| 180-degree rotation Rotation is centered on the edge of a cell
| [[Aircraft carrier]]
| [[File:Symmetry C2_2.png|33px]]
|-
! C2_4
! .k
! .v
| 180-degree rotation Rotation is centered on the vertex of a cell
| [[Snake]]
| [[File:Symmetry C2_4.png|33px]]
|-
! D4_+1
! +c
! +f
| Two lines of orthogonal mirror symmetry Both lines pass through cell centers and edges
| [[Hat siamese hat]]
| [[File:Symmetry D4_+1.png|33px]]
|-
! D4_+2
! colspan="2" | +e
| Two lines of orthogonal mirror symmetry One lines passes through cell centers and edges One line passes through cell edges and vertices
| [[Beehive]]
| [[File:Symmetry D4_+2.png|33px]]
|-
! D4_+4
! +k
! +v
| Two lines of orthogonal mirror symmetry Both lines pass through cell edges and vertices
| (1.5.4)
| [[File:Symmetry D4_+4.png|33px]]
|-
! D4_x1
! xc
! xf
| Two lines of diagonal mirror symmetry Lines meet at the center of a cell
| [[Ship]]
| [[File:Symmetry D4_x1.png|33px]]
|-
! D4_x4
! xk
! xv
| Two lines of diagonal mirror symmetry Lines meet at the vertex of a cell
| [[Barge]]
| [[File:Symmetry D4_x4.png|33px]]
|-
! C4_1
! rc
! rf
| 90-degree rotation Rotation is centered on the center of a cell
| [[Spiral]]
| [[File:Symmetry C4_1.png|33px]]
|-
! C4_4
! rk
! rv
| 90-degree rotation Rotation is centered on the vertex of a cell
| (1.5.5)
| [[File:Symmetry C4_4.png|33px]]
|-
! D8_1
! *c
! *f
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell centers and edges
| [[Tub]]
| [[File:Symmetry D8_1.png|33px]]
|-
! D8_4
! *k
! *v
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell edges and vertices
| [[Block]]
| [[File:Symmetry D8_4.png|33px]]
|}

==== Oscillators ====
For oscillators which have a mod identical to their period, refer to the still lifes table above.

"Composite symmetry" refers to the resulting symmetry of the pattern created from each of the oscillator's "identical" phases:
* for patterns with a mod half their period, the union of the pattern's initial state and the state it appears in at half its period
* for patterns with a mod a quarter their period, the union of the pattern's initial phase, generation (period/4), generation (period/2) and generation (3period/4)

{| class="wikitable"
! Hickerson name
! Wiki name
! Static symmetry
! Composite symmetry
! period/mod
! Description
! Example
! Image
|-
! n-c
! n-f
! C1
! D2_+1
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell centers and edges
| [[Champagne glass]]
| pending
|-
! colspan="2" | n-e
! C1
! D2_+2
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell edges and vertices
| [[Rob's p16]]
| pending
|-
! colspan="2" | n/
! C1
! D2_x
| 2
| Pattern is asymmetric Appears flipped across a diagonal line during (period/2)
| [[30P6.1]]
| pending
|-
! n.c
! n.f
! C1
! C2_1
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the center of a cell
| [[Baker's dozen]]
| pending
|-
! colspan="2" | n.e
! C1
! C2_2
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the edge of a cell
| Trans-[[queen bee shuttle]]
| pending
|-
! n.k
! n.v
! C1
! C2_4
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the vertex of a cell
| [[Blocker]]
| pending
|-
! nrc
! nrf
! C1
! C4_1
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the center of a cell
| [[Four eaters hassling lumps of muck]]
| pending
|-
! nrk
! nrv
! C1
! C4_4
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the vertex of a cell
| [[Twirling T-tetsons 2]]
| pending
|-
! -c+c
! -f+f
! D2_+1
! D4_+1
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| [[Tumbler]]
| pending
|-
! -c+e
! -f+e
! D2_+1
! D4_+2
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| [[Eureka]]
| pending
|-
! -e+e
! -e+e
! D2_+2
! D4_+2
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| Fully symmetric [[heavyweight emulator]]
| pending
|-
! -e+k
! -e+v
! D2_+2
! D4_+4
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| [[p30 traffic light hassler]]
| pending
|-
! /xc
! /xf
! D2_x
! D4_x1
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the center of a cell
| [[46P10]]
| pending
|-
! /xk
! /xv
! D2_x
! D4_x4
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the vertex of a cell
| [[p24 shuttle]]
| pending
|-
! .c+c
! .f+f
! C2_1
! D4_+1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
| [[2.2.6]]
| pending
|-
! .cxc
! .fxf
! C2_1
! D4_x1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the center of a cell
| [[Achim's p8]]
| pending
|-
! .crc
! .frf
! C2_1
! C4_1
| 2
| Pattern has C2_1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the center of a cell
| [[Merzenich's p64]]
| pending
|-
! .e+e
! .e+e
! C2_2
! D4_+2
| 2
| Pattern has C2_2 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Line may pass through either cell centers and edges, or cell edges and vertices
| [[Achim's p144]]
| pending
|-
! .k+k
! .v+v
! C2_4
! D4_+4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| [[Two pre-L hasslers]]
| pending
|-
! .kxk
! .vxv
! C2_4
! D4_x4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the vertex of a cell
| [[p196 pi-heptomino hassler]]
| pending
|-
! .krk
! .vrv
! C2_4
! C4_4
| 2
| Pattern has C2_4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the vertex of a cell
| [[Windmill]]
| pending
|-
! +c*c
! +f*f
! D4_+1
! D8_1
| 2
| Pattern has D4_+1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[68P32.1]]
| pending
|-
! +k*k
! +v*v
! D4_+4
! D8_4
| 2
| Pattern has D4_+4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| [[A for all]]
| pending
|-
! xc*c
! xf*f
! D4_x1
! D8_1
| 2
| Pattern has D4_x1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[Washing machine]]
| pending
|-
! xk*k
! xv*v
! D4_x4
! D8_4
| 2
| Pattern has D4_x4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| [[Unicycle]]
| pending
|-
! rc*c
! rf*f
! C4_1
! D8_1
| 2
| Pattern has C4_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
| [[Achim's p16]]
| pending
|-
! rk*k
! rv*v
! C4_4
! D8_4
| 2
| Pattern has C4_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| [[44P10]]
| pending
|}

{{EmbedViewer
|viewerconfig = #C [[ GPS 20 THUMBLAUNCH THUMBSIZE 2 WIDTH 2000 HEIGHT 1500 THEME 6 ]]
|pname = temporalsymmetrytypes
|position = center
|caption = All 43 temporal symmetry types}}

== On a hexagonal grid ==
There does not seem to have been an attempt at describing all possible oscillator and spaceship time symmetries on {6,3} and {3,6} so far.

== References ==
<references>
<ref name="post138823">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 138823
|author = GUYTU6J
|date = December 13, 2021
}}</ref>
</references>

[[Category:Everything else]]

Kinetic symmetry

2022-01-12T12:01:31Z

Freywa: /* Oscillators */ import some oscillators from my stamp collection at https://conwaylife.com/forums/viewtopic.php?f=2&t=1437&p=134265

A '''kinetic symmetry''' (contrast [[static symmetry]]) describes the spatial and temporal symmetries of a periodic pattern such as a [[still life]], [[oscillator]] or [[spaceship]]. It combines a pattern's spatial (rotational and reflectional) symmetries from the more general [[static symmetry]] with symmetrical transformations of said pattern arising from its evolution.<ref name="post138823" />

== On a square grid ==
There are a total of 43 different kinetic symmetries possible on a usual [[square grid]], comprised of the 16 static symmetries (D8_2 is excluded) with 27 possible time transformations.

Oscillators have a much wider range of possible kinetic symmetries than still lifes. It is very easy to see that the 27 time transformations cannot apply to still lifes by definition, as they require the pattern to have distinct phases which can be compared to each other, and therefore for the pattern to evolve, which still lifes do not. As such, oscillators can only have 16 of the possible 43 kinetic symmetry types, which therefore corresponds with the 16 different static symmetry types. The symmetry class is the symmetry class of the oscillator in a single generation followed by the symmetry class of the union of the generation and its congruent successors.<ref>{{CiteHickersonOscillators|accessdate=December 13, 2021}}</ref>

Both still lifes and oscillators can exhibit a wider range than spaceships can, at least as far as isotropic rules are concerned. Many higher kinetic symmetries, notably those involving rotation or with reflection happening on more than one axis, would forbid the pattern from having a nonzero displacement, as the symmetry would either force it to move in two directly opposing directions or redirect it back to its starting point. Many spaceships can have glide symmetry, which oscillators cannot have due to having no overall displacement, however glide symmetry very closely resembles certain mirror symmetries which oscillators do exhibit.

The ratio of a pattern's [[mod]] to its [[period]], for rules on a square grid, can only be 1, 2 or 4.

=== Kinetic symmetry naming system ===
[[Dean Hickerson]] invented a compact naming system for kinetic symmetries.

For still lifes, as well as oscillators and spaceships which have identical mods to periods, an initial symbol stand for a kind of transformation, and a symbol following it refers to the type of region where said transformation is centered.

Oscillators and spaceships of unequal period and mod will follow this string with another string detailing how the pattern is transformed after cycling through its mod.

Hickerson's naming scheme initially used "c" for the center of a cell and "k" for the vertex of a cell - these have been revised to "f" for the face of a cell and "v" for the vertex of a cell to clarify things and reduce any confusion that may arise due to homophones.

==== Symbols ====
{| class="wikitable"
! Hickerson name
! Wiki name
! Meaning
|-
! colspan="2" | n
| No symmetry
|-
! colspan="2" | -
| One line of orthogonal mirror symmetry
|-
! colspan="2" | /
| One line of diagonal mirror symmetry
|-
! colspan="2" | +
| Two lines of orthogonal mirror symmetry
|-
! colspan="2" | x
| Two lines of diagonal mirror symmetry
|-
! colspan="2" | *
| Two lines each of orthogonal and diagonal mirror symmetry
|-
! colspan="2" | r
| 90-degree rotational symmetry
|-
! colspan="2" | .
| 180-degree rotational symmetry
|-
! c
! f
| Transformation is centered on the center of a cell
|-
! colspan="2" | e
| Transformation is centered on the edge of a cell
|-
! k
! v
| Transformation is centered on the vertex of a cell
|}

=== List ===
==== Still lifes ====
These are equivalent to static symmetries (excluding D8_2). The corresponding static symmetries are detailed in the table for each type.

{| class="wikitable"
! Equivalent static symmetry
! Hickerson name
! Wiki name
! Description
! Example
! Image
|-
! C1
! colspan="2" | n
| No symmetry
| [[Eater 1]]
| [[File:Symmetry C1.png|33px]]
|-
! D2_+1
! -c
! -f
| One line of orthogonal mirror symmetry Line passes through cell centers and edges
| [[Hat]]
| [[File:Symmetry D2_+1.png|33px]]
|-
! D2_+2
! colspan="2" | -e
| One line of orthogonal mirror symmetry Line passes through cell edges and vertices
| [[Cap and table]]
| [[File:Symmetry D2_+2.png|33px]]
|-
! D2_x
! colspan="2" | /
| One line of diagonal mirror symmetry
| [[Boat]]
| [[File:Symmetry D2_x.png|33px]]
|-
! C2_1
! .c
! .f
| 180-degree rotation Rotation is centered on the center of a cell
| [[Long snake]]
| [[File:Symmetry C2_1.png|33px]]
|-
! C2_2
! colspan="2" | .e
| 180-degree rotation Rotation is centered on the edge of a cell
| [[Aircraft carrier]]
| [[File:Symmetry C2_2.png|33px]]
|-
! C2_4
! .k
! .v
| 180-degree rotation Rotation is centered on the vertex of a cell
| [[Snake]]
| [[File:Symmetry C2_4.png|33px]]
|-
! D4_+1
! +c
! +f
| Two lines of orthogonal mirror symmetry Both lines pass through cell centers and edges
| [[Hat siamese hat]]
| [[File:Symmetry D4_+1.png|33px]]
|-
! D4_+2
! colspan="2" | +e
| Two lines of orthogonal mirror symmetry One lines passes through cell centers and edges One line passes through cell edges and vertices
| [[Beehive]]
| [[File:Symmetry D4_+2.png|33px]]
|-
! D4_+4
! +k
! +v
| Two lines of orthogonal mirror symmetry Both lines pass through cell edges and vertices
| (1.5.4)
| [[File:Symmetry D4_+4.png|33px]]
|-
! D4_x1
! xc
! xf
| Two lines of diagonal mirror symmetry Lines meet at the center of a cell
| [[Ship]]
| [[File:Symmetry D4_x1.png|33px]]
|-
! D4_x4
! xk
! xv
| Two lines of diagonal mirror symmetry Lines meet at the vertex of a cell
| [[Barge]]
| [[File:Symmetry D4_x4.png|33px]]
|-
! C4_1
! rc
! rf
| 90-degree rotation Rotation is centered on the center of a cell
| [[Spiral]]
| [[File:Symmetry C4_1.png|33px]]
|-
! C4_4
! rk
! rv
| 90-degree rotation Rotation is centered on the vertex of a cell
| (1.5.5)
| [[File:Symmetry C4_4.png|33px]]
|-
! D8_1
! *c
! *f
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell centers and edges
| [[Tub]]
| [[File:Symmetry D8_1.png|33px]]
|-
! D8_4
! *k
! *v
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell edges and vertices
| [[Block]]
| [[File:Symmetry D8_4.png|33px]]
|}

==== Oscillators ====
For oscillators which have a mod identical to their period, refer to the still lifes table above.

"Composite symmetry" refers to the resulting symmetry of the pattern created from each of the oscillator's "identical" phases:
* for patterns with a mod half their period, the union of the pattern's initial state and the state it appears in at half its period
* for patterns with a mod a quarter their period, the union of the pattern's initial phase, generation (period/4), generation (period/2) and generation (3period/4)

{| class="wikitable"
! Hickerson name
! Wiki name
! Static symmetry
! Composite symmetry
! period/mod
! Description
! Example
! Image
|-
! n-c
! n-f
! C1
! D2_+1
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell centers and edges
| (2.2.4)
| pending
|-
! colspan="2" | n-e
! C1
! D2_+2
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell edges and vertices
| [[Griddle and block]]
| pending
|-
! colspan="2" | n/
! C1
! D2_x
| 2
| Pattern is asymmetric Appears flipped across a diagonal line during (period/2)
| [[Muttering moat 1]]
| pending
|-
! n.c
! n.f
! C1
! C2_1
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the center of a cell
| (2.2.7)
| pending
|-
! colspan="2" | n.e
! C1
! C2_2
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the edge of a cell
| [[Laputa]]
| pending
|-
! n.k
! n.v
! C1
! C2_4
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the vertex of a cell
| (2.2.0)
| pending
|-
! nrc
! nrf
! C1
! C4_1
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the center of a cell
| [[Sixty-nine]]
| pending
|-
! nrk
! nrv
! C1
! C4_4
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the vertex of a cell
| [[Dinner table]]
| pending
|-
! -c+c
! -f+f
! D2_+1
! D4_+1
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| [[Piston]]
| pending
|-
! -c+e
! -f+e
! D2_+1
! D4_+2
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| [[by flops]]
| pending
|-
! -e+e
! -e+e
! D2_+2
! D4_+2
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| (2.5.0)
| pending
|-
! -e+k
! -e+v
! D2_+2
! D4_+4
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| (2.5.2)
| pending
|-
! /xc
! /xf
! D2_x
! D4_x1
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the center of a cell
| (2.4.2)
| pending
|-
! /xk
! /xv
! D2_x
! D4_x4
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the vertex of a cell
| [[Tripole]]
| pending
|-
! .c+c
! .f+f
! C2_1
! D4_+1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
| (2.4.0)
| pending
|-
! .cxc
! .fxf
! C2_1
! D4_x1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the center of a cell
| [[Bipole]]
| pending
|-
! .crc
! .frf
! C2_1
! C4_1
| 2
| Pattern has C2_1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the center of a cell
| (2.5.5)
| pending
|-
! .e+e
! .e+e
! C2_2
! D4_+2
| 2
| Pattern has C2_2 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Line may pass through either cell centers and edges, or cell edges and vertices
| (2.6.1)
| pending
|-
! .k+k
! .v+v
! C2_4
! D4_+4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| (2.3.3)
| pending
|-
! .kxk
! .vxv
! C2_4
! D4_x4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the vertex of a cell
| [[Clock]]
| pending
|-
! .krk
! .vrv
! C2_4
! C4_4
| 2
| Pattern has C2_4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the vertex of a cell
| (2.8.0)
| pending
|-
! +c*c
! +f*f
! D4_+1
! D8_1
| 2
| Pattern has D4_+1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[68P32.1]]
| pending
|-
! +k*k
! +v*v
! D4_+4
! D8_4
| 2
| Pattern has D4_+4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| [[A for all]]
| pending
|-
! xc*c
! xf*f
! D4_x1
! D8_1
| 2
| Pattern has D4_x1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[Washing machine]]
| pending
|-
! xk*k
! xv*v
! D4_x4
! D8_4
| 2
| Pattern has D4_x4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| [[Unicycle]]
| pending
|-
! rc*c
! rf*f
! C4_1
! D8_1
| 2
| Pattern has C4_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
| [[Achim's p16]]
| pending
|-
! rk*k
! rv*v
! C4_4
! D8_4
| 2
| Pattern has C4_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| [[44P10]]
| pending
|}

{{EmbedViewer
|viewerconfig = #C [[ GPS 20 THUMBLAUNCH THUMBSIZE 2 WIDTH 2000 HEIGHT 1500 THEME 6 ]]
|pname = temporalsymmetrytypes
|position = center
|caption = All 43 temporal symmetry types}}

== On a hexagonal grid ==
There does not seem to have been an attempt at describing all possible oscillator and spaceship time symmetries on {6,3} and {3,6} so far.

== References ==
<references>
<ref name="post138823">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 138823
|author = GUYTU6J
|date = December 13, 2021
}}</ref>
</references>

[[Category:Everything else]]

Kinetic symmetry

2022-01-12T11:31:38Z

Freywa: /* Still lifes */

A '''kinetic symmetry''' (contrast [[static symmetry]]) describes the spatial and temporal symmetries of a periodic pattern such as a [[still life]], [[oscillator]] or [[spaceship]]. It combines a pattern's spatial (rotational and reflectional) symmetries from the more general [[static symmetry]] with symmetrical transformations of said pattern arising from its evolution.<ref name="post138823" />

== On a square grid ==
There are a total of 43 different kinetic symmetries possible on a usual [[square grid]], comprised of the 16 static symmetries (D8_2 is excluded) with 27 possible time transformations.

Oscillators have a much wider range of possible kinetic symmetries than still lifes. It is very easy to see that the 27 time transformations cannot apply to still lifes by definition, as they require the pattern to have distinct phases which can be compared to each other, and therefore for the pattern to evolve, which still lifes do not. As such, oscillators can only have 16 of the possible 43 kinetic symmetry types, which therefore corresponds with the 16 different static symmetry types. The symmetry class is the symmetry class of the oscillator in a single generation followed by the symmetry class of the union of the generation and its congruent successors.<ref>{{CiteHickersonOscillators|accessdate=December 13, 2021}}</ref>

Both still lifes and oscillators can exhibit a wider range than spaceships can, at least as far as isotropic rules are concerned. Many higher kinetic symmetries, notably those involving rotation or with reflection happening on more than one axis, would forbid the pattern from having a nonzero displacement, as the symmetry would either force it to move in two directly opposing directions or redirect it back to its starting point. Many spaceships can have glide symmetry, which oscillators cannot have due to having no overall displacement, however glide symmetry very closely resembles certain mirror symmetries which oscillators do exhibit.

The ratio of a pattern's [[mod]] to its [[period]], for rules on a square grid, can only be 1, 2 or 4.

=== Kinetic symmetry naming system ===
[[Dean Hickerson]] invented a compact naming system for kinetic symmetries.

For still lifes, as well as oscillators and spaceships which have identical mods to periods, an initial symbol stand for a kind of transformation, and a symbol following it refers to the type of region where said transformation is centered.

Oscillators and spaceships of unequal period and mod will follow this string with another string detailing how the pattern is transformed after cycling through its mod.

Hickerson's naming scheme initially used "c" for the center of a cell and "k" for the vertex of a cell - these have been revised to "f" for the face of a cell and "v" for the vertex of a cell to clarify things and reduce any confusion that may arise due to homophones.

==== Symbols ====
{| class="wikitable"
! Hickerson name
! Wiki name
! Meaning
|-
! colspan="2" | n
| No symmetry
|-
! colspan="2" | -
| One line of orthogonal mirror symmetry
|-
! colspan="2" | /
| One line of diagonal mirror symmetry
|-
! colspan="2" | +
| Two lines of orthogonal mirror symmetry
|-
! colspan="2" | x
| Two lines of diagonal mirror symmetry
|-
! colspan="2" | *
| Two lines each of orthogonal and diagonal mirror symmetry
|-
! colspan="2" | r
| 90-degree rotational symmetry
|-
! colspan="2" | .
| 180-degree rotational symmetry
|-
! c
! f
| Transformation is centered on the center of a cell
|-
! colspan="2" | e
| Transformation is centered on the edge of a cell
|-
! k
! v
| Transformation is centered on the vertex of a cell
|}

=== List ===
==== Still lifes ====
These are equivalent to static symmetries (excluding D8_2). The corresponding static symmetries are detailed in the table for each type.

{| class="wikitable"
! Equivalent static symmetry
! Hickerson name
! Wiki name
! Description
! Example
! Image
|-
! C1
! colspan="2" | n
| No symmetry
| [[Caterer]]
| [[File:Symmetry C1.png|33px]]
|-
! D2_+1
! -c
! -f
| One line of orthogonal mirror symmetry Line passes through cell centers and edges
| [[1-2-3-4]]
| [[File:Symmetry D2_+1.png|33px]]
|-
! D2_+2
! colspan="2" | -e
| One line of orthogonal mirror symmetry Line passes through cell edges and vertices
| [[Short keys]]
| [[File:Symmetry D2_+2.png|33px]]
|-
! D2_x
! colspan="2" | /
| One line of diagonal mirror symmetry
| [[Heart]]
| [[File:Symmetry D2_x.png|33px]]
|-
! C2_1
! .c
! .f
| 180-degree rotation Rotation is centered on the center of a cell
| [[Honey thieves]]
| [[File:Symmetry C2_1.png|33px]]
|-
! C2_2
! colspan="2" | .e
| 180-degree rotation Rotation is centered on the edge of a cell
| [[Beluchenko's p40]]
| [[File:Symmetry C2_2.png|33px]]
|-
! C2_4
! .k
! .v
| 180-degree rotation Rotation is centered on the vertex of a cell
| [[22P36]]
| [[File:Symmetry C2_4.png|33px]]
|-
! D4_+1
! +c
! +f
| Two lines of orthogonal mirror symmetry Both lines pass through cell centers and edges
| [[Gray counter]]
| [[File:Symmetry D4_+1.png|33px]]
|-
! D4_+2
! colspan="2" | +e
| Two lines of orthogonal mirror symmetry One lines passes through cell centers and edges One line passes through cell edges and vertices
| [[Pentadecathlon]]
| [[File:Symmetry D4_+2.png|33px]]
|-
! D4_+4
! +k
! +v
| Two lines of orthogonal mirror symmetry Both lines pass through cell edges and vertices
| [[101]]
| [[File:Symmetry D4_+4.png|33px]]
|-
! D4_x1
! xc
! xf
| Two lines of diagonal mirror symmetry Lines meet at the center of a cell
| [[Merzenich's p11]]
| [[File:Symmetry D4_x1.png|33px]]
|-
! D4_x4
! xk
! xv
| Two lines of diagonal mirror symmetry Lines meet at the vertex of a cell
| [[Jason's p6]]
| [[File:Symmetry D4_x4.png|33px]]
|-
! C4_1
! rc
! rf
| 90-degree rotation Rotation is centered on the center of a cell
| [[Kok's galaxy]]
| [[File:Symmetry C4_1.png|33px]]
|-
! C4_4
! rk
! rv
| 90-degree rotation Rotation is centered on the vertex of a cell
| [[48P22.1]]
| [[File:Symmetry C4_4.png|33px]]
|-
! D8_1
! *c
! *f
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell centers and edges
| [[Diamond ring]]
| [[File:Symmetry D8_1.png|33px]]
|-
! D8_4
! *k
! *v
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell edges and vertices
| [[Octagon 2]]
| [[File:Symmetry D8_4.png|33px]]
|}

==== Oscillators ====
For oscillators which have a mod identical to their period, refer to the still lifes table above.

"Composite symmetry" refers to the resulting symmetry of the pattern created from each of the oscillator's "identical" phases:
* for patterns with a mod half their period, the union of the pattern's initial state and the state it appears in at half its period
* for patterns with a mod a quarter their period, the union of the pattern's initial phase, generation (period/4), generation (period/2) and generation (3period/4)

{| class="wikitable"
! Hickerson name
! Wiki name
! Static symmetry
! Composite symmetry
! period/mod
! Description
! Example
! Image
|-
! n-c
! n-f
! C1
! D2_+1
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell centers and edges
| (2.2.4)
| pending
|-
! colspan="2" | n-e
! C1
! D2_+2
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell edges and vertices
| [[Griddle and block]]
| pending
|-
! colspan="2" | n/
! C1
! D2_x
| 2
| Pattern is asymmetric Appears flipped across a diagonal line during (period/2)
| [[Muttering moat 1]]
| pending
|-
! n.c
! n.f
! C1
! C2_1
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the center of a cell
| (2.2.7)
| pending
|-
! colspan="2" | n.e
! C1
! C2_2
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the edge of a cell
| [[Laputa]]
| pending
|-
! n.k
! n.v
! C1
! C2_4
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the vertex of a cell
| (2.2.0)
| pending
|-
! nrc
! nrf
! C1
! C4_1
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the center of a cell
| [[Sixty-nine]]
| pending
|-
! nrk
! nrv
! C1
! C4_4
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the vertex of a cell
| [[Dinner table]]
| pending
|-
! -c+c
! -f+f
! D2_+1
! D4_+1
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| [[Piston]]
| pending
|-
! -c+e
! -f+e
! D2_+1
! D4_+2
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| [[by flops]]
| pending
|-
! -e+e
! -e+e
! D2_+2
! D4_+2
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| (2.5.0)
| pending
|-
! -e+k
! -e+v
! D2_+2
! D4_+4
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| (2.5.2)
| pending
|-
! /xc
! /xf
! D2_x
! D4_x1
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the center of a cell
| (2.4.2)
| pending
|-
! /xk
! /xv
! D2_x
! D4_x4
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the vertex of a cell
| [[Tripole]]
| pending
|-
! .c+c
! .f+f
! C2_1
! D4_+1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
| (2.4.0)
| pending
|-
! .cxc
! .fxf
! C2_1
! D4_x1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the center of a cell
| [[Bipole]]
| pending
|-
! .crc
! .frf
! C2_1
! C4_1
| 2
| Pattern has C2_1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the center of a cell
| (2.5.5)
| pending
|-
! .e+e
! .e+e
! C2_2
! D4_+2
| 2
| Pattern has C2_2 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Line may pass through either cell centers and edges, or cell edges and vertices
| (2.6.1)
| pending
|-
! .k+k
! .v+v
! C2_4
! D4_+4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| (2.3.3)
| pending
|-
! .kxk
! .vxv
! C2_4
! D4_x4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the vertex of a cell
| [[Clock]]
| pending
|-
! .krk
! .vrv
! C2_4
! C4_4
| 2
| Pattern has C2_4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the vertex of a cell
| (2.8.0)
| pending
|-
! +c*c
! +f*f
! D4_+1
! D8_1
| 2
| Pattern has D4_+1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[Blinker]]
| pending
|-
! +k*k
! +v*v
! D4_+4
! D8_4
| 2
| Pattern has D4_+4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| (2.7.1)
| pending
|-
! xc*c
! xf*f
! D4_x1
! D8_1
| 2
| Pattern has D4_x1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[Washing machine]]
| pending
|-
! xk*k
! xv*v
! D4_x4
! D8_4
| 2
| Pattern has D4_x4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| (2.6.4)
| pending
|-
! rc*c
! rf*f
! C4_1
! D8_1
| 2
| Pattern has C4_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
|
| pending
|-
! rk*k
! rv*v
! C4_4
! D8_4
| 2
| Pattern has C4_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| [[Quad]]
| pending
|}

{{EmbedViewer
|viewerconfig = #C [[ GPS 20 THUMBLAUNCH THUMBSIZE 2 WIDTH 2000 HEIGHT 1500 THEME 6 ]]
|pname = temporalsymmetrytypes
|position = center
|caption = All 43 temporal symmetry types}}

== On a hexagonal grid ==
There does not seem to have been an attempt at describing all possible oscillator and spaceship time symmetries on {6,3} and {3,6} so far.

== References ==
<references>
<ref name="post138823">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 138823
|author = GUYTU6J
|date = December 13, 2021
}}</ref>
</references>

[[Category:Everything else]]

Kinetic symmetry

2022-01-12T11:20:09Z

Freywa: /* Oscillators */

A '''kinetic symmetry''' (contrast [[static symmetry]]) describes the spatial and temporal symmetries of a periodic pattern such as a [[still life]], [[oscillator]] or [[spaceship]]. It combines a pattern's spatial (rotational and reflectional) symmetries from the more general [[static symmetry]] with symmetrical transformations of said pattern arising from its evolution.<ref name="post138823" />

== On a square grid ==
There are a total of 43 different kinetic symmetries possible on a usual [[square grid]], comprised of the 16 static symmetries (D8_2 is excluded) with 27 possible time transformations.

Oscillators have a much wider range of possible kinetic symmetries than still lifes. It is very easy to see that the 27 time transformations cannot apply to still lifes by definition, as they require the pattern to have distinct phases which can be compared to each other, and therefore for the pattern to evolve, which still lifes do not. As such, oscillators can only have 16 of the possible 43 kinetic symmetry types, which therefore corresponds with the 16 different static symmetry types. The symmetry class is the symmetry class of the oscillator in a single generation followed by the symmetry class of the union of the generation and its congruent successors.<ref>{{CiteHickersonOscillators|accessdate=December 13, 2021}}</ref>

Both still lifes and oscillators can exhibit a wider range than spaceships can, at least as far as isotropic rules are concerned. Many higher kinetic symmetries, notably those involving rotation or with reflection happening on more than one axis, would forbid the pattern from having a nonzero displacement, as the symmetry would either force it to move in two directly opposing directions or redirect it back to its starting point. Many spaceships can have glide symmetry, which oscillators cannot have due to having no overall displacement, however glide symmetry very closely resembles certain mirror symmetries which oscillators do exhibit.

The ratio of a pattern's [[mod]] to its [[period]], for rules on a square grid, can only be 1, 2 or 4.

=== Kinetic symmetry naming system ===
[[Dean Hickerson]] invented a compact naming system for kinetic symmetries.

For still lifes, as well as oscillators and spaceships which have identical mods to periods, an initial symbol stand for a kind of transformation, and a symbol following it refers to the type of region where said transformation is centered.

Oscillators and spaceships of unequal period and mod will follow this string with another string detailing how the pattern is transformed after cycling through its mod.

Hickerson's naming scheme initially used "c" for the center of a cell and "k" for the vertex of a cell - these have been revised to "f" for the face of a cell and "v" for the vertex of a cell to clarify things and reduce any confusion that may arise due to homophones.

==== Symbols ====
{| class="wikitable"
! Hickerson name
! Wiki name
! Meaning
|-
! colspan="2" | n
| No symmetry
|-
! colspan="2" | -
| One line of orthogonal mirror symmetry
|-
! colspan="2" | /
| One line of diagonal mirror symmetry
|-
! colspan="2" | +
| Two lines of orthogonal mirror symmetry
|-
! colspan="2" | x
| Two lines of diagonal mirror symmetry
|-
! colspan="2" | *
| Two lines each of orthogonal and diagonal mirror symmetry
|-
! colspan="2" | r
| 90-degree rotational symmetry
|-
! colspan="2" | .
| 180-degree rotational symmetry
|-
! c
! f
| Transformation is centered on the center of a cell
|-
! colspan="2" | e
| Transformation is centered on the edge of a cell
|-
! k
! v
| Transformation is centered on the vertex of a cell
|}

=== List ===
==== Still lifes ====
These are equivalent to static symmetries (excluding D8_2). The corresponding static symmetries are detailed in the table for each type.

{| class="wikitable"
! Equivalent static symmetry
! Hickerson name
! Wiki name
! Description
! Example
! Image
|-
! C1
! colspan="2" | n
| No symmetry
| [[Eater 1]]
| [[File:Symmetry C1.png|33px]]
|-
! D2_+1
! -c
! -f
| One line of orthogonal mirror symmetry Line passes through cell centers and edges
| [[Hat]]
| [[File:Symmetry D2_+1.png|33px]]
|-
! D2_+2
! colspan="2" | -e
| One line of orthogonal mirror symmetry Line passes through cell edges and vertices
| [[Cap and table]]
| [[File:Symmetry D2_+2.png|33px]]
|-
! D2_x
! colspan="2" | /
| One line of diagonal mirror symmetry
| [[Boat]]
| [[File:Symmetry D2_x.png|33px]]
|-
! C2_1
! .c
! .f
| 180-degree rotation Rotation is centered on the center of a cell
| [[Long snake]]
| [[File:Symmetry C2_1.png|33px]]
|-
! C2_2
! colspan="2" | .e
| 180-degree rotation Rotation is centered on the edge of a cell
| [[Aircraft carrier]]
| [[File:Symmetry C2_2.png|33px]]
|-
! C2_4
! .k
! .v
| 180-degree rotation Rotation is centered on the vertex of a cell
| [[Snake]]
| [[File:Symmetry C2_4.png|33px]]
|-
! D4_+1
! +c
! +f
| Two lines of orthogonal mirror symmetry Both lines pass through cell centers and edges
| [[Hat siamese hat]]
| [[File:Symmetry D4_+1.png|33px]]
|-
! D4_+2
! colspan="2" | +e
| Two lines of orthogonal mirror symmetry One lines passes through cell centers and edges One line passes through cell edges and vertices
| [[Beehive]]
| [[File:Symmetry D4_+2.png|33px]]
|-
! D4_+4
! +k
! +v
| Two lines of orthogonal mirror symmetry Both lines pass through cell edges and vertices
| (1.5.4)
| [[File:Symmetry D4_+4.png|33px]]
|-
! D4_x1
! xc
! xf
| Two lines of diagonal mirror symmetry Lines meet at the center of a cell
| [[Ship]]
| [[File:Symmetry D4_x1.png|33px]]
|-
! D4_x4
! xk
! xv
| Two lines of diagonal mirror symmetry Lines meet at the vertex of a cell
| [[Barge]]
| [[File:Symmetry D4_x4.png|33px]]
|-
! C4_1
! rc
! rf
| 90-degree rotation Rotation is centered on the center of a cell
| [[Spiral]]
| [[File:Symmetry C4_1.png|33px]]
|-
! C4_4
! rk
! rv
| 90-degree rotation Rotation is centered on the vertex of a cell
| (1.5.5)
| [[File:Symmetry C4_4.png|33px]]
|-
! D8_1
! *c
! *f
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell centers and edges
| [[Tub]]
| [[File:Symmetry D8_1.png|33px]]
|-
! D8_4
! *k
! *v
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell edges and vertices
| [[Block]]
| [[File:Symmetry D8_4.png|33px]]
|}

==== Oscillators ====
For oscillators which have a mod identical to their period, refer to the still lifes table above.

"Composite symmetry" refers to the resulting symmetry of the pattern created from each of the oscillator's "identical" phases:
* for patterns with a mod half their period, the union of the pattern's initial state and the state it appears in at half its period
* for patterns with a mod a quarter their period, the union of the pattern's initial phase, generation (period/4), generation (period/2) and generation (3period/4)

{| class="wikitable"
! Hickerson name
! Wiki name
! Static symmetry
! Composite symmetry
! period/mod
! Description
! Example
! Image
|-
! n-c
! n-f
! C1
! D2_+1
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell centers and edges
| (2.2.4)
| pending
|-
! colspan="2" | n-e
! C1
! D2_+2
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell edges and vertices
| [[Griddle and block]]
| pending
|-
! colspan="2" | n/
! C1
! D2_x
| 2
| Pattern is asymmetric Appears flipped across a diagonal line during (period/2)
| [[Muttering moat 1]]
| pending
|-
! n.c
! n.f
! C1
! C2_1
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the center of a cell
| (2.2.7)
| pending
|-
! colspan="2" | n.e
! C1
! C2_2
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the edge of a cell
| [[Laputa]]
| pending
|-
! n.k
! n.v
! C1
! C2_4
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the vertex of a cell
| (2.2.0)
| pending
|-
! nrc
! nrf
! C1
! C4_1
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the center of a cell
| [[Sixty-nine]]
| pending
|-
! nrk
! nrv
! C1
! C4_4
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the vertex of a cell
| [[Dinner table]]
| pending
|-
! -c+c
! -f+f
! D2_+1
! D4_+1
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| [[Piston]]
| pending
|-
! -c+e
! -f+e
! D2_+1
! D4_+2
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| [[by flops]]
| pending
|-
! -e+e
! -e+e
! D2_+2
! D4_+2
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| (2.5.0)
| pending
|-
! -e+k
! -e+v
! D2_+2
! D4_+4
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| (2.5.2)
| pending
|-
! /xc
! /xf
! D2_x
! D4_x1
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the center of a cell
| (2.4.2)
| pending
|-
! /xk
! /xv
! D2_x
! D4_x4
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the vertex of a cell
| [[Tripole]]
| pending
|-
! .c+c
! .f+f
! C2_1
! D4_+1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
| (2.4.0)
| pending
|-
! .cxc
! .fxf
! C2_1
! D4_x1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the center of a cell
| [[Bipole]]
| pending
|-
! .crc
! .frf
! C2_1
! C4_1
| 2
| Pattern has C2_1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the center of a cell
| (2.5.5)
| pending
|-
! .e+e
! .e+e
! C2_2
! D4_+2
| 2
| Pattern has C2_2 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Line may pass through either cell centers and edges, or cell edges and vertices
| (2.6.1)
| pending
|-
! .k+k
! .v+v
! C2_4
! D4_+4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| (2.3.3)
| pending
|-
! .kxk
! .vxv
! C2_4
! D4_x4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the vertex of a cell
| [[Clock]]
| pending
|-
! .krk
! .vrv
! C2_4
! C4_4
| 2
| Pattern has C2_4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the vertex of a cell
| (2.8.0)
| pending
|-
! +c*c
! +f*f
! D4_+1
! D8_1
| 2
| Pattern has D4_+1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[Blinker]]
| pending
|-
! +k*k
! +v*v
! D4_+4
! D8_4
| 2
| Pattern has D4_+4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| (2.7.1)
| pending
|-
! xc*c
! xf*f
! D4_x1
! D8_1
| 2
| Pattern has D4_x1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[Washing machine]]
| pending
|-
! xk*k
! xv*v
! D4_x4
! D8_4
| 2
| Pattern has D4_x4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| (2.6.4)
| pending
|-
! rc*c
! rf*f
! C4_1
! D8_1
| 2
| Pattern has C4_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
|
| pending
|-
! rk*k
! rv*v
! C4_4
! D8_4
| 2
| Pattern has C4_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| [[Quad]]
| pending
|}

{{EmbedViewer
|viewerconfig = #C [[ GPS 20 THUMBLAUNCH THUMBSIZE 2 WIDTH 2000 HEIGHT 1500 THEME 6 ]]
|pname = temporalsymmetrytypes
|position = center
|caption = All 43 temporal symmetry types}}

== On a hexagonal grid ==
There does not seem to have been an attempt at describing all possible oscillator and spaceship time symmetries on {6,3} and {3,6} so far.

== References ==
<references>
<ref name="post138823">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 138823
|author = GUYTU6J
|date = December 13, 2021
}}</ref>
</references>

[[Category:Everything else]]

RLE:Temporalsymmetrytypes

2022-01-12T11:11:07Z

Freywa: Created page with "x = 409, y = 241, rule = B3/S23 34b2o298b2o$35bo25b2o8b2o33bo37b2o189bo$35bobo9b2o12b2o7bo33b3o37bobo 188bobo$14b3o19b2o9bo25bo29bo39bo4bo5bo178b2obobo$12bo32bobo21b2obo30b 2o..."

x = 409, y = 241, rule = B3/S23
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48bo31b2o125bo22b2o11b2o$10b2o32b2o50b2obo$10bo33b2o52bo$10bo$10bo2$
59b2o15b2o$59b2o15b2o8$14bo$14bobo23bo$2b2o11bobo21bobo$2b2o11bo2bo3b
2o12b2o2bo2b2o$15bobo4b2o12bob2o4bo45b2o10b2o93bo4bo$14bobo21b2ob2o47b
2o10b2o91b2ob4ob2o17b2o$14bo21bo4b2obo152bo4bo19b2o$36b2o2bo2b2o45bo
12bo66bo7bo$39bobo47bobo10bobo64bobo5bobo$40bo48bo2bo8bo2bo65bo7bo44bo
$90bo2bo6bo2bo94bo4bo18b3o$198bo4bo17bo2bo$90bo2bo3bo2bo2bo67bo5bo19bo
4bo12b2o5b2o$90b2o4bobo3b2o67bo5bo20bobo14b2o$99bo70bobo3bobo19bobo$
98bo72bo5bo50b2o$95bo75bo5bo42b2o5bob2o2b2o$94bo103bobo20bo5bobo3b2o$
90b2o3bobo4b2o94bobo21b2o4bo$90bo2bo2bo3bo2bo93bo4bo20bo$198bo4bo$43bo
46bo2bo6bo2bo94bo4bo$41b2obo44bo2bo8bo2bo65bo7bo$15bobo21bo4bo44bobo
10bobo64bobo5bobo46b2o$14bo23b3o49bo12bo66bo7bo47b2o$9b2o2bo4bo178bo4b
o$9b2obo2bob2o21b3o47b2o10b2o91b2ob4ob2o$13b2o21bo4bo48b2o10b2o93bo4bo
$36bob2o$37bo16$108bo$11b2o5b2o87bobo$11bo7bo78b2o7bobo$8b2obo7bob2o
75b2o6b2ob3o$8bo2b2o5b2o2bo89bo$9b2o6bo2b2o84b2ob3o$11b3o4b2o86b2obo$
11bo4bo2bo77b2o$12b7o79b2o$97b2o$14b3o$13bo3bo$13b2ob2o$109b2o$109b2o
5$81b2o$81b2o4$93b2o$92b2o$13b2o78b2o$13b2ob2o64bob2o$18bo61b3ob2o$13b
2o64bo$13bo66b3ob2o6b2o$11bo2bo3b2o62bobo7b2o$11bo3b5o62bobo$11bo71bo
13$14b2o$8bob2obobo$8b2obobo$12b2o2$14bo4b2o$13bo3bo2bo$13bo4b2o$14bob
o$18b2o$19bo$18bo$18b2o8$obobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobo11$7bo$7b3o$10bo9b2o$9b2o9bo$18bobo$12b2o4b2o$11bo2bo$
14bo$11bo2bo$13bo2$7b2o$6bobo$6bo9b2o$5b2o9bo$17b3o$19bo12$9b2o3b2o$8b
o7bo$11bobo$9b2o3b2o4$23b3o$22b3o$15bo$2b3o9b3o$3b3o$22b3o$23b3o2$3b3o
$2b3o9b3o$15bo3$12b2o3b2o$14bobo$11bo7bo$12b2o3b2o!

Kinetic symmetry

2022-01-12T11:10:43Z

Freywa: /* Oscillators */

A '''kinetic symmetry''' (contrast [[static symmetry]]) describes the spatial and temporal symmetries of a periodic pattern such as a [[still life]], [[oscillator]] or [[spaceship]]. It combines a pattern's spatial (rotational and reflectional) symmetries from the more general [[static symmetry]] with symmetrical transformations of said pattern arising from its evolution.<ref name="post138823" />

== On a square grid ==
There are a total of 43 different kinetic symmetries possible on a usual square grid, comprised of the 16 static symmetries (D8_2 is excluded) with 27 possible time transformations.

Oscillators have a much wider range of possible kinetic symmetries than still lifes. It is very easy to see that the 27 time transformations cannot apply to still lifes by definition, as they require the pattern to have distinct phases which can be compared to each other, and therefore for the pattern to evolve, which still lifes do not. As such, oscillators can only have 16 of the possible 43 kinetic symmetry types, which therefore corresponds with the 16 different static symmetry types. The symmetry class is the symmetry class of the oscillator in a single generation followed by the symmetry class of the union of the generation and its congruent successors.<ref>{{CiteHickersonOscillators|accessdate=December 13, 2021}}</ref>

Both still lifes and oscillators can exhibit a wider range than spaceships can, at least as far as isotropic rules are concerned. Many higher kinetic symmetries, notably those involving rotation or with reflection happening on more than one axis, would forbid the pattern from having a nonzero displacement, as the symmetry would either force it to move in two directly opposing directions or redirect it back to its starting point. Many spaceships can have glide symmetry, which oscillators cannot have due to having no overall displacement, however glide symmetry very closely resembles certain mirror symmetries which oscillators do exhibit.

The ratio of a pattern's [[mod]] to its [[period]], for rules on a square grid, can only be 1, 2 or 4.

=== Kinetic symmetry naming system ===
[[Dean Hickerson]] invented a compact naming system for kinetic symmetries.

For still lifes, as well as oscillators and spaceships which have identical mods to periods, an initial symbol stand for a kind of transformation, and a symbol following it refers to the type of region where said transformation is centered.

Oscillators and spaceships of unequal period and mod will follow this string with another string detailing how the pattern is transformed after cycling through its mod.

Hickerson's naming scheme initially used "c" for the center of a cell and "k" for the vertex of a cell - these have been revised to "f" for the face of a cell and "v" for the vertex of a cell to clarify things and reduce any confusion that may arise due to homophones.

==== Symbols ====
{| class="wikitable"
! Hickerson name
! Wiki name
! Meaning
|-
! colspan="2" | n
| No symmetry
|-
! colspan="2" | -
| One line of orthogonal mirror symmetry
|-
! colspan="2" | /
| One line of diagonal mirror symmetry
|-
! colspan="2" | +
| Two lines of orthogonal mirror symmetry
|-
! colspan="2" | x
| Two lines of diagonal mirror symmetry
|-
! colspan="2" | *
| Two lines each of orthogonal and diagonal mirror symmetry
|-
! colspan="2" | r
| 90-degree rotational symmetry
|-
! colspan="2" | .
| 180-degree rotational symmetry
|-
! c
! f
| Transformation is centered on the center of a cell
|-
! colspan="2" | e
| Transformation is centered on the edge of a cell
|-
! k
! v
| Transformation is centered on the vertex of a cell
|}

=== List ===
==== Still lifes ====
These are equivalent to static symmetries (excluding D8_2). The corresponding static symmetries are detailed in the table for each type.

{| class="wikitable"
! Equivalent static symmetry
! Hickerson name
! Wiki name
! Description
! Example
! Image
|-
! C1
! colspan="2" | n
| No symmetry
| [[Eater 1]]
| [[File:Symmetry C1.png|33px]]
|-
! D2_+1
! -c
! -f
| One line of orthogonal mirror symmetry Line passes through cell centers and edges
| [[Hat]]
| [[File:Symmetry D2_+1.png|33px]]
|-
! D2_+2
! colspan="2" | -e
| One line of orthogonal mirror symmetry Line passes through cell edges and vertices
| [[Cap and table]]
| [[File:Symmetry D2_+2.png|33px]]
|-
! D2_x
! colspan="2" | /
| One line of diagonal mirror symmetry
| [[Boat]]
| [[File:Symmetry D2_x.png|33px]]
|-
! C2_1
! .c
! .f
| 180-degree rotation Rotation is centered on the center of a cell
| [[Long snake]]
| [[File:Symmetry C2_1.png|33px]]
|-
! C2_2
! colspan="2" | .e
| 180-degree rotation Rotation is centered on the edge of a cell
| [[Aircraft carrier]]
| [[File:Symmetry C2_2.png|33px]]
|-
! C2_4
! .k
! .v
| 180-degree rotation Rotation is centered on the vertex of a cell
| [[Snake]]
| [[File:Symmetry C2_4.png|33px]]
|-
! D4_+1
! +c
! +f
| Two lines of orthogonal mirror symmetry Both lines pass through cell centers and edges
| [[Hat siamese hat]]
| [[File:Symmetry D4_+1.png|33px]]
|-
! D4_+2
! colspan="2" | +e
| Two lines of orthogonal mirror symmetry One lines passes through cell centers and edges One line passes through cell edges and vertices
| [[Beehive]]
| [[File:Symmetry D4_+2.png|33px]]
|-
! D4_+4
! +k
! +v
| Two lines of orthogonal mirror symmetry Both lines pass through cell edges and vertices
| (1.5.4)
| [[File:Symmetry D4_+4.png|33px]]
|-
! D4_x1
! xc
! xf
| Two lines of diagonal mirror symmetry Lines meet at the center of a cell
| [[Ship]]
| [[File:Symmetry D4_x1.png|33px]]
|-
! D4_x4
! xk
! xv
| Two lines of diagonal mirror symmetry Lines meet at the vertex of a cell
| [[Barge]]
| [[File:Symmetry D4_x4.png|33px]]
|-
! C4_1
! rc
! rf
| 90-degree rotation Rotation is centered on the center of a cell
| [[Spiral]]
| [[File:Symmetry C4_1.png|33px]]
|-
! C4_4
! rk
! rv
| 90-degree rotation Rotation is centered on the vertex of a cell
| (1.5.5)
| [[File:Symmetry C4_4.png|33px]]
|-
! D8_1
! *c
! *f
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell centers and edges
| [[Tub]]
| [[File:Symmetry D8_1.png|33px]]
|-
! D8_4
! *k
! *v
| Two lines each of orthogonal and diagonal mirror symmetry Orthogonal lines pass through cell edges and vertices
| [[Block]]
| [[File:Symmetry D8_4.png|33px]]
|}

==== Oscillators ====
For oscillators which have a mod identical to their period, refer to the still lifes table above.

"Composite symmetry" refers to the resulting symmetry of the pattern created from each of the oscillator's "identical" phases:
* for patterns with a mod half their period, the union of the pattern's initial state and the state it appears in at half its period
* for patterns with a mod a quarter their period, the union of the pattern's initial phase, generation (period/4), generation (period/2) and generation (3period/4)

{| class="wikitable"
! Hickerson name
! Wiki name
! Static symmetry
! Composite symmetry
! period/mod
! Description
! Example
! Image
|-
! n-c
! n-f
! C1
! D2_+1
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell centers and edges
| (2.2.4)
| pending
|-
! colspan="2" | n-e
! C1
! D2_+2
| 2
| Pattern is asymmetric Appears flipped across an orthogonal line during (period/2) Line passes through cell edges and vertices
| [[Griddle and block]]
| pending
|-
! colspan="2" | n/
! C1
! D2_x
| 2
| Pattern is asymmetric Appears flipped across a diagonal line during (period/2)
| [[Muttering moat 1]]
| pending
|-
! n.c
! n.f
! C1
! C2_1
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the center of a cell
| (2.2.7)
| pending
|-
! colspan="2" | n.e
! C1
! C2_2
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the edge of a cell
| [[Laputa]]
| pending
|-
! n.k
! n.v
! C1
! C2_4
| 2
| Pattern is asymmetric Appears rotated 180 degrees during (period/2) Rotation is centered on the vertex of a cell
| (2.2.0)
| pending
|-
! nrc
! nrf
! C1
! C4_1
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the center of a cell
| [[Sixty-nine]]
| pending
|-
! nrk
! nrv
! C1
! C4_4
| 4
| Pattern is asymmetric Appears rotated 90 degrees every (period/4) Rotation is centered on the vertex of a cell
| [[Dinner table]]
| pending
|-
! -c+c
! -f+f
! D2_+1
! D4_+1
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| [[Piston]]
| pending
|-
! -c+e
! -f+e
! D2_+1
! D4_+2
| 2
| Pattern has D2_+1 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| [[by flops]]
| pending
|-
! -e+e
! -e+e
! D2_+2
! D4_+2
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell centers and edges
| (2.5.0)
| pending
|-
! -e+k
! -e+v
! D2_+2
! D4_+4
| 2
| Pattern has D2_+2 symmetry Appears flipped across a perpendicular orthogonal line during (period/2) Line passes through cell edges and vertices
| (2.5.2)
| pending
|-
! /xc
! /xf
! D2_x
! D4_x1
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the center of a cell
| (2.4.2)
| pending
|-
! /xk
! /xv
! D2_x
! D4_x4
| 2
| Pattern has D2_x symmetry Appears flipped across a perpendicular diagonal line during (period/2) Lines meet at the vertex of a cell
| [[Tripole]]
| pending
|-
! .c+c
! .f+f
! C2_1
! D4_+1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
| (2.4.0)
| pending
|-
! .cxc
! .fxf
! C2_1
! D4_x1
| 2
| Pattern has C2_1 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the center of a cell
| [[Bipole]]
| pending
|-
! .crc
! .frf
! C2_1
! C4_1
| 2
| Pattern has C2_1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the center of a cell
| (2.5.5)
| pending
|-
! .e+e
! .e+e
! C2_2
! D4_+2
| 2
| Pattern has C2_2 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Line may pass through either cell centers and edges, or cell edges and vertices
| (2.6.1)
| pending
|-
! .k+k
! .v+v
! C2_4
! D4_+4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| (2.3.3)
| pending
|-
! .kxk
! .vxv
! C2_4
! D4_x4
| 2
| Pattern has C2_4 symmetry Appears flipped across one of two diagonal lines during (period/2) Lines meet at the vertex of a cell
| [[Clock]]
| pending
|-
! .krk
! .vrv
! C2_4
! C4_4
| 2
| Pattern has C2_4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Rotation is centered on the vertex of a cell
| (2.8.0)
| pending
|-
! +c*c
! +f*f
! D4_+1
! D8_1
| 2
| Pattern has D4_+1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[Blinker]]
| pending
|-
! +k*k
! +v*v
! D4_+4
! D8_4
| 2
| Pattern has D4_+4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as diagonal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| (2.7.1)
| pending
|-
! xc*c
! xf*f
! D4_x1
! D8_1
| 2
| Pattern has D4_x1 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the center of a cell
| [[Washing machine]]
| pending
|-
! xk*k
! xv*v
! D4_x4
! D8_4
| 2
| Pattern has D4_x4 symmetry Appears rotated 90 degrees either clockwise or anticlockwise during (period/2) Could also be interpreted as horizontal flipping on one of two lines Rotation is centered on/lines intersect at the vertex of a cell
| (2.6.4)
| pending
|-
! rc*c
! rf*f
! C4_1
! D8_1
| 2
| Pattern has C4_1 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell centers and edges
|
| pending
|-
! rk*k
! rv*v
! C4_4
! D8_4
| 2
| Pattern has C4_4 symmetry Appears flipped across one of two perpendicular orthogonal lines during (period/2) Both lines pass through cell edges and vertices
| [[Quad]]
| pending
|}

{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 20 Y 0 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 7 HEIGHT 320 ]]
|pname = temporalsymmetrytypes
|position = center
|caption = All 43 temporal symmetry types}}

== On a hexagonal grid ==
There does not seem to have been an attempt at describing all possible oscillator and spaceship time symmetries on {6,3} and {3,6} so far.

== References ==
<references>
<ref name="post138823">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 138823
|author = GUYTU6J
|date = December 13, 2021
}}</ref>
</references>

[[Category:Everything else]]

P96 honey farm hassler

2022-01-12T10:53:23Z

Freywa: That synthed in 24G

{{Oscillator
|name = p96 honey farm hassler
|pname = p96honeyfarmhassler
|c = 63
|bx = 36
|by = 24
|p = 96
|m = 48
|h = 66.00
|v = 0.97
|sv = 0.47
|discoverer = David Raucci
|discoveryear = 2021
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B34c5e/S234c5k6i
|synthesis = 20
|rle = true
|viewerconfig = #C [[ GPS 12 THUMBSIZE 2 ]]
|apgcode = xp96_yaooo777zgfny7111z1op1y3ggzy54ba7y2cczye2mo6zwgggeeey733zw333
}}
The '''p96 honey farm hassler''' is a {{period|96}} [[oscillator]] discovered by [[David Raucci]] on July 14, {{year|2021}}.<ref name="post133504"/> It was later minimized by [[Matthias Merzenich]] on the same day.<ref name="post133518"/> In terms of its minimum population of {{cells|63}} [[cell]]s, it was the smallest known non-trivial period-96 oscillator until January 11, 2022, when a boat-bit doubled [[period-48 glider gun|p48 glider gun]] was found.

[[Jeremy Tan]] found a {{gliders|20}} [[synthesis]] for this oscillator, also on the same day.<ref name="post133534"/>

==References==
<references>
<ref name="post133504">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 133504
|author = David Raucci
|date = July 14, 2021
}}</ref>
<ref name="post133518">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 133518
|author = Matthias Merezenich
|date = July 14, 2021
}}</ref>
<ref name="post133534">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 133534
|author = Jeremy Tan
|date = July 14, 2021
}}</ref>
</references>

==External links==
{{LinkCatagolue|xp96_yaooo777zgfny7111z1op1y3ggzy54ba7y2cczye2mo6zwgggeeey733zw333|patternname=p96 honey farm hassler}}

{{DISPLAYTITLE:p96 honey farm hassler}}
{{symmetry|osc=turn180}}

RLE:Fluttershy

2021-09-25T15:47:40Z

Freywa: RLE

x = 68, y = 67, rule = B3/S23
obo$o$o3bo$b2obo$3bo$5b2o7bo$5b4obo2bo$6bo4bo2bo$7bo2bo3bo3bo$6b2obo5b
2ob2o$6bobo6b2ob2o$6bo11bo2bo$8bo9bo3bo$6bobo10bob2obo$5b2obo6b2o3bo2b
o$6bob2o4bo2bo5b2obo$7bo2bo3bo11bo$8bo5b2o$7bo5b2o11b2o$7bo3b3o12bobo$
9bobobo$10bo15bo$11b2o13bo3bo$11b2o14bo3b2o$12b2o13b2ob3o$16b2o16bo$
14b5o8b2o4bo$14b2o4b3o4b2o4b2o$20b3o2b2o8b2o$26bobob6obo$23bo2bobo4bob
3o$23bo3bo2b4o2b2o$23bob2obob2o10b2o$24bob2ob2o6bo3b2o$24bo2bo10bo3bo$
27bo3b2o4b3ob2o$26b5o2bo6b3o$27b2o4bo9bo$32bo9b2o3b2o$29bo2bo2b2o5b2o
3bo$35bo7b5o$34b2o5b2ob2o$31b2o3bo4bobo7bo$31bo5bo3bo3bo3b2obo$32b2o4b
o6bo2bobo$34b2o2bo3bo5bo4bo$36b3o5b2o3b2o2b2o$44b2obobo2bo$38b3o6b3ob
3o$44bo4bo2bobo$43bo8bo3b2obo$41b2o7bobo3bo2b3o$43bo5bo3bob2o2b3o$45b
6o2bobo3b2o$47bo6bo$46bo6b2o$46bo4bo4b2o$49b2obo3b3obo$48bo3b2o2b2obo
3b2o$49bo2bo4bo2b2o3bo$50b2o4b2o4bo2bo$57bo5bob3o2$58b2o$58b2o$58bobo$
60b3o!

Gallus

2021-09-25T15:42:29Z

Freywa: page created after so long

{{Oscillator
|name = Gallus
|pname = gallus
|f1 = Relay
|c = 105
|bx = 39
|by = 25
|p = 98
|m = 49
|h = 51.96
|v = 0.94
|sv = 0.37
|discoverer = Jeremy Tan
|discoveryear = 2021
|rulemin = B3/S23
|rulemax = B37/S2378
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-c/S23-ky
|isorulemax = B34nt5e6ce7/S234cetz5ekn6-ck78
|synthesis = 50
|plaintext = true
|rle = true
|viewerconfig = #C [[ LOOP 98 GPS 14 THUMBSIZE 2 ZOOM 10 ]]
|apgcode = xp98_w33y133zgo6iqxqi6ogxjjz01qpy1pq1xgdpxccz0gye8k8z121y5ggy1ggz33xooy111y111zy1ccx8s3pdxdp3s8zy8dcy1cd
}}
'''Gallus''' is the smallest known {{period|98}} [[oscillator]], being the smallest example of a [[relay]] construction using [[34P14 shuttle]]s allowing all oscillators of periods 98 + 56n to be constructed with 105 cells.

==See also==
*[[Ocellus]]

==External links==
{{LinkCatagolue|xp98_w33y133zgo6iqxqi6ogxjjz01qpy1pq1xgdpxccz0gye8k8z121y5ggy1ggz33xooy111y111zy1ccx8s3pdxdp3s8zy8dcy1cd}}

{{symmetry|osc=turn180}}

RLE:Gallus

2021-09-25T15:35:46Z

Freywa: RLE

x = 39, y = 23, rule = B3/S23
12b2o4bo$12b2o3bobo12b2o$18bo5b2o5bob2o2b2o$24b2o5bobo3b2o$31bo$5b2o2b
2o18bo$5b2o2b2o5bo$14bobo12bo$15b2o14bo$24b2o5bobo3b2o$24b2o5bob2o2b2o
$8b2o22b2o$2o5bob2o2b2o$2o5bobo3b2o$7bo$5bo$28b2o2b2o$5bo22b2o2b2o$7bo
$2o5bobo3b2o$2o5bob2o2b2o5bo$8b2o9bobo3b2o$20bo4b2o!

Glider synthesis

2021-09-25T13:26:20Z

Freywa: /* Still life syntheses */ this was announced by Martin in the SL synthesis thread

{{EmbedViewer
|pname = loafer_synth
|position = right
|caption = An 8-glider synthesis of a [[loafer]] 
|viewerconfig = #C [[ ZOOM 8 ]]
}}
{{Glossary}}
'''Glider synthesis''' (or '''glider construction''') is the construction of an object by means of collisions of [[glider]]s and glider-constructible spaceships. It is generally assumed that the gliders should be arranged so that they could come from infinity - that is, gliders should not have had to pass through one another to achieve the initial arrangement (or else it is considered “not fully functional”). [[LWSS]]es, [[MWSS]]es and [[HWSS]]es can also be used in syntheses; these spaceships can themselves be easily synthesized from gliders at any point along their trajectory, so this conversion is often left as an implicit step.

==Features of syntheses==
Four main characterizing features of a synthesis are the ''geometry'', ''construction time'', ''glider cost'', and ''number of stages''.

The '''geometry''' is the number of directions of incoming gliders:
* four-directional: gliders collide from all four directions
* three-directional: gliders collide from all directions but one
* two-directional; further divisible in head-on and 90° syntheses. All two-glider syntheses are necessarily two-directional.
* unidirectional, which assumes the initial presence of a '''target''' (usually a [[still life]] or an [[oscillator]]) to be hit with gliders.
Since gliders are themselves glider-constructible, any multidirectional synthesis can be technically downgraded to a fewer-directional one, usually at the cost of increasing the construction time, cost, and/or number of stages needed for the synthesis. More challenging is finding a two- or three-directional synthesis for a particular object where few or no parts of the synthesis reactions extend outside the final pattern's [[bounding box]] in a particular direction. This is especially important for the synthesis of temporary [[bait]] objects, which will need to be placed sometimes quite close to other components without perturbing them. For especially tight locations, sometimes it will be useful to construct an [[LWSS]] (or another standard c/2 spaceship) some distance away from the synthesis nexus and let that collide with a glider in the final stages; this allows synthesis at a 45° angle, rather than a 90° angle as required for synthesis by gliders from separate directions.

The '''construction time''' is simply the number of [[generation]]s it takes to complete a synthesis. For multi-stage syntheses, each stage has its own construction time.

The '''number of stages''' is a count of how many separate operations a synthesis can be divided into, with pauses of arbitrary length between the stages. Often a particular synthesis operation cannot be achieved by a direct collision of gliders, and a synthesis procedure instead requires first synthesizing a number of [[bait]] objects, and then hitting these with gliders to produce the final result.

The '''cost''' is the number of gliders expended over the course of the synthesis. Similar to the construction time, it can be defined also for individual synthesis stages. A *WSS is considered to cost 3 gliders. The discovery of the [[reverse caber tosser]] in 2018 proved that there is a universal constant upper bound on the cost to synthesise any synthesisable object; currently, the best known upper bound is {{Reverse caber tosser/Lower bound}} gliders.

Of particular interest is [[salvo|slow salvo synthesis]]: unidirectional synthesis where every stage has a glider cost of one. Perhaps surprisingly, anything that is glider synthesizable is also slow salvo synthesizable; a result that crucially depends on the existence of [[movable target]]s, [[one-time]] [[turner]]s, and [[splitter]]s.

==Still life syntheses==
In the 1990s, glider syntheses for all [[still life]]s and known [[oscillator]]s with at most 14 [[cell]]s were found by [[David Buckingham]]. Almost all of these were successfully reduced to a synthesis cost of less than 1 glider per ON cell, or "1 glider per bit".<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=&p=21500#p20597 |title=Re: 4 glider syntheses |work=ConwayLife.com forums |author=Mark D. Niemiec|date=June 20, 2015|accessdate=February 21, 2018}}</ref>

A collaborative effort ending in May 2014 completed glider syntheses of all still lifes with 17 or fewer cells.<ref>{{cite web|url=http://pentadecathlon.com/lifeNews/2014/05/constructions_known_for_all_st.html |title=Constructions Known for All Still Lifes up to 17 Bits |work=Game of Life News |author=Dave Greene |date=May 23, 2014|accessdate=September 17, 2014}}</ref><ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1276 |title=17-bit SL Syntheses (100% Complete!) |work=ConwayLife.com forums |author=Martin Grant|date=January 6, 2014 |accessdate=September 17, 2014}}</ref><ref name="post11972" /> A second, longer effort claimed to have completed all the 18-bit still lifes in November 2014,<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1467#p13607 |title=18-bit SL Syntheses (100% Complete!)|work=ConwayLife.com forums |author=Martin Grant|date=October 2, 2014|accessdate=February 21, 2018}}</ref><ref name="post14272" /> but it was later found that some of these syntheses were erroneous.{{citation needed}} The project was finally completed for real in October 2019.<ref name="post83979" /> The syntheses for 19-bit still lifes were completed in February 2020,<ref name="post89061" /> and 20-bit still lifes in March 2021.<ref name="post125259" /> Later optimization projects reduced the maximum cost of construction for 15-bit,<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2441|title=15 in 15: Efficient 15-bit Synthesis Project (DONE!)|work=ConwayLife.com forums |author=BlinkerSpawn|date=October 27, 2016|accessdate=February 21, 2018}}</ref><ref name="post37438" /> 16-bit,<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2642 |title=16 in 16: Efficient 16-bit Synthesis Project |work=ConwayLife.com forums |author=Bob Shemyakin|date=December 20, 2016|accessdate=February 21, 2018}}</ref><ref name="post43734" /> and 17-bit<ref name="post82560" /> still lifes to less than one glider per bit, in November 2016, May 2017, and September 2019 respectively.

In September 2020, the 17-glider reverse caber-tosser proved that all synthesizable still lifes could theoretically be constructed with no more than one glider per bit.<ref name="post104484" />

The following table displays statistics about the costs (excluding RCT constructions) for strict and pseudo still lifes with up to 21 cells as of August 28, 2021.<ref>{{CiteCatagolue|page=syntheses|title=Syntheses|accessdate=August 28, 2021}}</ref>

{| class="wikitable" style="text-align:center"
! rowspan=2 | Live cells !! colspan=4 | Strict still lifes !! colspan=3 | Pseudo still lifes
|-
! Count ({{OEIS|A019473}}) !! Min. cost !! Avg. cost !! Max. cost !! Count ({{OEIS|A056613}}) !! Min. cost !! Max. cost
|-
| 4 || {{A019473|4}} || 2 || 2.500 || 3 || {{A056613|4}} || – || –
|-
| 5 || {{A019473|5}} || 2 || 2.000 || 2 || {{A056613|5}} || – || –
|-
| 6 || {{A019473|6}} || 2 || 3.200 || 4 || {{A056613|6}} || – || –
|-
| 7 || {{A019473|7}} || 2 || 2.750 || 4 || {{A056613|7}} || – || –
|-
| 8 || {{A019473|8}} || 2 || 3.556 || 4 || {{A056613|8}} || 2 || 2
|-
| 9 || {{A019473|9}} || 3 || 4.000 || 5 || {{A056613|9}} || 3 || 3
|-
| 10 || {{A019473|10}} || 4 || 4.360 || 5 || {{A056613|10}} || 3 || 5
|-
| 11 || {{A019473|11}} || 4 || 4.848 || 7 || {{A056613|11}} || 3 || 6
|-
| 12 || {{A019473|12}} || 4 || 5.653 || 7 || {{A056613|12}} || 3 || 9
|-
| 13 || {{A019473|13}} || 4 || 6.263 || 8 || {{A056613|13}} || 4 || 9
|-
| 14 || {{A019473|14}} || 3 || 7.100 || 10 || {{A056613|14}} || 3 || 11
|-
| 15 || {{A019473|15}} || 4 || 8.201 || 11 || {{A056613|15}} || 4 || 12
|-
| 16 || {{A019473|16}} || 3 || 9.237 || 14 || {{A056613|16}} || 4 || style="background-color:#ffff80;" | 23{{refn|group=n|name=RCT}}{{refn|group=n|All but 4 16-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of August 28, 2021.}}
|-
| 17 || {{A019473|17}} || 4 || 10.427 || 16 || {{A056613|17}} || 4 || style="background-color:#ffff80;" | 19{{refn|group=n|name=RCT}}{{refn|group=n|All but 4 17-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of August 28, 2021.}}
|-
| 18 || {{A019473|18}} || 4 || 11.829 || style="background-color:#ffff80;" | 30{{refn|group=n|name=RCT|{{Reverse caber tosser/Lower bound}} gliders using the [[reverse caber-tosser]]}}{{refn|group=n|All but 572 18-bit strict still lifes can be constructed with strictly less than one glider per bit as of August 28, 2021.}} || {{A056613|18}}|| 4 || style="background-color:#ffff80;" | 67{{refn|group=n|name=RCT}}{{refn|group=n|All but 38 18-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of August 28, 2021.}}
|-
| 19 || {{A019473|19}} || 4 || 13.260 || style="background-color:#ffff80;" | 61{{refn|group=n|name=RCT}}{{refn|group=n|All but 2,867 19-bit strict still lifes can be constructed with strictly less than one glider per bit as of August 28, 2021.}} || {{A056613|19}} || 4 || style="background-color:#ffff80;" | 42{{refn|group=n|name=RCT}}{{refn|group=n|All but 84 19-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of August 28, 2021.}}
|-
| 20 || {{A019473|20}} || 4 || 14.966 || style="background-color:#ffff80;" | 119{{refn|group=n|name=RCT}}{{refn|group=n|All but 12,095 20-bit strict still lifes can be constructed with strictly less than one glider per bit as of August 28, 2021.}} || {{A056613|20}} || 4 || style="background-color:#ff8080;" | 128 unsynthesized
|-
| 21 || {{A019473|21}} || 5 || colspan=2 style="background-color:#ff8080;" | 756 unsynthesized{{refn|group=n|All but 42,152 21-bit strict still lifes can be constructed with strictly less than one glider per bit as of August 28, 2021.}} || {{A056613|21}} || colspan="2" style="background-color:#c0c0c0;" | {{refn|group=n|21-bit pseudo still lifes are currently not fully tabulated on Catagolue.}}
|}
<references group=n />

==Spaceship syntheses==
Perhaps the most interesting glider syntheses are those of [[spaceship]]s, because these can be used to create corresponding [[gun]]s and [[rake]]s. Many of the [[c/2]] spaceships that are based on standard spaceships have been synthesized, mostly by [[Mark Niemiec]]. In June {{year|1998}}, [[Stephen Silver]] found syntheses for some of the [[Cordership]]s (although it was not until July {{year|1999}} that [[Jason Summers]] used this to build a Cordership gun). Many larger Corderships also have known glider syntheses, and others could easily be generated using the same techniques. In general, larger Corderships have declined in importance after the discovery of four-, three- and two-engine versions.

In May {{year|2000}}, [[Noam Elkies]] suggested that [[60P5H2V0]], a [[2c/5]] spaceship found by [[Tim Coe]] in May {{year|1996}} might be a candidate for glider synthesis. Initial attempts to construct a synthesis for this spaceship got fairly close, but it was only in March {{year|2003}} that Summers and Elkies managed to find a way to perform the crucial last step. Summers then used the new synthesis to build a c/2 forward rake for the 2c/5 spaceship; this was the first example in [[Conway's Game of Life|Life]] of a rake which fires spaceships that travel in the same direction as the rake but more slowly.

After the [[loafer]] was discovered and synthesized in 2013, a number of new spaceship syntheses were found during a short period of time in late 2014 and early 2015, including the [[dart]], [[crab]], [[25P3H1V0.2]], [[30P5H2V0]], [[x66]], and [[weekender]]. Most of this was due to the work of [[Martin Grant]].


{| class="wikitable sortable"
! rowspan="2" | Name !! rowspan="2" | Speed !! colspan="2" | First synthesis !! Best current synthesis
|-
! Date !! Discoverer !! Fewest gliders
|-
| [[60P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2003-03-17 || [[Noam Elkies]] || 37
|-
| [[loafer]] || data-sort-value="o 0.142857" | [[c/7 orthogonal]] || 2013-02-17 || [[Adam P. Goucher]] || 8
|-
| [[dart]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2014-12-02 || [[Ivan Fomichev]], [[Mark Niemiec]], [[Martin Grant]], [[Michael Simkin]] || 25
|-
| [[crab]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2014-12-26 || [[Brett Berger]], [[Martin Grant]], [[Tanner Jacobi]] || 14
|-
| [[Parallel HBK]] || data-sort-value="oblique" | [[(6,3)c/245912]] || 2014-12-31 || [[Michael Simkin]] || 38,380
|-
| [[30P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2015-01-01 || [[Martin Grant]], [[Matthias Merzenich]], [[Tanner Jacobi]] || 39
|-
| [[25P3H1V0.1]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2015-01-06 || [[Martin Grant]] || 19
|-
| [[x66]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-01-11 || [[Martin Grant]], [[Tanner Jacobi]] || 12
|-
| [[weekender]] || data-sort-value="o 0.285714" | [[2c/7 orthogonal]] || 2015-01-25 || [[Chris Cain]], [[Martin Grant]], [[Tanner Jacobi]] || 33
|-
| [[pufferfish spaceship]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-02-11 || [[Chris Cain]] || 51
|-
| [[Gemini]] || data-sort-value="oblique" | [[(2560,512)c/16849793]] || 2015-02-16 || [[Dave Greene]] || 173,449
|-
| half-[[x66]] with [[HWSS]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-03-08 || [[Adam P. Goucher]], [[Aidan F. Pierce]], [[Chris Cain]], [[Matthias Merzenich]] || 9
|-
| [[B29]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2015-04-06 || [[Tanner Jacobi]] || 25
|-
| [[Pushalong 1]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-06-12 || [[Martin Grant]] || 14
|-
| [[30P4H2V0.4]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-09-10 || [[Tanner Jacobi]] || 50
|-
| [[0hd Demonoid]] || data-sort-value="d 0.000148114" | [[65c/438852 diagonal]] || 2015-12-06 || [[Chris Cain]] || 12,016
|-
| [[copperhead]] || data-sort-value="o 0.1" | [[c/10 orthogonal]] || 2016-03-05 || [[Aidan F. Pierce]] || 13
|-
| [[fireship]] || data-sort-value="o 0.1" | [[c/10 orthogonal]] || 2016-03-21 || [[Nico Brown]], [[Tanner Jacobi]] || 18
|-
| [[25P3H1V0.2]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2017-12-15 || [[Martin Grant]] || 24
|-
| [[Orthogonoid]] || data-sort-value="o 0.0000736475" | [[16c/217251 orthogonal]] || 2017-12-30 || [[Dave Greene]] || 37,625
|-
| [[2-engine Cordership]] || data-sort-value="d 0.0833" | [[c/12 diagonal]] || 2017-12-31 || [[Dave Greene]] || 9
|-
| [[46P4H1V0]] || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2019-02-04 || [[Martin Grant]], [[Tanner Jacobi]] || 57
|-
| [[spider]] || data-sort-value="o 0.2" | [[c/5 orthogonal]] || 2019-03-07 || [[Martin Grant]] || 233
|-
| [[camelship]] || data-sort-value="oblique" | [[(3,1)c/3948264]] || 2019-05-04 || [[Dave Greene]] || 26,614
|-
| [[27P4H1V1]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2019-10-28 || [[Goldtiger997]], [[Tanner Jacobi]] || 31
|-
| [[orthogonal loopship]] || data-sort-value="o 0.0499977" | [[1000130c/20003511 orthogonal]] || 2020-01-08 || [[Dave Greene]] || 56,643
|-
| [[56P6H1V0]] || data-sort-value="o 0.167" | [[c/6 orthogonal]] || 2020-03-25 || [[AforAmpere]], [[Aidan F. Pierce]], [[Goldtiger997]], [[Martin Grant]], [[Tanner Jacobi]] || 292
|-
| [[58P5H1V1]] || data-sort-value="d 0.2" | [[c/5 diagonal]] || 2020-04-03 || [[Adam P. Goucher]], [[Blinkerspawn]], [[Goldtiger997]], [[Peter Naszvadi]], [[Tanner Jacobi]] || 100
|-
| [[31P8H4V0]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2020-04-10 || [[Goldtiger997]] || 36
|-
| [[70P2H1V0.1]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2020-07-18 || [[Martin Grant]] || 185
|-
| [[44P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2020-08-29 || [[Goldtiger997]] || 37
|-
| [[55P9H3V0]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2020-09-19 || [[Goldtiger997]] || 231
|-
| [[Speed Demonoid]] || data-sort-value="d 0.1992019" | [[1642811c/8246964 diagonal]] || 2020-09-26 || [[Dave Greene]] || 31,822
|-
| [[57P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2020-11-02 || [[Goldtiger997]] || 394
|-
| [[turtle]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2020-12-04 || [[Goldtiger997]] || 228
|-
| [[doo-dah]] || data-sort-value="o 0.285714" | [[2c/7 orthogonal]] || 2020-12-06 || [[Goldtiger997]] || 39
|-
| [[edge-repair spaceship 1]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2021-01-24 || [[bubblegum]], [[goldenratio]] || 17
|-
| {{LinkCatagolue|xq4_2534uof1u0u1fou4352zy087084048078zx3igi3x3igi3|patternname=72P4H1V0|style=raw}}<ref name="post124810" /> || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2021-03-08 || [[Tanner Jacobi]], [[Goldtiger997]] || 196
|-
| {{LinkCatagolue|xq4_y2oo7t0t7ooz2qgx8t2rgr2t8xgq2z122166y5661221|patternname=61P4H1V0|style=raw}}<ref name="post128012" /> || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2021-04-10 || [[Goldtiger997]] || 89
|-
| [[Canada Grey]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2021-07-01 || [[Goldtiger997]], [[Martin Grant]] || 611
|-
| [[self-synthesizing oblique loopship]] || data-sort-value="oblique" | [[(16461006,16460963)c/75568091]] || 2021-08-02 || [[Goldtiger997]] || 144,221
|}

==Other syntheses of note==
[[Image:glider_synth_pentadecathlon.png|framed|right|A 3-glider synthesis of a [[pentadecathlon]].]]

A 3-glider synthesis of a [[pentadecathlon]] was found in April {{year|1997}} by [[Heinrich Koenig]], which came as a surprise because it was widely assumed that such a small synthesis would already be known.

Along similar lines, a 3-glider synthesis of a messy [[glider-producing switch engine]] was found in October {{year|2014}} by [[Michael Simkin]],<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?p=13988#p13988|title=Re: Making switch-engines|work=ConwayLife.com forums|author=Michael Simkin|date=October 24, 2014|accessdate=February 21, 2018}}</ref> and a 3-glider synthesis of a [[clean]] [[switch engine]] was discovered in March {{year|2017}} by [[Luka Okanishi]].<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=&p=41558#p41557|title=Re: Thread For Your Accidental Discoveries|work=ConwayLife.com forums|author=Luka Okanishi|date=March 12, 2017|accessdate=February 21, 2018}}</ref>

==2-glider syntheses==
{{main|2-glider collision}}

There are 71 distinct 2-glider collisions, of which 28 produce nothing, six produce a [[block]], five produce a [[honey farm]], three produce a [[B-heptomino]], three produce a [[pi-heptomino]], three produce a [[blinker]], three produce a [[traffic light]], two produce a [[glider]], two produce a [[pond]], two produce a [[loaf]] and a [[blinker]], one produces a [[boat]], one produces a [[beehive]], one produces a [[loaf]], one produces an [[eater 1]], one produces [[lumps of muck]], one produces a [[teardrop]], one produces an [[interchange]], one produces a traffic light and a glider, one produces an [[Polyomino#Octominoes|octomino]], one produces a [[bi-block]], one produces four blocks, one produces two blocks, one produces a blinker, loaf, [[tub]] and block, and one produces the so-called [[two-glider mess]], a [[methuselah]] stabilizing after 530 generations and consisting of four gliders, eight blinkers (including a traffic light), four blocks, a beehive and a [[ship]].

All 71 such syntheses can be seen below in a pattern put together by [[Jason Summers]] on January 29, {{year|2005}}:

{{EmbedViewer
|pname = twoglidersyntheses
|position = center
|caption = All 71 distinct 2-glider collisions, arranged by what they synthesize. 
|viewerconfig = #C [[ WIDTH 1200 HEIGHT 1200 ZOOM 3 ]]
}}

==See also==
*[[:Category:Patterns_constructible_by_a_given_number_of_gliders|List of known glider syntheses]]
*[[Salvo]]
*[[Tutorials/Glider syntheses]]
*[[Shinjuku]]

==References==
<references>
<ref name="post11972">{{LinkForumThread
|format = ref
|title = Re: 17-bit SL Syntheses
|p = 11972
|author = Martin Grant
|date = May 17, 2014
}}</ref>
<ref name="post14272">{{LinkForumThread
|format = ref
|title = Re: 18-bit SL Syntheses
|p = 14272
|author = Martin Grant
|date = November 12, 2014
}}</ref>
<ref name="post82560">{{LinkForumThread
|format = ref
|title = Re: 17 in 17: Efficient 17-bit synthesis project
|p = 82560
|author = Tanner Jacobi
|date = September 9, 2019
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title = Re: Binary slow salvos
|p = 104484
|author = Adam P. Goucher
|date = September 19, 2020
}}</ref>
<ref name="post83979">{{LinkForumThread
|format = ref
|title = Re: 18-bit SL Syntheses (100% Complete!)
|p = 83979
|author = Ian07
|date = October 9, 2019
}}</ref>
<ref name="post89061">{{LinkForumThread
|format = ref
|title = Re: 19-bit still life syntheses
|p = 89061
|author = Martin Grant
|date = February 8, 2020
}}</ref>
<ref name="post125259">{{LinkForumThread
|format = ref
|title = Re: 20-bit still life syntheses
|p = 125259
|author = Martin Grant
|date = March 12, 2021
}}</ref>
<ref name="post37438">{{LinkForumThread
|format = ref
|title = Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain)
|p = 37438
|author = Martin Grant
|date = November 19, 2016
}}</ref>
<ref name="post43734">{{LinkForumThread
|format = ref
|title = Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain)
|p = 43734
|author = Goldtiger997
|date = May 24, 2017
}}</ref>
<ref name="post124810">{{LinkForumThread
|format = ref
|title = Re: Small Spaceship Syntheses
|p = 124810
|author = Goldtiger997
|date = March 8, 2021
}}</ref>
<ref name="post128012">{{LinkForumThread
|format = ref
|title = Re: Small Spaceship Syntheses
|p = 128012
|author = Goldtiger997
|date = April 10, 2021
}}</ref>
</references>

==External links==
*[https://catagolue.hatsya.com/syntheses Catagolue synthesis database]
*[http://codercontest.com/mniemiec/lifepage.htm Mark Niemiec's glider synthesis database]
*[http://radicaleye.com/DRH/life.html Dean Hickerson's Life page] with four pages of glider syntheses
*[http://conwaylife.com/forums/viewtopic.php?p=46552#p46552 Martin Grant's synthesis component database], version 3
*[http://pentadecathlon.com/constructions/components/components.php Heinrich Koenig's component catalog] on pentadecathlon.com
{{LinkLexicon|lex_g.htm#glidersynthesis}}
===Forum threads===
{{LinkForumThread|f=2|t=3267|title=Still Life Synthesis Thread}}
{{LinkForumThread|f=2|t=1155|title=Synthesising Oscillators}}
{{LinkForumThread|f=2|t=1557|title=Small Spaceship Syntheses}}
{{LinkForumThread|f=2|t=3960|title=Soup-based syntheses}}
{{LinkForumThread|f=2|t=4257|title=Randomly enumerating glider syntheses}}
{{LinkForumThread|f=2|t=1394|title=4 glider syntheses}}
{{LinkForumThread|f=2|t=4063|title=Synthesis components}}

Dinner table

2021-09-25T12:51:57Z

Freywa: synthed, Kazyan

{{Oscillator
|name = Dinner table
|pname = dinnertable
|c = 33
|bx = 13
|by = 13
|p = 12
|m = 3
|h = 10.0
|v = 0.55
|sv = 0.53
|discoverer = Robert Wainwright
|discoveryear = 1972
|rulemin = B3/S23
|rulemax = B378/S23678
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-cknr/S2-in3ainqr
|isorulemax = B2i34-ajnr5-aqy6-k78/S234-jktw5-i678
|synthesis = 19
|plaintext = true
|rle = true
|animated = yes
|viewerconfig = #C [[ GPS 4 LOOP 12 THUMBSIZE 3 WIDTH 480 HEIGHT 480 ]]
|apgcode = xp12_032acy0oge2z0g8ow77ggz23y21226
|pentadecathlonid = 33P12.1
}}
'''Dinner table''' is a {{period|12}} [[oscillator]]. It was the first period 12 oscillator to be found, and was discovered by [[Robert Wainwright]] in {{year|1972}}.<ref>{{CiteHickersonOscillators}}</ref> It consists of four [[eater 1]]s [[hassle|hassling]] a [[pre-beehive]]. In terms of its minimum population of {{cells|33}} [[cell]]s, it is the smallest known non-trivial period 12 oscillator, although the trivial [[mold on long hook eating tub]] contains only {{cells|24}} cells.<ref>{{cite web|url=http://pentadecathlon.com/objects/class2/class2.php?part=1 |title=Class 2 Objects Catalog |accessdate=April 9, 2009}}</ref> It can also be extended as an [[agar]].

==Image gallery==
{|
|-
|[[Image:dinnertable_gen1.png|framed|left|Generation 1 reveals that the object being hassled is a pre-beehive]]
|[[Image:dinnertable_ext.png|framed|left|An extension of dinner table {{JavaRLE|dinnertableextension|brief}}]]
|}

==See also==
*[[Four eaters hassling lumps of muck]]
*[[Roteightor]]

==References==
<references />

==External links==
{{LinkLexicon|lex_d.htm#dinnertable}}
{{LinkCatagolue|xp12_032acy0oge2z0g8ow77ggz23y21226}}
{{LinkPentadecathlonObject|33P12.1}}

{{Symmetry|osc=turn90}}
__NOTOC__

P58 pre-pulsar shuttle

2021-09-11T19:22:26Z

Freywa: oops

{{Oscillator
|name = p58 pre-pulsar shuttle
|pname = prepulsarshuttle58
|f1 = Shuttle
|c = 104
|bx = 25
|by = 27
|p = 58
|m = 29
|h = 24.7
|v = 0.72
|sv = 0.63
|discoverer = Tanner Jacobi
|discoveryear = 2015
|rulemin = B3/S23
|rulemax = B3/S2378
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-k/S23-k
|isorulemax = B34q5ay6ac/S234cq5ajnr6in78
|synthesis = 188
|synthesis2 = 58
|plaintext = true
|rle = true
|animated = true
|apgcode = xp58_wj9ary9ra9jzwdl4cy9c4ldz311yf113z32qkgow262x262wogkq23zw6a8cy9c8a6zw3213y93123
|apgcode2 = xp58_xmkl3y73lkmzwra8py9p8arz6221yd1226z64k80gw4c4x4c4wg08k46zwdlhpy9phldzx62acy7ca26
|viewerconfig = #C [[ GPS 10 ZOOM 10 LOOP 58 ]]
}}
'''p58 pre-pulsar shuttle''' is a {{period|58}} [[shuttle]] [[oscillator]] discovered by [[Tanner Jacobi]] on April 25, {{year|2015}}<ref>{{Cite web|url=http://conwaylife.com/forums/viewtopic.php?p=19005#p19005|title=Re: Thread For Your Accidental Discoveries|author=Tanner Jacobi|date=April 25, 2015|accessdate=April 25, 2015}}</ref> and is the smallest known oscillator of that period. The previous record holder was the [[Snark]]-based period 58 glider loop.

[[Jeremy Tan]] found a {{gliders|188}} [[synthesis]] for this oscillator on September 11, {{year|2021}}.<ref name="post135668" />

==See also==
*[[Pre-pulsar shuttle oscillators]]

==References==
<references>
<ref name="post135668">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 135668
|author = Jeremy Tan
|date = September 11, 2021
}}</ref>
</references>

== External links ==
{{LinkCatagolue|xp58_wj9ary9ra9jzwdl4cy9c4ldz311yf113z32qkgow262x262wogkq23zw6a8cy9c8a6zw3213y93123|patternname=p58 pre-pulsar shuttle}}

{{Symmetry|orthogonal2|osc=flip}}
[[Category:Pre-pulsar shuttle oscillators]]
{{DISPLAYTITLE:p58 pre-pulsar shuttle}}

P58 pre-pulsar shuttle

2021-09-11T19:20:53Z

Freywa: canonical form synthed

{{Oscillator
|name = p58 pre-pulsar shuttle
|pname = prepulsarshuttle58
|f1 = Shuttle
|c = 104
|bx = 25
|by = 27
|p = 58
|m = 29
|h = 24.7
|v = 0.72
|sv = 0.63
|discoverer = Tanner Jacobi
|discoveryear = 2015
|rulemin = B3/S23
|rulemax = B3/S2378
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-k/S23-k
|isorulemax = B34q5ay6ac/S234cq5ajnr6in78
|synthesis = 188
|synthesis2 = 58
|plaintext = true
|rle = true
|animated = true
|apgcode = xp58_wj9ary9ra9jzwdl4cy9c4ldz311yf113z32qkgow262x262wogkq23zw6a8cy9c8a6zw3213y93123
|apgcode2 = xp58_xmkl3y73lkmzwra8py9p8arz6221yd1226z64k80gw4c4x4c4wg08k46zwdlhpy9phldzx62acy7ca26
|viewerconfig = #C [[ GPS 10 ZOOM 10 LOOP 58 ]]
}}
'''p58 pre-pulsar shuttle''' is a {{period|58}} [[shuttle]] [[oscillator]] discovered by [[Tanner Jacobi]] on April 25, {{year|2015}}<ref>{{Cite web|url=http://conwaylife.com/forums/viewtopic.php?p=19005#p19005|title=Re: Thread For Your Accidental Discoveries|author=Tanner Jacobi|date=April 25, 2015|accessdate=April 25, 2015}}</ref> and is the smallest known oscillator of that period. The previous record holder was the [[Snark]]-based period 58 glider loop.

[[Jeremy Tan]] found a [[glider synthesis]] for this oscillator in September {{year|2021}}.<ref name="post132920" />

==See also==
*[[Pre-pulsar shuttle oscillators]]

==References==
<references>
<ref name="post135668">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 135668
|author = Jeremy Tan
|date = September 11, 2021
}}</ref>
</references>

== External links ==
{{LinkCatagolue|xp58_wj9ary9ra9jzwdl4cy9c4ldz311yf113z32qkgow262x262wogkq23zw6a8cy9c8a6zw3213y93123|patternname=p58 pre-pulsar shuttle}}

{{Symmetry|orthogonal2|osc=flip}}
[[Category:Pre-pulsar shuttle oscillators]]
{{DISPLAYTITLE:p58 pre-pulsar shuttle}}

Fumarole on 34P14 shuttle

2021-09-11T16:26:59Z

Freywa: fix bounding box

{{Oscillator
|name = Fumarole on 34P14 shuttle
|pname = fumaroleon34p14shuttle
|c = 52
|bx = 15
|by = 23
|p = 70
|m = 70
|h = 35.69
|v = 0.89
|sv = 0.01
|discoveryear = 2018
|rulemin = B3/S23
|rulemax = B378/S2378
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-ce/S23-cky
|isorulemax = B34etz5ace6ce78/S234cetz5-ainq6-a78
|synthesis = 23
|plaintext = true
|rle = true
|viewerconfig = #C [[ GPS 7 THUMBSIZE 2 ZOOM 16 HEIGHT 400 LOOP 71 ]]
|apgcode = xp70_033y133y1o62453zo4maxam4oy132156z1ppy1pp1
}}
'''Fumarole on 34P14 shuttle''' is the smallest known non-trivial {{period|70}} [[oscillator]]. Although it consists of a [[fumarole]] and a [[34P14 shuttle]] (which have periods of {{period|5|brief}} and {{period|14|brief}} respectively), it is considered non-trivial because it has one cell which is alive in [[generation]] 61 and dead in the other 69 phases.

==See also==
* [[Mold on 34P14 shuttle]]
* [[Unix on 34P14 shuttle]]

==External links==
{{LinkCatagolue|xp70_033y133y1o62453zo4maxam4oy132156z1ppy1pp1}}

[[Category:Least-common-multiple oscillators]]

Mold on 41P7.2

2021-09-11T16:10:54Z

Freywa: synthed

{{Oscillator
|name = Mold on 41P7.2
|pname = moldon41p7.2
|c = 53
|bx = 15
|by = 14
|p = 28
|m = 28
|h = 13.6
|v = 0.45
|sv = 0.01
|rulemin = B3/S23
|rulemax = B378/S2378
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B34ce5i6n78/S234cekqt5-eijq6-c78
|synthesis = 105
|plaintext = true
|rle = true
|animated = true
|apgcode = xp28_c84cgcip688gzy3nk5o7ioz37bkicw343
|viewerconfig = #C [[ GPS 7 ZOOM 14 LOOP 28 ]]
}}
'''Mold on 41P7.2''' is a {{period|28}} [[oscillator]] composed of a [[mold]] and [[41P7.2]]. Although it is composed of two oscillators of smaller periods ({{period|4|brief}} and {{period|7|brief}} respectively), it is considered non-trivial because it has a single [[cell]] that is alive in [[generation]] 13 and dead in the other 27 [[phase]]s of the oscillator. In terms of its {{cells|53}} cells, it was tied with [[T-nosed p4 on 28P7.4]] and a [[pre-pulsar shuttle 28]] variant as the smallest known non-trivial period 28 oscillator until the discovery of [[mold on 34P14 shuttle]] in {{year|2018}}.

==Image gallery==
{|
|-
|[[Image:moldon41p7.2_gen13.png|framed|left|Generation 13 reveals the single cell that oscillates at the full period (in green).]]
|}

==See also==
*[[Mold on 36P22]]
*[[Mold on fumarole]]
*[[Mold on pentadecathlon]]
*[[Unix on 41P7.2]]

== External links ==
{{LinkCatagolue|xp28_c84cgcip688gzy3nk5o7ioz37bkicw343}}

[[Category:Least-common-multiple oscillators]]

Mold on Jason's p33

2021-09-11T16:00:46Z

Freywa: synthed

{{Oscillator
|name = Mold on Jason's p33
|pname = moldonjasonsp33
|c = 72
|bx = 30
|by = 24
|p = 132
|m = 132
|h = 61.68
|v = 0.95
|sv = 0.003
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B38/S234e5e6i8
|synthesis = 23
|plaintext = true
|rle = true
|viewerconfig = #C [[ LOOP 132 THUMBSIZE 2 GPS 22 ZOOM 9 ]]
|apgcode = xp132_252w253zy0gxggg0ooozy13w3488a61oml1hiswcgzw695qsoy3111zyica4w4a4
}}
'''Mold on Jason's p33''' is a {{period|132}} [[oscillator]] that is composed of a [[mold]] and [[Jason's p33]]. Although it is composed of two oscillators of smaller periods ({{period|4|brief}} and {{period|33|brief}} respectively), it is considered non-trivial because it contains a single [[cell]] that is alive in [[generation]] 55 and dead in the other 131 [[phase]]s of the oscillator. In terms of its {{cells|72}} cells, it is the smallest known non-trivial period 132 oscillator.

==External links==
{{LinkCatagolue|xp132_252w253zy0gxggg0ooozy13w3488a61oml1hiswcgzw695qsoy3111zyica4w4a4}}

[[Category:Least-common-multiple oscillators]]

Mold on 34P14 shuttle

2021-09-11T15:47:06Z

Freywa: synthed

{{Oscillator
|name = Mold on 34P14 shuttle
|pname = moldon34p14shuttle
|c = 46
|bx = 15
|by = 19
|p = 28
|m = 28
|h = 29.93
|v = 0.90
|sv = 0.01
|discoveryear = 2018
|rulemin = B3/S23
|rulemax = B378/S2378
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23-ky
|isorulemax = B34entz5ae6ce78/S234cetz5-ijq6-c78
|synthesis = 22
|plaintext = true
|rle = true
|viewerconfig = #C [[ GPS 7 THUMBSIZE 2 ZOOM 12 HEIGHT 400 LOOP 28 ]]
|apgcode = xp28_033y133zo4maxam4oy1ggz1ppy1pp1xsta43
}}
'''Mold on 34P14 shuttle''' is the smallest known non-trivial {{period|28}} [[oscillator]]. Although it consists of a [[mold]] and a [[34P14 shuttle]] (which have periods of {{period|4|brief}} and {{period|14|brief}} respectively), it is considered non-trivial because it has one cell which is alive in [[generation]] 19 and dead in the other 27 phases.

==See also==
* [[Unix on 34P14 shuttle]]
* [[Fumarole on 34P14 shuttle]]

==External links==
{{LinkCatagolue|xp28_033y133zo4maxam4oy1ggz1ppy1pp1xsta43}}

[[Category:Least-common-multiple oscillators]]

Table of oscillators by period

2021-09-11T14:54:55Z

Freywa: and the same here

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|- align=center valign=center
! colspan="24" | Smallest [[oscillator]]s for each period
|- align=center valign=center
| style="background-color:#c6efce" | [[block|1]]
| style="background-color:#c6efce" | [[blinker|2]]
| style="background-color:#c6efce" | [[caterer|3]]
| style="background-color:#c6efce" | [[mold|4]]
| style="background-color:#c6efce" | [[pseudo-barberpole|5]]
| style="background-color:#c6efce" | [[unix|6]]
| style="background-color:#c6efce" | [[burloaferimeter|7]]
| style="background-color:#c6efce" | [[figure eight|8]]
| style="background-color:#c6efce" | [[29P9|9]]
| style="background-color:#c6efce" | [[24P10|10]]
| style="background-color:#c6efce" | [[rattlesnake|11]]
| style="background-color:#c6efce" | [[dinner table|12]]
| style="background-color:#c6efce" | [[Beluchenko's p13|13]]
| style="background-color:#c6efce" | [[tumbler|14]]
| style="background-color:#c6efce" | [[pentadecathlon|15]]
| style="background-color:#c6efce" | [[Rob's p16|16]]
| style="background-color:#c6efce" | [[honey thieves|17]]
| style="background-color:#c6efce" | [[p18 bi-block hassler|18]]
| style="background-color:#ff0000" | 19
| style="background-color:#80ff80" | [[mold on fumarole|20]]
| style="background-color:#80ff80" | [[Caterer on 28P7.3|21]]
| style="background-color:#c6efce" | [[Jason's p22|22]]
| style="background-color:#c6efce" | [[David Hilbert|23]]
| style="background-color:#80ff80" | [[caterer on figure eight|24]]
|- align=center valign=center
| style="background-color:#c6efce" | [[p25 pre-pulsar shuttle|25]]
| style="background-color:#80ff80" | [[87P26|26]]
| style="background-color:#c6efce" | [[56P27|27]]
| style="background-color:#80ff80" | [[mold on 34P14 shuttle|28]]
| style="background-color:#c6efce" | [[pre-pulsar shuttle 29|29]]
| style="background-color:#c6efce" | [[queen bee shuttle|30]]
| style="background-color:#c6efce" | [[Merzenich's p31|31]]
| style="background-color:#c6efce" | [[p32 honey farm hassler|32]]
| style="background-color:#80ff80" | [[caterer on rattlesnake|33]]
| style="background-color:#ffff00" | [[honey thieves with test tube baby|34]]
| style="background-color:#c6efce" | [[p35 honey farm hassler|35]]
| style="background-color:#c6efce" | [[22P36|36]]
| style="background-color:#c6efce" | [[Beluchenko's p37|37]]
| style="background-color:#ff0000" | 38
| style="background-color:#80ff80" | [[caterer on Beluchenko's p13|39]]
| style="background-color:#c6efce" | [[Beluchenko's p40|40]]
| style="background-color:#ff0000" | 41
| style="background-color:#80ff80" | [[unix on 34P14 shuttle|42]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|43]]
| style="background-color:#80ff80" | [[mold on rattlesnake|44]]
| style="background-color:#80ff80" | [[pentadecathlon on thumb 1|45]]
| style="background-color:#c6efce" | [[twin bees shuttle|46]]
| style="background-color:#c6efce" | [[p47 pre-pulsar shuttle|47]]
| style="background-color:#80ff80" | [[unix on Rich's p16|48]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[p49 bumper loop|49]]
| style="background-color:#c6efce" | [[p50 traffic jam|50]]
| style="background-color:#80ff80" | [[90P51|51]]
| style="background-color:#c6efce" | [[Four eaters hassling lumps of muck|52]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|53]]
| style="background-color:#c6efce" | [[p54 shuttle|54]]
| style="background-color:#80ff80" | [[pseudo-barberpole on rattlesnake|55]]
| style="background-color:#c6efce" | [[p56 B-heptomino shuttle|56]]
| style="background-color:#ccaaff" | [[p57 bumper loop|57]]
| style="background-color:#c6efce" | [[p58 pre-pulsar shuttle|58]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|59]]
| style="background-color:#80ff80" | [[mold on pentadecathlon|60]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|61]]
| style="background-color:#c6efce" | [[110P62|62]]
| style="background-color:#80ff80" | [[snacker on 38P7.2|63]]
| style="background-color:#c6efce" | [[Merzenich's p64|64]]
| style="background-color:#80ff80" | [[fumarole on Beluchenko's p13|65]]
| style="background-color:#80ff80" | [[caterer on Jason's p22|66]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|67]]
| style="background-color:#80ff80" | [[72P68|68]]
| style="background-color:#ccaaff" | [[p57 bumper loop|69]]
| style="background-color:#80ff80" | [[fumarole on 34P14 shuttle|70]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|71]]
| style="background-color:#80ff80" | [[figure eight on 22P36|72]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[Adjustable glider loops|73]]
| style="background-color:#c6efce" | [[Raucci's p74|74]]
| style="background-color:#d0b65a" | [[6 bits|75]]
| style="background-color:#c6efce" | [[p76 pi-heptomino hassler|76]]
| style="background-color:#80ff80" | [[77P77|77]]
| style="background-color:#80ff80" | [[p6 thumb on Beluchenko's p13|78]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|79]]
| style="background-color:#80ff80" | [[fumarole on Rich's p16|80]]
| style="background-color:#ccaaff" | [[p57 bumper loop|81]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|82]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|83]]
| style="background-color:#c6efce" | [[52P84|84]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|85]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|86]]
| style="background-color:#c6efce" | [[84P87|87]]
| style="background-color:#80ff80" | [[figure eight on rattlesnake|88]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|89]]
| style="background-color:#80ff80" | [[thumb 1 on queen bee shuttle|90]]
| style="background-color:#80ff80" | [[44P7 on Beluchenko's p13|91]]
| style="background-color:#c6efce" | [[50P92.1|92]]
| style="background-color:#80ff80" | [[caterer on Merzenich's p31|93]]
| style="background-color:#c6efce" | [[AK-94|94]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|95]]
| style="background-color:#c6efce" | [[p96 honey farm hassler|96]]
|- align=center valign=center
| style="background-color:#ccaaff" | [[Adjustable glider loops|97]]
| style="background-color:#d0b65a" | [[Gallus|98]]
| style="background-color:#80ff80" | [[48P9 on rattlesnake|99]]
| style="background-color:#c6efce" | [[centinal|100]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|101]]
| style="background-color:#ccaaff" | [[p6 bumper|102]]
| style="background-color:#ccaaff" | [[Adjustable glider loops|103]]
| style="background-color:#80ff80" | [[figure eight on Beluchenko's p13|104]]
| style="background-color:#80ff80" | [[pentadecathlon on 37P7.1|105]]
| style="background-color:#ccaaff" | [[rectifier|106]]
| style="background-color:#ccaaff" | [[rectifier|107]]
| style="background-color:#80ff80" | [[22P4.3 on 56P27|108]]
| style="background-color:#ccaaff" | [[rectifier|109]]
| style="background-color:#80ff80" | [[pseudo-barberpole on Jason's p22|110]]
| style="background-color:#ccaaff" | [[rectifier|111]]
| style="background-color:#80ff80" | [[tumbler on Rich's p16|112]]
| style="background-color:#c6efce" | [[nihonium|113]]
| style="background-color:#d0b65a" | [[Ocellus|114]]
| style="background-color:#ccaaff" | [[rectifier|115]]
| style="background-color:#80ff80" | [[102P116|116]]
| style="background-color:#80ff80" | [[117P117|117]]
| style="background-color:#ccaaff" | [[rectifier|118]]
| style="background-color:#ccaaff" | [[rectifier|119]]
| style="background-color:#80ff80" | [[figure eight on pentadecathlon|120]]
|- align=center valign=center
| style="background-color:#ffffff" | 121
| style="background-color:#ffffff" | 122
| style="background-color:#ffffff" | 123
| style="background-color:#80ff80" | [[mold on Merzenich's p31|124]]
| style="background-color:#ffffff" | 125
| style="background-color:#80ff80" | [[snacker on 34P14 shuttle|126]]
| style="background-color:#ffffff" | 127
| style="background-color:#c6efce" | [[p128 wing hassler|128]]
| style="background-color:#ccaaff" | [[p57 bumper loop|129]]
| style="background-color:#80ff80" | [[55P10 on Beluchenko's p13|130]]
| style="background-color:#ffffff" | 131
| style="background-color:#80ff80" | [[mold on Jason's p33|132]]
| style="background-color:#ffffff" | 133
| style="background-color:#ffffff" | 134
| style="background-color:#80ff80" | [[pentadecathlon on 56P27|135]]
| style="background-color:#ffffff" | 136
| style="background-color:#ffffff" | 137
| style="background-color:#c6efce" | [[Gabriel's p138|138]]
| style="background-color:#ffffff" | 139
| style="background-color:#ffffff" | 140
| style="background-color:#c6efce" | [[114P141|141]]
| style="background-color:#ffffff" | 142
| style="background-color:#ffffff" | 143
| style="background-color:#c6efce" | [[Achim's p144|144]]
|- align=center valign=center
| style="background-color:#ffffff" | 145
| style="background-color:#ffffff" | 146
| style="background-color:#ffffff" | 147
| style="background-color:#ffffff" | 148
| style="background-color:#ffffff" | 149
| style="background-color:#d0b65a" | [[buckaroo|150]]
| style="background-color:#ffffff" | 151
| style="background-color:#ffffff" | 152
| style="background-color:#ffffff" | 153
| style="background-color:#ffffff" | 154
| style="background-color:#ffffff" | 155
| style="background-color:#c6efce" | [[Jason's p156|156]]
| style="background-color:#ffffff" | 157
| style="background-color:#ffffff" | 158
| style="background-color:#ffffff" | 159
| style="background-color:#ffffff" | 160
| style="background-color:#ffffff" | 161
| style="background-color:#ffffff" | 162
| style="background-color:#ffffff" | 163
| style="background-color:#ffffff" | 164
| style="background-color:#d0b65a" | 165
| style="background-color:#ffffff" | 166
| style="background-color:#ffffff" | 167
| style="background-color:#ffffff" | 168
|- align=center valign=center
| style="background-color:#ffffff" | 169
| style="background-color:#ffffff" | 170
| style="background-color:#ffffff" | 171
| style="background-color:#ffffff" | 172
| style="background-color:#ffffff" | 173
| style="background-color:#ffffff" | 174
| style="background-color:#ffffff" | 175
| style="background-color:#ffffff" | 176
| style="background-color:#c6efce" | [[Karel's p177|177]]
| style="background-color:#ffffff" | 178
| style="background-color:#ffffff" | 179
| style="background-color:#ffffff" | 180
| style="background-color:#ffffff" | 181
| style="background-color:#ffffff" | 182
| style="background-color:#ffffff" | 183
| style="background-color:#c6efce" | [[period-184 glider gun|184]]
| style="background-color:#ffffff" | 185
| style="background-color:#80ff80" | [[unix on Merzenich's p31|186]]
| style="background-color:#ffffff" | 187
| style="background-color:#c6efce" | [[AK-94|188]]
| style="background-color:#ffffff" | 189
| style="background-color:#ffffff" | 190
| style="background-color:#ffffff" | 191
| style="background-color:#ffffff" | 192
|- align=center valign=center
| style="background-color:#ffffff" | 193
| style="background-color:#ffffff" | 194
| style="background-color:#ffffff" | 195
| style="background-color:#c6efce" | [[p196 pi-heptomino hassler|196]]
| style="background-color:#ffffff" | 197
| style="background-color:#ffffff" | 198
| style="background-color:#ffffff" | 199
| style="background-color:#80ff80" | [[figure eight on centinal|200]]
| style="background-color:#ffffff" | 201
| style="background-color:#ffffff" | 202
| style="background-color:#ffffff" | 203
| style="background-color:#ffffff" | 204
| style="background-color:#ffffff" | 205
| style="background-color:#ffffff" | 206
| style="background-color:#ffffff" | 207
| style="background-color:#ffffff" | 208
| style="background-color:#ffffff" | 209
| style="background-color:#ffffff" | 210
| style="background-color:#ffffff" | 211
| style="background-color:#ffffff" | 212
| style="background-color:#ffffff" | 213
| style="background-color:#ffffff" | 214
| style="background-color:#ffffff" | 215
| style="background-color:#ffffff" | 216
|- align=center valign=center
| style="background-color:#ffffff" | 217
| style="background-color:#ffffff" | 218
| style="background-color:#ffffff" | 219
| style="background-color:#ffffff" | 220
| style="background-color:#ffffff" | 221
| style="background-color:#ffffff" | 222
| style="background-color:#ffffff" | 223
| style="background-color:#ffffff" | 224
| style="background-color:#ffffff" | 225
| style="background-color:#c6efce" | [[nihonium*|226]]
| style="background-color:#ffffff" | 227
| style="background-color:#ffffff" | 228
| style="background-color:#ffffff" | 229
| style="background-color:#80ff80" | [[fumarole on twin bees shuttle|230]]
| style="background-color:#ffffff" | 231
| style="background-color:#80ff80" | [[figure eight on p29 pre-pulsar shuttle|232]]
| style="background-color:#ffffff" | 233
| style="background-color:#ffffff" | 234
| style="background-color:#ffffff" | 235
| style="background-color:#ffffff" | 236
| style="background-color:#ffffff" | 237
| style="background-color:#ffffff" | 238
| style="background-color:#ffffff" | 239
| style="background-color:#80ff80" | [[pentadecathlon on Rob's p16|240]]
|- align=center valign=center
| style="background-color:#ffffff" | 241
| style="background-color:#ffffff" | 242
| style="background-color:#ffffff" | 243
| style="background-color:#ffffff" | 244
| style="background-color:#ffffff" | 245
| style="background-color:#c6efce" | [[period-246 glider gun|246]]
| style="background-color:#ffffff" | 247
| style="background-color:#ffffff" | 248
| style="background-color:#ffffff" | 249
| style="background-color:#ffffff" | 250
| style="background-color:#ffffff" | 251
| style="background-color:#ffffff" | 252
| style="background-color:#ffffff" | 253
| style="background-color:#ffffff" | 254
| style="background-color:#ffffff" | 255
| style="background-color:#c6efce" | [[period-256 glider gun|256]]
| style="background-color:#ffffff" | 257
| style="background-color:#ffffff" | 258
| style="background-color:#ffffff" | 259
| style="background-color:#ffffff" | 260
| style="background-color:#ffffff" | 261
| style="background-color:#ffffff" | 262
| style="background-color:#ffffff" | 263
| style="background-color:#ffffff" | 264
|- align=center valign=center
| style="background-color:#ffffff" | 265
| style="background-color:#ffffff" | 266
| style="background-color:#ffffff" | 267
| style="background-color:#ffffff" | 268
| style="background-color:#ffffff" | 269
| style="background-color:#ffffff" | 270
| style="background-color:#ffffff" | 271
| style="background-color:#ffffff" | 272
| style="background-color:#ffffff" | 273
| style="background-color:#ffffff" | 274
| style="background-color:#ffffff" | 275
| style="background-color:#80ff80" | [[caterer on 50P92.1|276]]
| style="background-color:#ffffff" | 277
| style="background-color:#ffffff" | 278
| style="background-color:#ffffff" | 279
| style="background-color:#ffffff" | 280
| style="background-color:#ffffff" | 281
| style="background-color:#d0b65a" | [[92P114|282]]
| style="background-color:#ffffff" | 283
| style="background-color:#ffffff" | 284
| style="background-color:#ffffff" | 285
| style="background-color:#ffffff" | 286
| style="background-color:#ffffff" | 287
| style="background-color:#ffffff" | 288
|- align=center valign=center
| style="background-color:#ffffff" | 289
| style="background-color:#ffffff" | 290
| style="background-color:#ffffff" | 291
| style="background-color:#ffffff" | 292
| style="background-color:#ffffff" | 293
| style="background-color:#ffffff" | 294
| style="background-color:#ffffff" | 295
| style="background-color:#ffffff" | 296
| style="background-color:#ffffff" | 297
| style="background-color:#ffffff" | 298
| style="background-color:#ffffff" | 299
| style="background-color:#d0b65a" | [[p60 glider shuttle|300]]
| style="background-color:#ffffff" | 301
| style="background-color:#ffffff" | 302
| style="background-color:#ffffff" | 303
| style="background-color:#ffffff" | 304
| style="background-color:#ffffff" | 305
| style="background-color:#ffffff" | 306
| style="background-color:#ffffff" | 307
| style="background-color:#ffffff" | 308
| style="background-color:#ffffff" | 309
| style="background-color:#ffffff" | 310
| style="background-color:#ffffff" | 311
| style="background-color:#c6efce" | [[60P312|312]]
|- align=center valign=center
| style="background-color:#ffffff" | 313
| style="background-color:#ffffff" | 314
| style="background-color:#ffffff" | 315
| style="background-color:#ffffff" | 316
| style="background-color:#ffffff" | 317
| style="background-color:#ffffff" | 318
| style="background-color:#ffffff" | 319
| style="background-color:#80ff80" | [[fumarole on Merzenich's p64|320]]
| style="background-color:#ffffff" | 321
| style="background-color:#ffffff" | 322
| style="background-color:#ffffff" | 323
| style="background-color:#ffffff" | 324
| style="background-color:#ffffff" | 325
| style="background-color:#ffffff" | 326
| style="background-color:#ffffff" | 327
| style="background-color:#ffffff" | 328
| style="background-color:#ccaaff" | [[rectifier|329]]
| style="background-color:#ffffff" | 330
| style="background-color:#ffffff" | 331
| style="background-color:#ffffff" | 332
| style="background-color:#ffffff" | 333
| style="background-color:#ffffff" | 334
| style="background-color:#ffffff" | 335
| style="background-color:#ffffff" | 336
|- align=center valign=center
| style="background-color:#ffffff" | 337
| style="background-color:#ffffff" | 338
| style="background-color:#ffffff" | 339
| style="background-color:#ffffff" | 340
| style="background-color:#ffffff" | 341
| style="background-color:#ffffff" | 342
| style="background-color:#ffffff" | 343
| style="background-color:#ffffff" | 344
| style="background-color:#ffffff" | 345
| style="background-color:#ffffff" | 346
| style="background-color:#ffffff" | 347
| style="background-color:#ffffff" | 348
| style="background-color:#ffffff" | 349
| style="background-color:#ffffff" | 350
| style="background-color:#ffffff" | 351
| style="background-color:#ffffff" | 352
| style="background-color:#ffffff" | 353
| style="background-color:#ffffff" | 354
| style="background-color:#ffffff" | 355
| style="background-color:#ffffff" | 356
| style="background-color:#ffffff" | 357
| style="background-color:#ffffff" | 358
| style="background-color:#ffffff" | 359
| style="background-color:#80ff80" | [[thumb 1 on Beluchenko's p40|360]]
|- align=center valign=center
| style="background-color:#ffffff" | 361
| style="background-color:#ffffff" | 362
| style="background-color:#ffffff" | 363
| style="background-color:#ffffff" | 364
| style="background-color:#ffffff" | 365
| style="background-color:#ffffff" | 366
| style="background-color:#ffffff" | 367
| style="background-color:#c6efce" | [[period-184 glider gun|368]]
| style="background-color:#ffffff" | 369
| style="background-color:#ffffff" | 370
| style="background-color:#ffffff" | 371
| style="background-color:#ffffff" | 372
| style="background-color:#ffffff" | 373
| style="background-color:#ffffff" | 374
| style="background-color:#ffffff" | 375
| style="background-color:#ffffff" | 376
| style="background-color:#ffffff" | 377
| style="background-color:#ffffff" | 378
| style="background-color:#ffffff" | 379
| style="background-color:#ffffff" | 380
| style="background-color:#ffffff" | 381
| style="background-color:#ffffff" | 382
| style="background-color:#ffffff" | 383
| style="background-color:#ffffff" | 384
|-
! colspan="24" |
|- align=center valign=center
| colspan="3" | Key:
| colspan="3" style="background-color:#c6efce" | known
| colspan="3" style="background-color:#80ff80" | LCM
| colspan="3" style="background-color:#ddaaff" | glider loop
| colspan="3" style="background-color:#d0b65a" | glider shuttle
| colspan="3" style="background-color:#ff0000" | undiscovered
| colspan="3" style="background-color:#ffff00" | [[trivial]]
| colspan="3" style="background-color:#ffffff" | unknown
|}

[[Category:Oscillators| ]]

Oscillator

2021-09-11T14:54:00Z

Freywa: SKOP232 from the Catagolue pages

{{Glossary}}
An '''oscillator''' is a [[pattern]] that is a [[predecessor]] of itself. That is, it is a pattern that repeats itself after a fixed number of [[generation]]s (known as its [[period]]). The term is usually restricted to finite patterns that are not [[still life]]s, though still lifes may be thought of as oscillators with period 1. An oscillator is divided into a [[rotor]] (the individual [[cell]]s that actually oscillate) and a [[stator]] (the cells which remain alive throughout its whole period).

[[Cellular automaton]] theory recognizes shift periodicity, which refers to a configuration reappearing in shifted form after a lapse of one or more generations. Without the shift, it is an oscillator, but if it moves it would be called a [[spaceship]].

==Important oscillators by period==
A list of the first-discovered oscillator of each period, as well the current smallest-known oscillator of that period, is provided here. Note that only non-trivial oscillators are considered here, in the sense that there must be at least one cell that oscillates at the full period. In some cases, it is not known for certain what the first-discovered oscillator of a given period is, and in such situations all possible candidates are listed. For any period 61 or greater an oscillator can be constructed using the Herschel track method. In April, {{year|2013}} [[Mike Playle]] found a small 90-degree [[stable reflector]] known as the [[Snark]] that allows oscillators of all periods 43 or greater to be constructed.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Period
! First discovered
! Discoverer
! Year of discovery
| rowspan="500" style="border: none;" |
! Smallest known
! Minimum # of cells
|-
! {{period|2|brief}}
| [[blinker]]
|[[John Conway]]
| {{year|1970}}
| [[blinker]]
| {{cells|3}}
|-
! {{period|3|brief}}
| [[pulsar]]
|John Conway
| 1970
| [[caterer]]
| {{cells|12}}
|-
! {{period|4|brief}}
| [[pinwheel]]
|[[Simon Norton]]
| 1970
| [[mazing]], [[mold]]
| {{cells|12}}
|-
! {{period|5|brief}}
| [[octagon 2]]
|[[Sol Goodman]], [[Arthur Taber]]
| {{year|1971}}
| [[pseudo-barberpole]]
| {{cells|15}}
|-
! {{period|6|brief}}
| [[$rats]]
|[[David Buckingham]]
| {{year|1972}}
| [[unix]]
| {{cells|16}}
|-
! {{period|7|brief}}
| [[burloaferimeter]]
|David Buckingham
| 1972
| [[28P7.1]], [[28P7.2]], [[28P7.3]], [[burloaferimeter]]
| {{cells|28}}
|-
! {{period|8|brief}}
| [[figure eight]]
|Simon Norton
| 1970
| [[figure eight]]
| {{cells|12}}
|-
! {{period|9|brief}}
| [[worker bee]]
|David Buckingham
| 1972
| [[29P9]]
| {{cells|29}}
|-
! {{period|10|brief}}
| [[42P10.3]]
|David Buckingham
| ≤{{year|1976}}
| [[24P10]]
| {{cells|24}}
|-
! {{period|11|brief}}
| [[38P11.1]]
|David Buckingham
| {{year|1977}}
| [[rattlesnake]]
| {{cells|33}}
|-
! {{period|12|brief}}
| [[dinner table]]
|[[Robert Wainwright]]
| {{year|1972}}
| [[dinner table]]
| {{cells|33}}
|-
! {{period|13|brief}}
| [[Buckingham's p13]]
|David Buckingham
| 1976
| [[Beluchenko's p13]]
| {{cells|34}}
|-
! {{period|14|brief}}
| [[tumbler]]
|[[George Collins]]
| 1970
| [[tumbler]]
| {{cells|16}}
|-
! {{period|15|brief}}
| [[pentadecathlon]]
|John Conway
| 1970
| [[pentadecathlon]]
| {{cells|12}}
|-
! {{period|16|brief}}
| [[two pre-L hasslers]]
|Robert Wainwright
| {{year|1983}}
| [[Rob's p16]]
| {{cells|21}}
|-
! {{period|17|brief}}
| [[54P17.1]]
|[[Dean Hickerson]]
| {{year|1997}}
| [[honey thieves]]
| {{cells|36}}
|-
! {{period|18|brief}}
| [[117P18]]{{refn|group=note|name=lcm|An oscillator of this period can also be constructed from two [[sparker]]s both of which were known by an earlier date. However, this type of oscillator is generally considered "boring", and thus not listed here despite technically being [[non-trivial]].}}
|David Buckingham
| ≤{{year|1991}}
| [[p18 bi-block hassler]], [[p18 phase shifter]]
| {{cells|43}}
|-
! class="red_td" | 19
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|20|brief}}
| [[145P20]]{{refn|group=note|name=lcm}}
|[[Noam Elkies]]
| {{year|1995}}
| [[mold on fumarole]]
| {{cells|30}}
|-
! {{period|21|brief}}
| [[124P21]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1995
| [[caterer on 28P7.3]]
| {{cells|40}}
|-
! {{period|22|brief}}
| [[168P22.1]]
|Noam Elkies
| 1997
| [[Jason's p22]]
| {{cells|36}}
|-
! {{period|23|brief}}
| [[David Hilbert]]
|[[Luka Okanishi]], [[Aidan F. Pierce]]
| {{year|2019}}
| [[David Hilbert]]
| {{cells|122}}
|-
! {{period|24|brief}}
| [[186P24]]{{refn|group=note|name=lcm}}
|[[Bill Gosper]]
| {{year|1994}}
| [[caterer on figure eight]]
| {{cells|24}}
|-
! {{period|25|brief}}
| [[134P25]]
|Noam Elkies
| 1994
| [[p25 pre-pulsar shuttle]]
| {{cells|83}}
|-
! {{period|26|brief}}
| [[p26 pre-pulsar shuttle]]
|David Buckingham
| 1983
| [[87P26]]
| {{cells|87}}
|-
! {{period|27|brief}}
| [[123P27.1]]
|Noam Elkies
| {{year|2002}}
| [[56P27]]
| {{cells|56}}
|-
! {{period|28|brief}}
| [[newshuttle]]
|David Buckingham
| {{year|1973}}
| [[mold on 34P14 shuttle]]
| {{cells|46}}
|-
! {{period|29|brief}}
| [[p29 pre-pulsar shuttle]]
|David Buckingham
| {{year|1980}}
| [[p29 pre-pulsar shuttle]]
| {{cells|54}}
|-
! {{period|30|brief}}
| [[queen bee shuttle]]
|Bill Gosper
| 1970
| [[queen bee shuttle]]
| {{cells|20}}
|-
! {{period|31|brief}}
| [[Merzenich's p31]]
|[[Matthias Merzenich]]
| {{year|2010}}
| [[Merzenich's p31]]
| {{cells|48}}
|-
! {{period|32|brief}}
| [[gourmet]]
|David Buckingham
| {{year|1978}}
| [[p32 honey farm hassler]]
| {{cells|48}}
|-
! {{period|33|brief}}
| [[258P3 on Achim's p11]]
|Noam Elkies, [[Achim Flammenkamp]]
| 1997
| [[caterer on rattlesnake]]
| {{cells|46}}
|-
! {{period|34|brief}}
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''No non-trivial examples found''
|-
! {{period|35|brief}}
| [[p35 beehive hassler]]{{refn|group=note|name=lcm}}
|Dean Hickerson
| 1995
| [[p35 honey farm hassler]]
| {{cells|44}}
|-
! {{period|36|brief}}
| [[p36 toad hassler]]{{refn|group=note|name=lcm}}
|Robert Wainwright
| 1984
| [[22P36]]
| {{cells|22}}
|-
! {{period|37|brief}}
| [[Beluchenko's p37]]
|[[Nicolay Beluchenko]]
| {{year|2009}}
| [[Beluchenko's p37]]
| {{cells|124}}
|-
! class="red_td" | 38
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|39|brief}}
| [[134P39.1]]
|David Buckingham, Noam Elkies
| {{year|2000}}
| [[caterer on Beluchenko's p13]]
|{{cells|46}}
|-
! {{period|40|brief}}
| [[p40 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| 1991
| [[Beluchenko's p40]]
| {{cells|26}}
|-
! class="red_td" | 41
| colspan="6" style="background-color:#ffeeee; color:#880000" align="center" | ''None found''
|-
! {{period|42|brief}}
| [[p42 glider shuttle]]{{refn|group=note|name=lcm}}
|Noam Elkies
| 1994
| [[unix on 34P14 shuttle]]
| {{cells|50}}
|-
! {{period|43|brief}}
| [[p43 Snark loop]]
|[[Mike Playle]]
| {{year|2013}}
| [[p43 Snark loop]]
|{{cells|228}}
|-
! {{period|44|brief}}
| [[p44 pi-heptomino hassler]]
|David Buckingham
| 1992
| [[mold on rattlesnake]]
| {{cells|45}}
|-
! {{period|45|brief}}
| [[pentadecathlon on snacker]]
| [[Mark Niemiec]], John Conway
| ≤1995
| [[pentadecathlon on thumb 1]]
| {{cells|48}}
|-
! {{period|46|brief}}
| [[twin bees shuttle]]
|Bill Gosper
| 1971
| [[twin bees shuttle]]
| {{cells|28}}
|-
! {{period|47|brief}}
| [[p47 pre-pulsar shuttle]]
|David Buckingham
| {{year|1982}}
| [[p47 pre-pulsar shuttle]]
| {{cells|84}}
|-
! {{period|48|brief}}
| [[p48 toad hassler]]
|Bill Gosper
| 1994
| [[unix on Rich's p16]]
| {{cells|52}}
|-
! {{period|49|brief}}
| [[p49 glider shuttle]]
|Noam Elkies
| {{year|1999}}
| [[p49 bumper loop]]
| {{cells|206}}
|-
! {{period|50|brief}}
| [[p50 glider shuttle]]
|Dean Hickerson
| 1992
| [[p50 traffic jam]]
| {{cells|92}}
|-
! {{period|51|brief}}
| [[Beluchenko's p51]]
|Nicolay Beluchenko
| 2009
| [[90P51]]
| {{cells|90}}
|-
! {{period|52|brief}}
| [[Four eaters hassling lumps of muck]]
|David Buckingham
| 1977
| [[four eaters hassling lumps of muck]]
| {{cells|35}}
|-
! {{period|53|brief}}
| [[p53 Snark loop]]
|Mike Playle
| {{year|2013}}
| [[p53 Snark loop]]
|{{cells|228}}
|-
! {{period|54|brief}}
| [[p54 shuttle]]
|David Buckingham
| {{year|1973}}
| [[p54 shuttle]]
| {{cells|48}}
|-
! {{period|55|brief}}
| [[p55 pre-pulsar hassler]]
|David Buckingham
| {{year|1986}}
| [[pseudo-barberpole on rattlesnake]]
| {{cells|49}}
|-
! {{period|56|brief}}
| [[p56 B-heptomino shuttle]]{{refn|group=note|name=lcm}}
|David Buckingham
| ≤1991
| [[p56 B-heptomino shuttle]]
| {{cells|45}}
|-
! {{period|57|brief}}
| [[p57 Herschel loop 1]]
|[[Dietrich Leithner]]
| 1997
| [[p57 bumper loop]]
|{{cells|152}}
|-
! {{period|58|brief}}
| [[p58 toadsucker]]
|Bill Gosper
| 1994
| [[p58 pre-pulsar shuttle]]
| {{cells|104}}
|-
! {{period|59|brief}}
| [[p59 Herschel loop 1]]
|David Buckingham
| 1997
| [[Adjustable glider loop|p59 Snark loop]]
|{{cells|228}}
|-
! {{period|60|brief}}
| [[p60 glider shuttle]]
|David Buckingham
| ≤ 1971
| [[mold on pentadecathlon]]
| {{cells|24}}
|-
! {{period|61|brief}}
| [[p61 Herschel loop 1]]
|David Buckingham
| {{year|1996}}
| [[Adjustable glider loop|p61 Snark loop]]
|{{cells|228}}
|-
! {{period|62|brief}}
| ?
| ?
| ?
| [[110P62]]
| {{cells|110}}
|-
! {{period|63|brief}}
| ?
| ?
| ?
| [[snacker on 38P7.2]]
| {{cells|78}}
|-
! {{period|64|brief}}
| ?
| ?
| ?
| [[Merzenich's p64]]
| {{cells|34}}
|-
! {{period|65|brief}}
| ?
| ?
| ?
| [[fumarole on Beluchenko's p13]]
| {{cells|52}}
|-
! {{period|66|brief}}
| ?
| ?
| ?
| [[caterer on 36P22]]
| {{cells|48}}
|-
! {{period|67|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p67 Snark loop]]
|{{cells|228}}
|-
! {{period|68|brief}}
| ?
| ?
| ?
| [[72P68]]
|{{cells|72}}
|-
! {{period|69|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p69 bumper loop]]
|{{cells|152}}
|-
! {{period|70|brief}}
| ?
| ?
| ?
| [[fumarole on 34P14 shuttle]]
| {{cells|52}}
|-
! {{period|71|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p71 Snark loop]]
|{{cells|228}}
|-
! {{period|72|brief}}
| [[two blockers hassling R-pentomino]]
|Robert Wainwright
| 1990
| [[figure eight on 22P36]]
| {{cells|36}}
|-
! {{period|73|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p73 Snark loop]]
|{{cells|228}}
|-
! {{period|74|brief}}
| p74 Herschel loop
|David Buckingham
| 1996
| [[Raucci's p74]]
| {{cells|84}}
|-
! {{period|75|brief}}
| ?
| ?
| ?
| [[6 bits]]
|{{cells|49}}
|-
! {{period|76|brief}}
| ?
| ?
| ?
| [[p76 pi-heptomino hassler]]
| {{cells|82}}
|-
! {{period|77|brief}}
| ?
| ?
| ?
| [[77P77]]
|{{cells|77}}
|-
! {{period|78|brief}}
| ?
| ?
| ?
| [[p6 thumb on Beluchenko's p13]]
|{{cells|61}}
|-
! {{period|79|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p79 Snark loop]]
|{{cells|228}}
|-
! {{period|80|brief}}
| ?
| ?
| ?
| [[fumarole on Rob's p16]]
| {{cells|39}}
|-
! {{period|81|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p81 bumper loop]]
|{{cells|152}}
|-
! {{period|82|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p82 Snark loop]]
|{{cells|208}}
|-
! {{period|83|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p83 Snark loop]]
|{{cells|228}}
|-
! {{period|84|brief}}
| ?
| ?
| ?
| [[52P84]]
| {{cells|52}}
|-
! {{period|85|brief}}
| ?
| ?
| ?
| [[74P85]]
|{{cells|74}}
|-
! {{period|86|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p86 Snark loop]]
|{{cells|208}}
|-
! {{period|87|brief}}
| ?
| ?
| ?
| [[84P87]]
| {{cells|84}}
|-
! {{period|88|brief}}
| p88 glider loop
|David Buckingham
| 1992
| [[figure eight on rattlesnake]]
| {{cells|45}}
|-
! {{period|89|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p89 Snark loop]]
|{{cells|228}}
|-
! {{period|90|brief}}
| ?
| ?
| ?
| [[thumb 1 on queen bee shuttle]]
| {{cells|56}}
|-
! {{period|91|brief}}
| ?
| ?
| ?
| [[44P7 on Beluchenko's p13]]
|{{cells|78}}
|-
! {{period|92|brief}}
| ?
| ?
| ?
| [[50P92.1]], [[twin bees shuttle on 22P4.3]]
| {{cells|50}}
|-
! {{period|93|brief}}
| ?
| ?
| ?
| [[caterer on Merzenich's p31]]
|{{cells|60}}
|-
! {{period|94|brief}}
| capped [[AK-47 reaction|AK-47]] gun
|Dean Hickerson
| 1990
| {{LinkCatagolue|xp94_x696o8b9czy065x33xc871xggzooyd643zwgg04ahhha4y5c871z4701yfoozw8e13xggzy34701xmmggo5jzya146w343|patternname=capped|style=raw}} [[AK-94]]
| {{cells|110}}
|-
! {{period|95|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p95 Snark loop]]
|{{cells|228}}
|-
! {{period|96|brief}}
| ?
| ?
| ?
| [[p96 honey farm hassler]]
| {{cells|63}}
|-
! {{period|97|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p97 Snark loop]]
|{{cells|228}}
|-
! {{period|98|brief}}
| ?
| ?
| ?
| [[Gallus]]
| {{cells|105}}
|-
! {{period|99|brief}}
| ?
| ?
| ?
| [[48P9 on rattlesnake]]
|{{cells|82}}
|-
! {{period|100|brief}}
| [[centinal]]
|Bill Gosper
| ≤{{year|1987}}
| [[centinal]]
| {{cells|70}}
|-
! {{period|101|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p101 Snark loop]]
|{{cells|228}}
|-
! {{period|102|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp102_w660259gcy5ca23z8oy166y06msz0123wggyqcczy11243ykccwsq66zoomewccykg8gz0ccyp12210ggzyleqoy0oox1074zyeggkcy5c248g0oozye1ya11|patternname=p102 bumper loop|style=raw}}
| {{cells|122}}
|-
! {{period|103|brief}}
| ?
| ?
| ?
| [[Adjustable glider loop|p103 Snark loop]]
|{{cells|228}}
|-
! {{period|104|brief}}
| ?
| ?
| ?
| [[figure eight on Beluchenko's p13]]
| {{cells|46}}
|-
! {{period|105|brief}}
| ?
| ?
| ?
| [[pentadecathlon on 37P7.1]]
|{{cells|49}}
|-
! {{period|106|brief}}
| ?
| ?
| ?
| [[rectifier|p106 rectifier loop]]
|{{cells|169}}
|-
! {{period|107|brief}}
| ?
| ?
| ?
| [[rectifier|p107 rectifier loop]]
|{{cells|136}}
|-
! {{period|108|brief}}
| ?
| ?
| ?
| [[22P4.3 on 56P27]]
|{{cells|78}}
|-
! {{period|109|brief}}
| ?
| ?
| ?
| [[rectifier|p109 rectifier loop]]
|{{cells|156}}
|-
! {{period|110|brief}}
| [[p110 traffic jam]]
|Bill Gosper
| 1994
| [[pseudo-barberpole on Jason's p22]]
|{{cells|51}}
|-
! {{period|111|brief}}
| ?
| ?
| ?
| [[rectifier|p111 rectifier loop]]
|{{cells|136}}
|-
! {{period|112|brief}}
| ?
| ?
| ?
| [[tumbler on Rich's p16]]
|{{cells|50}}
|-
! {{period|113|brief}}
| ?
| ?
| ?
| [[nihonium]]
| {{cells|106}}
|-
! {{period|114|brief}}
| ?
| ?
| ?
| [[Ocellus]]
|{{cells|92}}
|-
! {{period|115|brief}}
| ?
| ?
| ?
| [[rectifier|p115 rectifier loop]]
|{{cells|136}}
|-
! {{period|116|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp116_y4o8bp688gz0gy6330pq2cggz121x225y49f023z8k8x44ay296zy8mmg6p2s82u08ozy81qaic3c4521|patternname=102P116|style=raw}}
|{{cells|102}}
|-
! {{period|117|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp117_y1o44mhar0rahm44ozwg8p7870167876107871zq6hcbagy1szg9gf99gfy26a8oz56o3t5zx1|patternname=117P117|style=raw}}
| {{cells|117}}
|-
! {{period|118|brief}}
| ?
| ?
| ?
| [[rectifier|p118 rectifier loop]]
|{{cells|154}}
|-
! {{period|119|brief}}
| ?
| ?
| ?
| [[rectifier|p119 rectifier loop]]
|{{cells|136}}
|-
! {{period|120|brief}}
| ?
| ?
| ?
| [[figure eight on pentadecathlon]]
| {{cells|24}}
|-
! {{period|121|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|122|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|123|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|124|brief}}
| [[p124 lumps of muck hassler]]
|Dean Hickerson
| 1994
| [[mold on Merzenich's p31]]
| {{cells|60}}
|-
! {{period|125|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|126|brief}}
| ?
| ?
| ?
| [[snacker on 34P14 shuttle]]
| {{cells|74}}
|-
! {{period|127|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|128|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp128_y3ca73oswcczyqg88gzy1ggyh6bbcxca4z8ko010onmcy04eewuscy26dt30g0352z4a6x6qqcyh11zy01221zyh66w73osa6|patternname=p128 wing hassler|style=raw}}
|{{cells|108}}
|-
! {{period|129|brief}}
| ?
| ?
| ?
| [[p57 bumper loop|p129 bumper loop]]
|{{cells|152}}
|-
! {{period|130|brief}}
| ?
| ?
| ?
| [[55P10 on Beluchenko's p13]]
| {{cells|89}}
|-
! {{period|131|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|132|brief}}
| p132 glider loop
|David Buckingham
| 1992
| [[mold on Jason's p33]]
| {{cells|72}}
|-
! {{period|133|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|134|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|135|brief}}
| [[106P135]]
|Bill Gosper
| {{year|1989}}
| [[pentadecathlon on 56P27]]
|{{cells|68}}
|-
! {{period|136|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|137|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|138|brief}}
| ?
| ?
| ?
| [[Gabriel's p138]]
| {{cells|36}}
|-
! {{period|139|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|140|brief}}
| p140 traffic jam
|Bill Gosper
| 1994
| [[34P14 shuttle on dockyard]]
| {{cells|82}}
|-
! {{period|141|brief}}
| ?
| ?
| ?
| [[p47 pre-pulsar shuttle phase-shifting 28P7.1]]
| {{cells|114}}
|-
! {{period|142|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|143|brief}}
| ?
| ?
| ?
| ?
| ?
|-
! {{period|144|brief}}
| capped p144 [[gunstar]]
|David Buckingham
| 1990
| [[Achim's p144]]
| {{cells|42}}
|-
! {{period|150|brief}}
| ?
| ?
| ?
| [[buckaroo|p150 buckaroo shuttle]]
| {{cells|51}}
|-
! {{period|152|brief}}
| ?
| ?
| ?
| [[figure eight on p76 pi-heptomino hassler]]
| {{cells|94}}
|-
! {{period|156|brief}}
| p156 [[traffic jam]] oscillator
|Bill Gosper
| 1994
| [[Jason's p156]]
| {{cells|92}}
|-
! {{period|165|brief}}
| ?
| ?
| ?
| [[rattlesnake on pentadecathlon]]
| {{cells|45}}
|-
! {{period|168|brief}}
| ?
| ?
| ?
| [[figure eight on p21 honey farm hassler]]
| {{cells|72}}
|-
! {{period|177|brief}}
| ?
| ?
| ?
| [[Karel's p177]]
| {{cells|104}}
|-
! {{period|184|brief}}
| ?
| ?
| ?
| [[figure eight on twin bees shuttle]]
| {{cells|40}}
|-
! {{period|186|brief}}
| ?
| ?
| ?
| [[unix on Merzenich's p31]]
| {{cells|64}}
|-
! {{period|188|brief}}
| ?
| ?
| ?
| [[AK-94]] {{LinkCatagolue|xp188_x696o8b9czy065x33xc871wbdzoozwgg04ahhha4y5c871z4701yfoozxggy0ggzx56w4701xmmggo5jzya146w343|patternname=with boat-bits|style=raw}}
| {{cells|108}}
|-
! {{period|196|brief}}
| ?
| ?
| ?
| [[p196 pi-heptomino hassler]]
| {{cells|66}}
|-
! {{period|200|brief}}
| p200 glider loop
|Bill Gosper
| ≤{{year|1987}}
| [[figure eight on centinal]]
|{{cells|82}}
|-
! {{period|226|brief}}
| ?
| ?
| ?
| [[nihonium*]]
| {{cells|107}}
|-
! {{period|230|brief}}
| ?
| ?
| ?
| [[fumarole on twin bees shuttle]]
|{{cells|46}}
|-
! {{period|232|brief}}
| ?
| ?
| ?
| [[figure eight on p29 pre-pulsar shuttle]]
|{{cells|66}}
|-
! {{period|240|brief}}
| ?
| ?
| ?
| [[pentadecathlon on Rob's p16]]
| {{cells|33}}
|-
! {{period|246|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp246_ya32acydg8k8ooozyu1utzzzybcirrd6y4cc4zy1ggy61zggwg9g89z14w61ye354c|patternname=relative|style=raw}}
| {{cells|68}}
|-
! {{period|256|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp256_yr33y166z0ggy033y4178cyb33y0ccz011w66z66yyg88czy4699voyn11zy38ox61zy1311yz66zyzx66woozy133y0ccyb31e8y4cczy566y1cc|patternname=capped|style=raw}} [[period-256 glider gun]]
| {{cells|104}}
|-
! {{period|276|brief}}
| ?
| ?
| ?
| [[caterer on 50P92.1]]
| {{cells|62}}
|-
! {{period|300|brief}}
| ?
| ?
| ?
| [[pentadecathlon on centinal]]
| {{cells|88}}
|-
! {{period|312|brief}}
| ?
| ?
| ?
| [[60P312]]
| {{cells|60}}
|-
! {{period|320|brief}}
| ?
| ?
| ?
| [[fumarole on Merzenich's p64]]
| {{cells|52}}
|-
! {{period|360|brief}}
| ?
| ?
| ?
| [[thumb 1 on Beluchenko's p40]]
| {{cells|62}}
|-
! {{period|368|brief}}
| ?
| ?
| ?
| [[period-184 glider gun]] {{LinkCatagolue|xp368_y0gy632aczy01156zzggyp62sgz56yc65134w16zync4ozy8o8goy911|patternname=with boat-bits|style=raw}}
| {{cells|50}}
|-
! {{period|460|brief}}
| ?
| ?
| ?
| [[pseudo-barberpole on 50P92.1]]
| {{cells|65}}
|-
! {{period|492|brief}}
| ?
| ?
| ?
| [[period-246 glider gun]] {{LinkCatagolue|xp492_y0o4qa344ozx118f0dc3z8oyago0ab2sycc871z0123y9126e431zy8ooz0mqzyt66w7bcczyy66|patternname=with boat-bit|style=raw}}
| {{cells|87}}
|-
! {{period|496|brief}}
| ?
| ?
| ?
| [[Rob's p16 on Merzenich's p31]]
| {{cells|69}}
|-
! {{period|504|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp504_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzyzygg88gxooy1uu06666mmzyzygcc07xccy1rroooo0vvzyzyh66|patternname=p504 glider shuttle|style=raw}}
| {{cells|109}}
|-
! {{period|512|brief}}
| ?
| ?
| ?
| [[period-256 glider gun]] {{LinkCatagolue|xp512_yr33y166z0ggy033y16426ye33y0ccz011w66yuggz66yz56zzzy2mqyz66zygckgk2a21ya66woozy133y0ccye6426y1cczy566y1cc|patternname=with boat-bits|style=raw}}
| {{cells|100}}
|-
! {{period|856|brief}}
| [[period-856 glider gun]]
| [[David Buckingham]]
| 1991
| {{LinkCatagolue|xp856_03bg2kgy1mm66660uuzy111y1vv0oooorrzwggx2c6z4701zzzzzzzzzzzzzzzzzzzzyzyzyl844oxccy1vv03333rrzyzyzyl6603x66y1ddcccc0ffzyzyzym33|patternname=p856 glider shuttle|style=raw}}
|{{cells|109}}
|-
! {{period|1008|brief}}
| ?
| ?
| ?
| {{LinkCatagolue|xp1008_y48oyc356zy432yi696y9o8gozyjc871zzy12552yg2bq4y4o8zca6y3oggyp113y3ca6zy823ys8kk8zzyogs26zx3123y9cicyi8ozymckoyc32|patternname=R126 loop with boat-bits|style=raw}}
| {{cells|107}}
|}

==Notes==
<references group=note />

==See also==
*[[List of common oscillators]]
*[[:Category:Oscillators|List of oscillators]]
*[[Omniperiodic]]
*[[Table of oscillators by period]]
*[[LifeWiki:Game_of_Life_Status_page#Oscillator_periods|Oscillator periods status table]]

==External links==
{{LinkWikipedia|Oscillator_(cellular_automaton)}}
{{LinkLexicon|lex_o.htm#oscillator}}

===Forum threads===
{{LinkForumThread|f=2|t=1437|title=Oscillator Discussion Thread}}
{{LinkForumThread|f=2|t=5338|title=Smallest Known Oscillators to p106 (and Beyond)}}
{{LinkForumThread|f=7|t=5351|title=First Known Oscillators for Each Period}}

__NOTOC__

50P92.1

2021-09-10T16:25:06Z

Freywa: Whaddya know, it features in SKOP276 and SKOP460

{{Oscillator
|name = 50P92.1
|pname = 50p92.1
|c = 50
|bx = 38
|by = 36
|p = 92
|m = 92
|h = 66.8
|v = 0.99
|sv = 0.27
|discoverer = Ivan Fomichev
|discoveryear = 2015
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B3/S234c6e
|synthesis = 14
|synthesis2 = 12
|plaintext = true
|rle = true
|viewerconfig = #C [[ LOOP 92 GPS 23 THUMBSIZE 2 ZOOM 6 ]]
|apgcode = xp92_yi33y133zzzyhckgsxsgkczz33y7c20197zccy734089e
|apgcode2 = xp92_y26wgo4koy1c20197y433z0owcu7jab01y334089ez161y01zzxckgsxsgkczzy0cc
}}
'''50P92.1''' is a {{period|92}} [[oscillator]] discovered by [[Ivan Fomichev]] in {{year|2015}}.<ref name="post15656"/> It is tied with [[twin bees shuttle on 22P4.3]] for the smallest known period-92 oscillator.

==See also==
* [[Twin bees shuttle]]

==References==
<references>
<ref name="post15656">{{LinkForumThread
|format = ref
|title = Re: Thread for your unsure discoveries
|p = 15656
|author = Ivan Fomichev
|date = January 5, 2015
}}</ref>
</references>

==External links==
{{LinkCatagolue|xp92_yi33y133zzzyhckgsxsgkczz33y7c20197zccy734089e}}
{{Sparker|p=92|type=domino|strength=strong}}
[[Category:Unnamed periodic objects]]