LifeWiki - User contributions [en]

Category:Spaceships with period 16777216

2025-10-28T08:24:28Z

TYCF: Created page with "{{SpaceshipPeriod|p=16777216}}"

Leaf bug 2

2025-10-28T07:48:27Z

TYCF: /* Gun */

{{Spaceship
|name = Leaf bug 2
|pname = leafbug2
|c = 24460
|bx = 12415
|by = 6315
|dir = Orthogonal
|p = 240
|m = 240
|s = 31c/240
|z = 31c/240
|h = 16724.9
|symmetry = n
|discoverer = Gustone
|discoveryear = 2025
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 850 HEIGHT 500 ]]
|mc = true
|plaintext = true
|rle = true
}}

'''Leaf bug 2''' is a [[31c/240 orthogonal]] [[spaceship]] using the [[31c/240 Herschel-pair climber]] that was constructed on June 4, {{year|2025}}, by [[Gustone]],<ref name="post212878"/> as an improvement over the earlier [[leaf bug]]. The first version, known as '''leaf bug 2a''', had a [[population]] of 29591 cells and a {{times|15129|7988}} [[bounding box]].<ref name="post212878"/> The following form, known as '''leaf bug 2a.1''', was created on June 7 with a population of 27507 cells and a bounding box of {{times|14285|7576}}.<ref name="post212983"/> On June 14, it was reduced to '''leaf bug 2c''', with a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213261"/> On June 22, it was finally reduced to '''leaf bug 2e''', with a population of 24861, and a bounding box of {{times|13179|6698}}.<ref name="post213595"/> On June 24, a variant of leaf bug 2c was created by Gustone, with a bounding box of {{times|12927|6576}}, and a population of 24814.<ref name="post213623"/> It is the smallest [[macro-spaceship]] constructed, both in bounding box, and in population.

A comparison with the original leaf bug can be seen below:
{{gallery top}}
{{gallery item|{{ThumbEnlarge|Leafbugandleafbug2.png}}}}
{{gallery bottom}}

==Synthesis==
On June 2, 2025, a [[dirty]] [[synthesis]] of a Leaf bug 2 variant was created by Gustone, based on earlier partial synthesis of the central pair, [[track]] builder, first [[LWSS]] [[rake]], and small diamond, also by Gustone.<ref name="post213923"/><ref name="post213982"/> A clean version of the synthesis was created by [[Entity Valkyrie]] on the same day, using 2988 [[glider]]s, 644 LWSSes, and 2 [[HWSS]]es (4926 gliders in total).<ref name="post214022"/> It was then reduced by 2 gliders by [[rabbit]].<ref name="post214023"/> On June 3, 2025, a smaller synthesis was created by [[EvinZL]].<ref name="post214048"/>
{{gallery top}}
{{gallery item|[[image:Leafbug2synth.png‎|thumb|left|EvinZL's synthesis of a variant of Leaf bug 2]]}}
{{gallery item|[[image:Leafbug2EVsynth.png‎|thumb|left|Entity Valkyrie's synthesis of a variant of Leaf bug 2]]}}
{{gallery bottom}}

==Gun==
A period 131072 [[gun]] was created by [[Entity Valkyrie]] on August 14, {{year|2025}}, to fire a variant of Leaf bug 2. It was the first gun created to fire a [[31c/240 orthogonal]] spaceship. The population of the gun is 16,225,032 cells, and it has a bounding box of {{times|1,097,252|829,150}}.<ref name="post216063"/>
{|class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
|[[image:Leafbug2EVgun.png‎|400px]]
|-
|Entity Valkyrie's p131072 gun of a variant of Leaf bug 2
|}
It was later reduced by [[Hippo.69]] thrice to a bounding box of {{times|66686|59697}} and a population of 131972.

== Versions ==
=== Leaf bug 2a ===
'''Leaf bug 2a''', which was constructed on June 4, 2025, was designed to minimize the amount of possible points of failure.<ref name="post212878"/> It was later reduced to '''leaf bug 2a.1'''.<ref name="post212983"/>
{{EmbedViewer
|pname = leafbug2a
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2a
}}

=== Leaf bug 2a.1 ===
'''Leaf bug 2a.1''', which was constructed on June 7, 2025, decreased the population to 27507 and the bounding box to {{times|14285|7576}}.<ref name="post212983"/> It was later reduced to '''leaf bug 2c'''.<ref name="post213261"/>
{{EmbedViewer
|pname = leafbug2a1
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 500 ]]
|position = center
|caption = Leaf bug 2a.1
}}
=== Leaf bug 2c ===
'''Leaf bug 2c''', which was constructed on June 14, 2025, was the first version that broke the record of the smallest macro-spaceship by both population and bounding box. It had a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213595"/> It was later reduced to '''leaf bug 2e''', which is displayed in the infobox.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2c
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2c
}}
==== Bounding box variant ====
A bounding box-optimised variant of Leaf bug c, was created by Gustone on June 24, 2025. It had a bounding box of {{times|12927|6576}}, and a population of 24814. It was however based on Leaf bug e.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2cbb
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Bounding box-optimised variant of Leaf bug 2c
}}

== References ==
<references>
<ref name="post212878">{{LinkForumThread
|format = ref
|p = 212878
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 4, 2025
}}</ref>
<ref name="post212983">{{LinkForumThread
|format = ref
|p = 212983
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 7, 2025
}}</ref>
<ref name="post213923">{{LinkForumThread
|format = ref
|p = 213923
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = June 30, 2025
}}</ref>
<ref name="post213982">{{LinkForumThread
|format = ref
|p = 213982
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = July 2, 2025
}}</ref>
<ref name="post214022">{{LinkForumThread
|format = ref
|p = 214022
|title = Re: Small Spaceship Syntheses
|author = Entity Valkyrie 2
|date = July 2, 2025
}}</ref>
<ref name="post213261">{{LinkForumThread
|format = ref
|p = 213261
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 14, 2025
}}</ref>
<ref name="post213595">{{LinkForumThread
|format = ref
|p = 213595
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 22, 2025
}}</ref>
<ref name="post213623">{{LinkForumThread
|format = ref
|p = 213623
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 24, 2025
}}</ref>
<ref name="post214023">{{LinkForumThread
|format = ref
|p = 214023
|title = Re: Small Spaceship Syntheses
|author = rabbit
|date = July 2, 2025
}}</ref>
<ref name="post214048">{{LinkForumThread
|format = ref
|p = 214048
|title = Re: Small Spaceship Syntheses
|author = EvinZL
|date = July 3, 2025
}}</ref>
<ref name="post216063">{{LinkForumThread
|format = ref
|p = 216063
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Entity Valkyrie 2
|date = August 14, 2025
}}</ref>
</references>

== External links ==
* [https://en.wikipedia.org/wiki/Phylliidae Leaf insect] at Wikipedia

[[Category:Engineered spaceships]]
[[Category:Macro-spaceships]]

Rule:GoldenTeeth

2025-10-26T06:44:47Z

TYCF: Created page with "@RULE GoldenTeeth rabbit, 2025-10-25 @TABLE n_states:5 neighborhood:Moore symmetries:permute var a1 = {0, 1, 2, 3, 4} var a2 = a1 var a3 = a1 var a4 = a1 var a5 = a1 var a6 = a1 var a7 = a1 var a8 = a1 var m1 = {0, 2} var m2 = m1 var m3 = m1 var m4 = m1 var m5 = m1 var m6 = m1 var tw = {0, 1} var sp = {1, 2, 3} var di = {3, 4} 0, 1, 1,m1,m2,m3,m4,m5,m6,2 1, 1, 1, 1, 1, 1, 1, 1, 1,4 1,tw,tw,m1,m2,m3,m4,m5,m6,3 # D0, D2 sp, 4,a1,a2,a3,a4,a5,a6,a7,4 # spread 2,a1,..."

@RULE GoldenTeeth

rabbit, 2025-10-25

@TABLE
n_states:5
neighborhood:Moore
symmetries:permute

var a1 = {0, 1, 2, 3, 4}
var a2 = a1
var a3 = a1
var a4 = a1
var a5 = a1
var a6 = a1
var a7 = a1
var a8 = a1

var m1 = {0, 2}
var m2 = m1
var m3 = m1
var m4 = m1
var m5 = m1
var m6 = m1

var tw = {0, 1}
var sp = {1, 2, 3}
var di = {3, 4}

0, 1, 1,m1,m2,m3,m4,m5,m6,2
1, 1, 1, 1, 1, 1, 1, 1, 1,4
1,tw,tw,m1,m2,m3,m4,m5,m6,3 # D0, D2
sp, 4,a1,a2,a3,a4,a5,a6,a7,4 # spread
2,a1,a2,a3,a4,a5,a6,a7,a8,1
di,a1,a2,a3,a4,a5,a6,a7,a8,0 # die

@COLORS
1 255 255 0
2 160 160 0
3 96 96 0
4 0 255 0

@NAMES
1 Tooth
2 BabyTooth
3 RottenTooth
4 Decay

@ICONS
XPM
"7 28 2 1"
". c #000000"
"A c #FFFFFF"

"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"

"..AAA.."
".AAAAA."
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
".AAAAA."
"..AAA.."

"...A..."
"...A..."
"..AAA.."
"AAAAAAA"
"..AAA.."
"...A..."
"...A..."

"AA...AA"
"AAA.AAA"
".AAAAA."
"..AAA.."
".AAAAA."
"AAA.AAA"
"AA...AA"

Paul

2025-10-23T19:02:10Z

TYCF: Created page with "{{disambig|name=Paul}} *Paul Callahan, a life enthusiast. *Paul Chapman *Paul Tooke, the discoverer of various spaceships *Paul Rendell, the constructor of the turing machine *Paul Schick, the discoverer of the schick engine"

{{disambig|name=Paul}}
*[[Paul Callahan]], a [[life enthusiast]].
*[[Paul Chapman]]
*[[Paul Tooke]], the discoverer of various [[spaceship]]s
*[[Paul Rendell]], the constructor of the [[turing machine]]
*[[Paul Schick]], the discoverer of the [[schick engine]]

Spaceship

2025-10-18T15:52:19Z

TYCF: /* Adjustable spaceships */

{{Glossary}}
[[File:Lwss.gif|thumb|right|The lightweight spaceship in [[Conway's Game of Life]]]]A '''spaceship''' (also referred to as a '''glider''',<ref>{{CiteLexicon|file=lex_g.htm#glider|name=Glider|accessdate=April 18, 2009}}</ref> or less commonly a '''fish''',<ref>{{CiteLexicon|file=lex_f.htm#fish|name=Fish|accessdate=April 18, 2009}}</ref> and commonly shortened to "ship") is a finite [[pattern]] that returns to its initial state after a number of [[generation]]s (known as its [[Period#Spaceships|period]]) but in a different location.

__TOC__

== Spaceship speed ==
{{main|Speed}}
The speed of a spaceship is the number of [[cell]]s that the pattern moves during its period, divided by the period length. This is expressed in terms of ''c'' (the metaphorical "speed of light") which is one cell per generation; thus, a spaceship with a period of five that moves two cells to the left during its period travels at the speed of [[2c/5 orthogonal|2c/5]].

Until the construction of [[Gemini]] in May {{year|2010}}, all known spaceships in [[Conway's Game of Life|Life]] traveled either orthogonally (only horizontal or vertical displacement) or diagonally (equal horizontal and vertical displacement); other [[oblique spaceship]]s have been constructed since then, e.g. [[waterbear]] and the [[Parallel HBK]]. It is known that Life has spaceships that travel in all rational directions at arbitrarily slow speeds (see [[universal constructor]]).

Spaceships traveling in other directions and at different speeds have also been constructed in other two-dimensional [[cellular automaton|cellular automata]].<ref name="fano_ca" />

The maximum speed for Life is [[c/2 orthogonal]] and [[c/4 diagonal]]<ref name="spaceship_speed_limits_in_life_like_cellular_automata" /> (and continually, (2, 1)c/6 for [[knightship|slope 2]], (3, 1)c/8 for [[slope]] 3, etc.); however, certain [[agar crawler]]s such as [[lightspeed wire]] can break this speed in their respective medium. Spaceships in the traditional [[Moore neighbourhood]] of range 1 have a maximum speed of c, although [[Larger than Life]] neighbourhoods can increase this limit depending on the interactable distance between cells. For Life, no spaceship can move at speed (''m'',''n'')c/''x'' where (''m''+''n'')/''x'' > 1/2; for other non-strobing [[Life-like cellular automaton|outer-totalistic]] and [[Non-totalistic cellular automaton|non-totalistic]] rules, the limit is at most 1, and in strobing rules, 3/2.<ref name="post56111">{{LinkForumThread|f=11|t=3193|p=56111|title=Re: B0 hyper-relativistic speeds|author=vyznev|date=February 4, 2018|format=raw}}, in which it was noted that INT rules have a speed limit of <tt>x+y ≤ {{frac|3|2}}*p</tt></ref>
Certain range-1 [[non-isotropic cellular automaton|non-isotropic]] rules can harbour [[c diagonal]] spaceships, giving a limit of 2.

== Spaceship types ==
{{main|Types of spaceships}}
Spaceships are most commonly sorted by their speed and direction, and sometimes their period. They can be separated into three fundamental categories:

=== Elementary spaceships ===
[[File:AlmostKnightship.png|thumb|right|An "[[almost knightship]]"]]
''Elementary spaceships'' are the smallest classification of spaceships. This class consists of naturally-occurring ships, as well as those found by direct computer search, such as the [[weekender]].

Despite their generally small size, only a few of them have been known to have emerged from [[soup]]s.

Constructing [[gun]]s for elementary spaceships is usually difficult, as only a few have known glider syntheses (with those that do generally requiring a lot of gliders in awkward positions), with larger elementary spaceships tending to contain high concentrations of [[space dust]].

The following table lists the smallest known cases for the lowest possible periods for each speed:

{| class="wikitable"
! Speed
! Slope
! Direction
! Smallest known
! Minimum # of [[cell]]s
|-
! [[c/2 orthogonal|c/2]]
! 0
| orthogonal
| [[64P2H1V0]]
| {{cells|64}}
|-
! [[c/3 orthogonal|c/3]]
! 0
| orthogonal
| [[25P3H1V0.1]]<ref group="n">[[25P3H1V0.2]] has the same population of 25, but has a more expansive bounding box</ref>
| {{cells|25}}
|-
! [[c/4 orthogonal|c/4]]
! 0
| orthogonal
| [[37P4H1V0]]
| {{cells|37}}
|-
! [[c/5 orthogonal|c/5]]
! 0
| orthogonal
| [[spider]]
| {{cells|58}}
|-
! [[2c/5 orthogonal|2c/5]]
! 0
| orthogonal
| [[30P5H2V0]]
| {{cells|30}}
|-
! [[c/6 orthogonal|c/6]]
! 0
| orthogonal
| [[56P6H1V0]]
| {{cells|56}}
|-
! [[c/7 orthogonal|c/7]]
! 0
| orthogonal
| [[loafer]]
| {{cells|20}}
|-
! [[2c/7 orthogonal|2c/7]]
! 0
| orthogonal
| [[weekender]]
| {{cells|36}}
|-
! [[3c/7 orthogonal|3c/7]]
! 0
| orthogonal
| [[232P7H3V0]]
| {{cells|232}}
|-
! [[c/10 orthogonal|c/10]]
! 0
| orthogonal
| [[copperhead]]
| {{cells|28}}
|-
! colspan="5" |
|-
! [[c/4 diagonal|c/4]]
! 1
| diagonal
| [[glider]]
| {{cells|5}}
|-
! [[c/5 diagonal|c/5]]
! 1
| diagonal
| [[58P5H1V1]]
| {{cells|58}}
|-
! [[c/6 diagonal|c/6]]
! 1
| diagonal
| [[77P6H1V1]]
| {{cells|77}}
|-
! [[c/7 diagonal|c/7]]
! 1
| diagonal
| [[lobster]]
| {{cells|83}}
|-
! [[c/8 diagonal|c/8]]
! 1
| diagonal
| [[walrus]]
| {{cells|68}}
|-
! colspan="5" |
|-
! [[(2,1)c/6]]
! 2
| [[knightwise]]
| [[Sir Robin]]
| {{cells|282}}
|}
<references group="n"/>

The following is an incomplete list of some higher-period ships which travel at the same velocities:<ref>{{CiteSummersPattern|name=jslife|accessdate=January 17, 2019}}</ref>
{| class="wikitable"
! Speed
! Direction
! Smallest known
! Minimum # of [[cell]]s
|-
! [[c/2 orthogonal|2c/4]]
| orthogonal
| [[lightweight spaceship]]
| {{cells|9}}
|-
! [[c/2 orthogonal|3c/6]]
| orthogonal
| [[86P6H3V0]]
| {{cells|86}}
|-
! [[c/3 orthogonal|2c/6]]
| orthogonal
| [[72P6H2V0]]
| {{cells|72}}
|-
! [[c/2 orthogonal|4c/8]]
| orthogonal
| [[31P8H4V0]]
| {{cells|31}}
|-
! [[c/4 orthogonal|2c/8]]
| orthogonal
| [[74P8H2V0]]
| {{cells|74}}
|-
! [[c/3 orthogonal|3c/9]]
| orthogonal
| [[55P9H3V0]]
| {{cells|55}}
|-
! [[c/2 orthogonal|5c/10]]
| orthogonal
| {{LinkCatagolue|xq10_wg0cc4625ggowgo8cy5gz4et915x137c4clkig0g0s6231fpogzx3l5e3y310665d0ew8owh6qaa33zx2d0ly9g0gwgo50d0vggaz0gom5536y0g0gc8bb5d0ry0gosb2245cz13d4klx4efp11dpigx132647czy0111325y41|patternname=214P10H5V0|style=raw}}
| {{cells|214}}
|-
! [[2c/5 orthogonal|4c/10]]
| orthogonal
| [[66P10H4V0]]
| {{cells|66}}
|-
! [[c/5 orthogonal|2c/10]]
| orthogonal
| {{LinkCatagolue|xq10_o8ul1431z12fe022420626c66z0rhh0rzg8ue08848z32flg4og|patternname=68P10H2V0|style=raw}}
| {{cells|68}}
|-
! [[c/2 orthogonal|6c/12]]
| orthogonal
| [[35P12H6V0]]
| {{cells|35}}
|-
! [[c/3 orthogonal|4c/12]]
| orthogonal
| {{LinkCatagolue|xq12_y6g81t0t18gzy4so4k7ece7k4oszy7l3i4i3lzy52q9fxf9q2z25c2ce057y7750ec2c52|patternname=103P12H4V0|style=raw}}
| {{cells|103}}
|-
! [[c/4 orthogonal|3c/12]]
| orthogonal
| {{LinkCatagolue|xq12_2d54031013045d2yd2d54031013045d2zvfg8sy1s8gfvy0oc2u0u2coy0vfg8sy1s8gfvzdsl211gng112lsdy15580855y1dsl211gng112lsdz058gsg131gsg85y0oo0lj0jl0ooy058gsg131gsg85zx55qxq55y2edh0hph0hdey255qxq55zy03626263y3114b616b411y33626263zyg2320232|patternname=314P12H3V0|style=raw}}
| {{cells|314}}
|-
! [[c/6 orthogonal|2c/12]]
| orthogonal
| {{LinkCatagolue|xq12_yj13922y022931zymo7q99q7ozyggg0nj611tuut116jn0ggzyi1y0gc44cgy01z03m0m3y03m0m3y8223322y93m0m3y03m0m3zw3gn3aaaa3ng3y7o035w530oy83gn3aaaa3ng3zwu97y279uy812222221y9u97y279uz22qggy2ggq220248oe2yb2eo842022qggy2ggq22zxq03q22q30qy526csssssssssssc62y5q03q22q30qzxdidy0didybe2i2eybdidy0didzyk8g40cscsc04g8zyjg0omb86068bmo0gzyj1247y37421zyk4ao9f9o9f9oa4zykg8kg0o5o0gk8gzyk12jg12121gj21zyj11cn4mo0om4nc11zyjgo0g61x16g0ogzyhegcd16b6g0g6b61dcgezyhc4g122e0a0a0e221g4czyh124epni2h0h2inpe421zyjg8mti47074itm8gzyg8u125g11gg0gg11g521u8zyj1h9o8pp0pp8o9h1zyj12t60uu0uu06t21zymora202arozyi80a191vg0gv191a08zyh18d6oy5o6d81zyk1gp4y14pg1zyhgg07g24gxg42g70ggzyh1210121y11210121|patternname=861P12H2V0|style=raw|format=extended}}
| {{cells|861}}
|-
! [[c/2 orthogonal|7c/14]]
| orthogonal
| {{LinkCatagolue|xq14_y6ogmm23zy427ekgi0gzy71q2n1zy71mgqzy5g0gr31w3mh0c0gwgxgy3gzwogmm23125dkl0eb8a9ll51x8h11y0311z27ekgi0gy1120612zx1q2n1zx1mgqzgosb2i13z0162qqggzy31|patternname=174P14H7V0|style=raw}}
| {{cells|174}}
|-
! [[c/3 orthogonal|5c/15]]
| orthogonal
| {{LinkCatagolue|xq15_sa408bb5z0344pa3t123z4ah0vwvv0a0ez0o44jaong8oy06mhgz7a402qqky1c4c111zy8br5gzya1|patternname=112P15H5V0|style=raw}}
| {{cells|112}}
|-
! [[c/5 orthogonal|3c/15]]
| orthogonal
| [[p15 pre-pulsar spaceship]]
| {{cells|252}}<ref name="post153692" />
|-
! [[c/2 orthogonal|8c/16]]
| orthogonal
| [[Coe ship]]
| {{cells|28}}
|-
! [[c/2 orthogonal|9c/18]]
| orthogonal
| {{LinkCatagolue|xq18_ykggy4g8go0v1s0gzyl364kg4li620hl0v0j220aigz59o0o4gg0th8a0sos0a8ht0gg4o0uh67y06os0v1kg880988zx1344421y71244431wggxg0ggqa1x1fc3t0g8xq2gk0ogo0kg2qx8g0giazyq24c0vge833y41127899431x111x134998721zyd8oy38o0u1coc72zye338fgps87431zyj1|patternname=293P18H9V0|style=raw|format=extended}}
| {{cells|293}}
|-
! [[c/3 orthogonal|6c/18]]
| orthogonal
| {{LinkCatagolue|xq18_061ugzw1cdcy3iccy1hmsgwa6my2ggz3jroy3gog4n081qq222q38c2agr2amf2of2z0gggx66wvvm9g609ggxg90999gg09pf0gzccd1y41g2e01855kkklc134l0d456fkhf4zw8jr3y3433y1863x566z0687|patternname=242P18H6V0|style=raw}}
| {{cells|242}}
|-
! [[c/6 orthogonal|3c/18]]
| orthogonal
| {{LinkCatagolue|xq18_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|patternname=861P18H3V0|style=raw|format=extended}}
| {{cells|861}}
|-
! [[c/2 orthogonal|10c/20]]
| orthogonal
| [[sidewinder]]
| {{cells|32}}
|-
! [[c/10 orthogonal|2c/20]]
| orthogonal
| [[Fireship|fireship tagalong]]
| {{cells|131}}
|-
! [[2c/7 orthogonal|6c/21]]
| orthogonal
| [[doo-dah]]
| {{cells|74}}
|-
! [[c/2 orthogonal|11c/22]]
| orthogonal
| {{LinkCatagolue|xq22_1fe2o2s0giay1gyfggxg0ggo8zx11avg180g4gu0749c8899988egs0g0g0g24c0vge833zy3131011y2k50t9895x234e8f0aoc72zy2ggy89l0gmd8zy377hs1u0o95w8a0u1cf1zy75fogk0oi8f211zya1|patternname=213P22H11V0|style=raw|format=extended}}
| {{cells|213}}
|-
! [[c/2 orthogonal|12c/24]]
| orthogonal
| {{LinkCatagolue|xq24_xo8ox6frcz0gh242hgz6d73037d6|patternname=39P24H12V0|style=raw}}
| {{cells|39}}
|-
! [[3c/7 orthogonal|12c/28]]
| orthogonal
| [[232P7H3V0|3c/7 wave stabilization]]
| {{cells|307}}
|-
! [[c/5 orthogonal|6c/30]]
| orthogonal
| [[pre-pulsar spaceship]]
| {{cells|128}}
|-
! [[c/2 orthogonal|18c/36]]
| orthogonal
| [[35P12H6V0]] with [[pufferfish]] [[tagalong]]
| {{cells|102}}
|-
! colspan="5" |
|-
! [[c/4 diagonal|2c/8]]
| diagonal
| [[p8 swan tagalong]]
| {{cells|117}}
|-
! [[c/4 diagonal|3c/12]]
| diagonal
| {{LinkCatagolue|xq12_ym8u0mwhhh0igxoozyfgg0ggwepg09f011whuby0562zy8o8cc46baqo046jrp6zy8g5ray34pczxc0k822ijr3x247zig831y0114oczx562|patternname=142P12H3V3|style=raw|format=extended}}
| {{cells|142}}
|}

=== Engineered spaceships ===
''Engineered spaceships'' are defined as spaceships consisting of small interacting components.<ref name="new_spaceship_speed_in_conways_game_of_life" /> Some engineered spaceships are composed of hundreds of thousands or even millions of active cells; these are also sometimes referred to as ''caterpillars'' after the first engineered [[macro-spaceship]]. Other simpler mechanisms like the [[Cordership]]s might need a relatively small number of components, down to a minimum of just two for the [[2-engine Cordership]]. Such spaceships have occurred [[natural]]ly in other rules, but not yet in [[Conway's Game of Life|Conway Life]].

Engineered spaceships have fixed speeds, because their mechanisms depend on supporting a specific active reaction that travels at one particular speed. Some rely on "[[crawler]]s", reactions in which a pattern reacts with another pattern, producing both the patterns in different positions as in the [[pi crawler]]. Others, like the [[Cordership]]s and [[pufferfish spaceship]]s, rely on ''stabilised [[puffer]] engines'', and are often referred to as "Corderoids". The process of stabilising a moving engine is referred to as [[corderisation]].

{| class="wikitable"
! Speed
! Direction
! Smallest known
! Minimum # of [[cell]]s
! Classification
|-
! [[17c/45 orthogonal|17c/45]]
| orthogonal
| [[caterpillar]]
| {{cells|11,880,039}}
| Crawler-based
|-
! [[31c/240 orthogonal|31c/240]]
| orthogonal
| [[leaf bug 2]]
| {{cells|26,571}}
| Crawler-based
|-
! [[:Category:Spaceships with speed (23,5)c/79|(23,5)c/79]]
| slope 23/5
| [[waterbear]]
| {{cells|197,896}}
| Crawler-based
|-
! [[:Category:Spaceships with speed (34,7)c/156|(34,7)c/156]]
| slope 34/7
| [[Much smaller (34,7)c/156 spaceship]]
| {{cells|647,595}}
| Crawler-based
|-
! [[:Category:Spaceships with speed (6,3)c/1024|(6,3)c/1024]]
| knightwise
| [[HBK caterpillar]]
| {{cells|329,071}}
| Crawler-based
|-
! colspan="5" |
|-
! [[c/2 orthogonal|c/2]]
| orthogonal
| [[pufferfish spaceship]]
| {{cells|235}}
| Stabilized puffer engine
|-
! [[c/12 diagonal|c/12]]
| diagonal
| [[2-engine Cordership]]
| {{cells|100}}
| Stabilized puffer engine
|}

==== Traveling signal loops ====
A traveling [[signal]] loop is a subcategory somewhat similar to an engineered spaceship, but with key differences. The usual reason for constructing a traveling signal loop is to extract an extra output glider at some point in each cycle, producing an [[engineless]] [[rake]]. Suppressing a rake's output glider will trivially produce a high-period spaceship.

One main difference between engineered spaceships and traveling signal loops is that the "specific active reactions that travel at one particular speed" are spaceships themselves, and don't need any additional support. The signals traveling in the signal loops can generally be removed without having any effect on the fleet of spaceships supporting the loop.

{| class="wikitable"
! Speed
! Direction
! Examples
! Classification
|-
! [[2c/7 orthogonal|2c/7]]
| orthogonal
| [[weekender distaff]]
| High-period signal loop
|-
! [[c/3 orthogonal|c/3]]
| orthogonal
| c/3 orthogonal rake
| High-period signal loop
|-
! [[c/4 orthogonal|c/4]]
| orthogonal
| p388 c/4 forward rake, David Bell's adjustable-period backrake
| High-period signal loop
|-
! [[c/5 orthogonal|c/5]]
| orthogonal
| c/5 orthogonal rake
| High-period signal loop
|-
! [[2c/5 orthogonal|2c/5]]
| orthogonal
| 2c/5 orthogonal rake
| High-period signal loop
|-
! [[c/4 diagonal|c/4]]
| diagonal
| c/4 diagonal rake
| High-period signal loop
|-
! [[c/5 diagonal|c/5]]
| diagonal
| [[c/5 diagonal rake]]
| High-period signal loop
|-
! [[c/12 diagonal|c/12]]
| diagonal
| c/12 diagonal rake
| High-period signal loop
|}

=== Adjustable spaceships ===
''Adjustable spaceships'' (formerly known as ''engineerable spaceships'') are the third extant class of spaceships. On average smaller than the engineered spaceships in terms of population, but much larger in bounding box, their magic comes from having (to an extent) adjustable features, usually speed. With some almost always trivial modifications, these spaceships can be made to travel at different velocities and even directions. Rather than being searched for, programs exist that explicitly construct the spaceships. Adjustable spaceships can be based on variable-speed reactions such as the half-bakery and glider reaction or the freezing/reanimation cycle of the Caterloopillar, or by reading instruction tapes as in the Gemini. Families of adjustable spaceships include the Geminoids, Demonoids, Orthogonoids, loopships, half-baked knightships and Caterloopillars.

{| class="wikitable"
! Speed
! Direction
! Smallest known
! Minimum # of [[cell]]s
|-
! All speeds slower than c/4
| orthogonal
| [[Caterloopillar]] variants
| [[:Category:Patterns with (number) cells|Varies]]
|-
! 16c/217251
| orthogonal
| [[Orthogonoid]]
| {{cells|467,746}}
|-
! [[c/16384 orthogonal|c/16384]]
| orthogonal
| [[Hashlife-friendly Orthogonoid]]
| {{cells|467,585}}
|-
! [[c/32768 orthogonal|c/32768]]
| orthogonal
| [[Double-wide Orthogonoid]]
| {{cells|467,346}}
|-
! 1000130c/20003511
| orthogonal
| [[loopship]]
| {{cells|267,672}}
|-
! colspan="5" |
|-
! (200,7)c/81976184
| slope 200/7
| [[Stable Storage Spaceship]]
| {{cells|633,388}}
|-
! (5120,1024)c/16849793
| slope 5 (ibiswise)
| [[Gemini]]
| {{cells|846,278}}
|-
! (3,1)c/3948264
| slope 3 (camelwise)
| [https://conwaylife.com/forums/viewtopic.php?p=66297#p66297 camelship]
| {{cells|239,822}}
|-
! (4096,2048)c/17783745
| slope 2 (knightwise)
| [https://conwaylife.com/forums/viewtopic.php?f=2&t=406&start=25#p2578 Gemini 2]
| [[:Category:Patterns with between 100,000 and 999,999 cells|<=872,252]]
|-
! (6,3)c/245912
| slope 2 (knightwise)
| [[Parallel HBK]]
| {{cells|132,945}}
|-
! (6,3)c/2621440
| slope 2 (knightwise)
| [[Half-baked knightship]]
| {{cells|1,049,395}}
|-
! colspan="5" |
|-
! 65c/438852
| diagonal
| [[Demonoid|0hd Demonoid]]
| {{cells|27,250}}
|-
! 65c/818356
| diagonal
| [[Demonoid|10hd Demonoid]]
| {{cells|47,701}}
|-
! 79c/1183842
| diagonal
| [[Demonoid|single-channel Demonoid]]
| {{cells|60,672}}
|-
! c/16384
| diagonal
| [[Demonoid|Scorbie's Demonoid]]
| {{cells|72,207}}
|-
! c/512
| diagonal
| [[Demonoid|Hashlife-friendly Demonoid]]
| {{cells|105,369}}
|-
! 511c/1677216
| diagonal
| [[Thessalonic Demonoid]]
| {{cells|328,699}}
|-
! 1746011c/8916896
| diagonal
| [[Demonoid|Speed Demonoid]]
| {{cells|1,021,124}}
|}

=== Other classifications ===
{{main|Types of spaceships|Spaceship types}}
[[File:Greyship2 H Holzwart.png|thumb|right|A greyship found by [[Hartmut Holzwart]]]]
Although spaceships are most commonly categorized by their speed and direction, other categorizations have been applied to spaceships based on their appearances, components, or other properties. One such categorization is the symmetry of spaceships: spaceships can be bilaterally symmetric (e.g. copperhead), exhibit [[Types of spaceships#Glide symmetric spaceship|glide symmetry]] (e.g. glider), or simply be asymmetric (e.g. loafer). Other somewhat subjective categorizations have also been made, such as [[greyship]]s, spaceships filled with large amounts of static, live cells in the form of an [[agar]], or [[Types of spaceships#Smoking ship|smoking ships]], which produce large [[spark]]s, a notable example being the [[Schick engine]]. A spaceship may also support other components which would not function as spaceships on their own. Given a freestanding spaceship, such additional components are often referred to as [[tagalong]]s; however they can be attached to any side of a spaceship, such as [[pushalong 1]] and [[sidecar]]. Unstable spaceships immersed in a sustaining cloud are known as [[Types of spaceships#Flotilla|flotillae]]. A well known example is that of the [[overweight spaceship]]s, which are unstable alone but may be 'escorted' by two or more smaller spaceships.

==History==

===1970s===
[[File:mwss.gif|thumb|right|A middleweight spaceship]]
The four smallest spaceships in life, the glider, lightweight spaceship, [[middleweight spaceship]] and [[heavyweight spaceship]], were all found by hand in {{year|1970}}. For almost twenty years spaceship development was limited to adding [[tagalong]]s to the known [[c/2 orthogonal|c/2]] spaceships, such as the Schick engine.

===1980s===
Significant advances in spaceship technology came in {{year|1989}}, when [[Dean Hickerson]] began using [[Computer search|automated searches]] based on a depth-first backtracking algorithm. These searches found orthogonal spaceships with speeds of [[c/3 orthogonal|c/3]] and [[c/4 orthogonal|c/4]], new [[c/2 orthogonal|c/2]] ships, and the first spaceship other than the glider to travel at the speed of [[c/4 diagonal]]ly, dubbed the [[big glider]].

===1990s===
Hickerson continued to find new spaceship speeds, the first of this decade being [[2c/5 orthogonal]], plus several ways to combine [[switch engine]]s to create the first [[c/12 diagonal]] spaceships, named [[Cordership]]s in honour of [[Charles Corderman]].

The next spaceship speed to be discovered was that of the orthogonal [[c/5 orthogonal|c/5]] [[snail]], found by [[Tim Coe]] in {{year|1996}}, with a program he had designed using breadth-first searching, and which could split tasks between multiple CPUs.<ref name="lifepage_patterns_p5ss" /> In the following year, [[David Bell]] found the much smaller c/5 [[spider]] using [[lifesrc]], a program based on Hickerson's search algorithm.<ref name="lifepage_patterns_newc5" />

In March of {{year|1998}} [[David Eppstein]] created [[gfind]], a breadth-first program that uses a depth-first search to limit the size of the search queue.<ref name="arxiv_0004003v2" />

===2000s===
[[File:Weekender small.gif|thumb|right|David Eppstein's weekender]]
Eppstein put his search program to good use in {{year|2000}}, discovering the first spaceship that travels at the speed of [[2c/7 orthogonal]]ly, the [[weekender]]. A search by [[Paul Tooke]] using the same program found the first [[c/6 orthogonal]] spaceship, the [[dragon]], later that year. Also in 2000, [[Jason Summers]] found the first [[c/5 diagonal]] spaceship using David Bell's lifesrc program.

In {{year|2004}} [[Gabriel Nivasch]], with the help of Jason Summers and David Bell, finished construction on the [[caterpillar]], the first known orthogonal [[17c/45 orthogonal|17c/45]] spaceship, which made use of the [[17c/45 reaction]].

===2010s===
[[File:Loafer.gif|thumb|right|Josh Ball's loafer]]
In May {{year|2010}} [[Andrew J. Wade]] created a universal constructor-based spaceship, [[Gemini]], which travels at a speed of (5120,1024)c/33699586.<ref>{{LinkGoLNews|2010/05/oblique_life_spaceship_created.html|title=Oblique Life spaceship created|date=May 19, 2010|author=Adam P. Goucher}}</ref> This was the first explicitly constructed spaceship in Life to travel in an [[Types of spaceships#Knightship|oblique]] direction, and also yielded the first explicit method of constructing arbitrarily slow spaceships.

In August {{year|2011}}, Matthias Merzenich discovered [[lobster]], the first c/7 diagonal spaceship.

In February 2013, the first c/7 orthogonal spaceship, [[loafer]], was discovered by Josh Ball.

2014 provided a handful of new engineered spaceships, using various new technologies. In July, several [[half-baked knightship|half-bakery-based knightships]] were constructed with a new technique not requiring universal-constructor circuitry. These produced spaceships that were both much slower and much smaller than the Gemini variants. In September, [[Dave Greene]] and Chris Cain completed two [[31c/240 orthogonal]] spaceships, along the same general lines as the original Caterpillar but using a number of new mechanisms. Finally, in December, an oblique caterpillar dubbed the [[Waterbear]] was completed by Brett Berger, traveling at (23,5)c/79. Richard Schank discovered [[pufferfish]], a c/2 puffer, and Ivan Fomichev found a c/2 fuse for its exhaust and combined two pufferfish with fuses to assemble the first wholly high-period c/2 spaceship.

In December 2015, Chris Cain completed a diagonal self-constructing spaceship -- a [[Demonoid|"0hd Demonoid"]] -- based on Geminoid technology, adapted from a larger 10hd version constructed in November in collaboration with Dave Greene.

[[File:Copperhead.gif|framed|right|The copperhead spaceship.]]
In March 2016, [[zdr]] discovered [[copperhead]], an extremely small c/10 spaceship. A [[Fireship|pseudo-tagalong]] for this spaceship, alongside many other c/10 technologies, were constructed within two months after the discovery of the ship.

In April 2016, Michael Simkin finished the adjustable [[caterloopillar]] project, making it possible to build spaceships of arbitrary orthogonal speeds slower than c/4.

In June 2016, Tim Coe found a large elementary 3c/7 orthogonal spaceship, the [[spaghetti monster]].

[[File:Sirrobin tiny.png|thumb|right|[[Sir Robin]], the first elementary knightship to be found. {{JavaRLE|sirrobin}}]]
In March 2018, [[Adam P. Goucher]] and [[Tomas Rokicki]] found the first elementary knightship, [[Sir Robin]], which translates itself by (2,1) every six generations.

===2020s===

Over the course of December 2020 and the first half of 2021, three speeds received versatile new technology, including the first intermediate-period 2c/7 orthogonal ships (based on the [[doo-dah]] by [[John Winston Garth]]), several smaller 3c/7 orthogonal ships by [[Dylan Chen]] allowing higher-period ships to be constructed, and higher-period (2,1)c/6 knightships based on the [[sprayer]] by Adam P. Goucher and Dylan Chen, all aided by the new [[ikpx2]] spaceship search program.

In 2023, the first elementary [[c/8 diagonal]] spaceship was found: the [[walrus]].

{| class="wikitable"
|-
! Speed
! Direction
! First discovered
! Discoverer
! Year of discovery
|-
! c/4
| diagonal
| [[glider]]
| [[Richard Guy]]
| {{year|1969}}
|-
! c/2
| orthogonal
| [[lightweight spaceship]]
| [[John Conway]]
| {{year|1970}}
|-
! c/3
| orthogonal
| [[84P3H1V0.1]]
| [[Dean Hickerson]]
| {{year|1989}}
|-
! c/4
| orthogonal
| [[119P4H1V0]]
| [[Dean Hickerson]]
| {{year|1989}}
|-
! c/12
| diagonal
| [[13-engine Cordership]]
| [[Dean Hickerson]]
| {{year|1991}}
|-
! 2c/5
| orthogonal
| [[44P5H2V0]]
| [[Dean Hickerson]]
| {{year|1991}}
|-
! c/5
| orthogonal
| [[snail]]
| [[Tim Coe]]
| {{year|1996}}
|-
! 2c/7
| orthogonal
| [[weekender]]
| [[David Eppstein]]
| {{year|2000}}
|-
! c/6
| orthogonal
| [[dragon]]
| [[Paul Tooke]]
| {{year|2000}}
|-
! c/5
| diagonal
| [[295P5H1V1]]
| [[Jason Summers]]
| {{year|2000}}
|-
! 17c/45
| orthogonal
| [[caterpillar]]
| [[Gabriel Nivasch]], [[Jason Summers]], and [[David Bell]]
| {{year|2004}}
|-
! c/6
| diagonal
| [[seal]]
| [[Nicolay Beluchenko]]
| {{year|2005}}
|-
! (5120,1024)c/16849793
| slope 5 (ibiswise)
| [[Gemini]]
| [[Andrew J. Wade]]
| {{year|2010}}
|-
! (4096,2048)c/17783745
| slope 2 (knightwise)
| [https://conwaylife.com/forums/viewtopic.php?f=2&t=406&start=25#p2578 Gemini 2]
| [[Dave Greene]]
| {{year|2010}}
|-
! (3072,1024)c/36000001
| slope 3 (camelwise)
| [https://conwaylife.com/forums/viewtopic.php?f=2&t=406&start=25#p2590 Gemini 3]
| [[Dave Greene]]
| {{year|2010}}
|-
! c/7
| diagonal
| [[Lobster]]
| [[Matthias Merzenich]]
| {{year|2011}}
|-
! c/7
| orthogonal
| [[loafer]]
| [[Josh Ball]]
| {{year|2013}}
|-
! (6,3)c/2621440
| slope 2 (knightwise)
| [[Half-baked knightship]]
| [[Adam P. Goucher]]
| {{year|2014}}
|-
! (6,3)c/245912
| slope 2 (knightwise)
| [[Parallel HBK]]
| [[Chris Cain]]
| {{year|2014}}
|-
! 31c/240
| orthogonal
| [[shield bug]]
| [[Dave Greene]]
| {{year|2014}}
|-
! (23,5)c/79
| slope 23/5
| [[waterbear]]
| [[Brett Berger]]
| {{year|2014}}
|-
! 130c/(1636712+16N)
| diagonal
| [[Demonoid|10hd Demonoid]]
| [[Chris Cain]] and [[Dave Greene]]
| {{year|2015}}
|-
! 65c/(438852+16N)
| diagonal
| [[Demonoid|0hd Demonoid]]
| [[Chris Cain]]
| {{year|2015}}
|-
! c/10
| orthogonal
| [[Copperhead‎‎]]
| [[zdr]]
| {{year|2016}}
|-
! All speeds slower than c/4
| orthogonal
| [[caterloopillar]]
| [[Michael Simkin]]
| {{year|2016}}
|-
! 3c/7
| orthogonal
| [[Spaghetti monster]]
| [[Tim Coe]]
| {{year|2016}}
|-
! (2,1)c/6
| slope 2 (knightwise)
| [[Sir Robin]]
| [[Adam P. Goucher]] and [[Tomas Rokicki]]
| {{year|2018}}
|-
! All speeds slower than c/4
| diagonal
| [[Speed Demonoid]]
| [[Pavel Grankovskiy]] and [[Dave Greene]]
| {{year|2020}}
|-
! c/8
| diagonal
| [[Walrus]]
| [[Adam P. Goucher]]
| {{year|2023}}
|}

The first known cases for unsimplified speeds are unknown.

== In other rules ==
{| class="infobox"
|-
|<tabs>
<tab name="Binary">[[File:OT_map_(non-Gray).png|thumb|right|A map of outer-totalistic rules. Birth conditions iterate in binary over the x axis (the right half has B0), survival in the y axis (the bottom half has S8). Outside of the bottom-left quadrant (where only the all-off agar is considered space), it is symmetrical due to the duality of [[black/white reversal]]. Green rules have known explicit examples of spaceships within them, red ones have been proven not to support any. (See file description for more details.)|256px]]</tab>
<tab name="Gray code">[[File:OT_spaceship_map.png|thumb|right|A map of outer-totalistic rules. Birth conditions iterate in a {{LinkWikipedia|Gray_code|name=Gray code|nobullet=no|nosuffix=no}} over the x axis, survival in the y axis. Green rules have known explicit examples of spaceships within them, red ones have been proven not to support any. (See file description for more details.)|256px]]</tab>
</tabs>
|}
Many [[Life-like cellular automata]] afford spaceships, as do their generalizations; this includes both [[outer-totalistic]] and [[isotropic non-totalistic]] rules, as well as [[non-isotropic]], [[Generations]] and [[Larger than Life]] rules.

Various segments of the Life-like [[rulespace]] cannot contain spaceships, however. For instance, assuming [[Birth on zero neighbours|B0]] is not active:

* In any rule with B1c, any pattern expands in all directions.
:* For totalistic rules, this is rounded up to B1.
* In any rule with all of S012acek3aijn4a (all survival conditions with a subset of the on cells in 4a), the [[trailing edge]] of a pattern cannot die.
:* For totalistic rules, this is rounded up to S01234.
* In any rule with B23/S0, the trailing edge of a pattern cannot die.
:*This is not the case for rules with B23 without S0; 12 of these have known [[photon]]s, and no slower spaceships may exist.<ref>{{LinkForumThread|f=11|t=5471|p=165127|title=Re: Speed limits and theorems about the existence of periodic objects|author=LaundryPizza03|date=August 15, 2023|format=ref}}</ref>
* In any rule with none of B1ce2ac3i, no pattern can escape its initial bounding box.
* In any rule with none of B1ce2ae3a, no pattern can escape its initial bounding diamond.
:* For totalistic rules, these are both rounded up to B123.
:* With B3 and none of B1245/S012345, with a pattern's bounding diamond replaced with that of its bounding box, it remains inescapable.<ref>David Eppstein, comment in [https://www.ics.uci.edu/~eppstein/ca/glider.c <tt>glider.c</tt>]</ref>
*It appears that in some rules patterns cannot escape the bounding box or the bounding diamond despite having the B3a or B2e condition. This is likely the case for {{rl|LongLife}} and {{rl|Assimilation}}.

In strobing rules with <tt>(not B1c) XOR S7c</tt> (such that one member of the pair of rules they emulate alternating between has B1c), a spaceship may move with velocity vector <tt>{{frac|(x,y)c|p}}</tt> only if <tt>x+y ≤ {{frac|3|2}}*p</tt>.<ref name="post56111" />

In rules with both of B3ai and none of B12ace, a spaceship may move at <tt>{{frac|(x,y)c|p}}</tt> only if <tt>2*max(x,y)+min(x,y) ≤ p</tt>.

In the subset without either S4w or S5a (such as Life), this criterion restricts to <tt>2*(x+y) ≤ p</tt>; the diagonal speed limit is (1,1)c/4, not (1,1)c/3, and the knightwise speed limit is (2,1)c/6, not (2,1)c/5 and so on. All patterns at the maximum speed in any direction travel at c/2 in the {{LinkWikipedia|Taxicab_metric|name=taxicab metric|nobullet=no|nosuffix=no}}.<ref name="spaceship_speed_limits_in_life_like_cellular_automata" />

The orthogonal limit without any of B1ec2a is c/2.

While assuming B0 is active, we can treat them as either [[strobing]] rules or [[black/white reversal]]s of rules. Over the outer-totalistics, this yields the following spaceshipless rulespaces:<ref>{{LinkForumThread
|format=ref|f=11|t=1074|p=93966|title=Re: Spaceships in Life-like cellular automata|author=LaundryPizza03|date=April 10, 2020}}</ref>
* Rules containing all of the transitions in at least one of {B0/S7,B08/S56,B05678/S6,B045678} without any of the transitions in at least one of {S01234,B3/S0123,B2/S0123,B23/S0,B1}
* Rules with B0234567 without S123456
Also:
* With B0/S6 and without either of B1/B2, or with B0/S67 without B2, all patterns expand at (2,1)c/2.
* With B0123 and without any of S567, patterns can never leave their bounding box.

The slowest known orthogonal elementary non-adjustable spaceship in any [[Life-like cellular automaton|Life-like rule]] is a c/5648 orthogonal spaceship in the rule {{rl|Gems}}, followed by a c/2068 orthogonal spaceship in {{rl|Gems Minor}}.
The slowest known (and highest-period) such spaceship in a range-1 [[isotropic non-totalistic rule]] is a 14c/63503454 ship in B2n3-ce4e5iy6ae/S2aei3cejk4eijkrw5cnry6-e78.<ref>{{LinkForumThread|f=11|t=6649|p=193960|title=Re: Foam Rules|author=NimbleRogue|date=September 12, 2024|format=raw}}, edit 2</ref>

=== Currently known speeds ===
There is currently an ongoing tabulation at the 5s project<ref>{{cite web|url=https://github.com/AforAmpere/sssss/tree/master/data|title=AforAmpere/sssss/tree/master/data}}</ref> cataloging the smallest known spaceships for each speed across different rules.

Alongside these, certain "series" of speeds can be proved to all exist in range-1 isotropic cellular automata:

* All orthogonal spaceships with the unsimplified speed c/n are known to exist; true-period [[Photon|c/1]], [[64P2H1V0|c/2]] and [[25P3H1V0.2|c/3]] spaceships are known.

* All orthogonal spaceships with the unsimplified speed mc/n are known to exist where n/m ≥ 9, in B2ck3ae4arw5n6k7c/S1e2-cn3aekry4-cnqw5jnry.<ref>{{LinkForumThread|f=11|t=3081|p=139574|title=Re: Re: Rules with small adjustable spaceships|author=silversmith|date=December 31, 2021|format=ref}}</ref>

==See also==
===General===
* [[Spaceship flotilla]]
* [[Spaceship terminology]]
* [[Types of spaceships]]
===Conway's Life===
* [[List of spaceships]]
* [[List of natural spaceships]]
* Subsections of [[LifeWiki:Game of Life Status page]], including [[LifeWiki:Game of Life Status page#Velocities of spaceships|velocities]] and [[LifeWiki:Game of Life Status page#Spaceship periods|periods]]
* [[LifeWiki:Spaceship Search Status Page]]
* {{CategoryLink|Spaceships}}
===Other cellular automata===
* [[Day_%26_Night#Spaceships|Day & Night#Spaceships]]
* [[HighLife#Spaceships]]
* {{rl|Grounded Life#Spaceships}}
* [[LifeWiki:Smallest Spaceships Supporting Specific Speeds]]

==References==
<references>
<ref name="arxiv_0004003v2">{{cite web
|url = https://arxiv.org/abs/cs/0004003v2
|title = Searching for Spaceships (PDF)
|author = David Eppstein
|date = April 26, 2000
|accessdate = December 4, 2023
}}</ref>
<ref name="fano_ca">{{cite web
|url = https://web.archive.org/web/20190408101245/http://fano.ics.uci.edu/ca/
|title = Gliders in Life-Like Cellular Automata
|publisher = David Eppstein
|accessdate = April 18, 2009
}}</ref>
<ref name="lifepage_patterns_newc5">{{cite web
|url = https://conwaylife.com/ref/lifepage/patterns/newc5/newc5.html
|title = New c/5 spaceship
|author = David Bell
|publisher = Paul's Page of Conway's Life Miscellany
|accessdate = April 18, 2009
}}</ref>
<ref name="lifepage_patterns_p5ss">{{cite web
|url = https://conwaylife.com/ref/lifepage/patterns/p5ss.html
|title = c/5 Orthogonal spaceship
|author = Tim Coe
|publisher = Paul's Page of Conway's Life Miscellany
|accessdate = April 18, 2009
}}</ref>
<ref name="new_spaceship_speed_in_conways_game_of_life">{{cite web
|url = https://niginsblog.wordpress.com/2016/03/07/new-spaceship-speed-in-conways-game-of-life/
|title = New Spaceship Speed in Conway’s Game of Life
|author = Alexey Nigin
|date = March 7, 2016
|accessdate = June 11, 2016
}}</ref>
<ref name="spaceship_speed_limits_in_life_like_cellular_automata">{{cite web
|url = http://www.njohnston.ca/2009/10/spaceship-speed-limits-in-life-like-cellular-automata/
|title = Spaceship Speed Limits in "B3" Life-Like Cellular Automata
|author = Nathaniel Johnston
|date = October 30, 2009
|accessdate = December 12, 2016
}}</ref>
<ref name="post153692">{{LinkForumThread
|format = ref
|p = 153692
|title = Re: Suggested LifeWiki edits
|author = Bullet51
|date = November 17, 2022
}}</ref>
</references>

==Further reading==
* [[Carter Bays]], ''Gliders in Cellular Automata'', in: Robert A. Meyers (ed). ''Encyclopedia of Complexity and Systems Science,'' Springer 2009, pp. 4240–4249.

==External links==
* {{LinkWikipedia|Spaceship_(cellular_automaton)}}
* {{LinkLexicon|filename=lex_s.htm#spaceship|patternname=Spaceship}}
* {{LinkForumThread|f=2|t=2031|title=Spaceship Discussion Thread}} (For Conway's Life)
* {{LinkForumThread|f=11|t=1074|title=Spaceships in Life-like cellular automata}} (For outer-totalistic rules)
* {{LinkForumThread|f=11|t=5175|title=Miscellaneous Spaceship (collections) in Other Cellular Automata}}

Thessalonic Demonoid

2025-10-18T15:45:10Z

TYCF:

{{Spaceship
|name = Thessalonic Demonoid
|pname = thessalonicdemonoid
|c = 328699
|bx = 1688769
|by = 1688326
|dir = Diagonal
|p = 1677216
|m = 1677216
|s = 511c/1677216
|z = 511c/1677216
|symmetry = n
|discoverer = PK22
|discoveryear = 2025
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23
|rulespecial = [[Conway's Game of Life]]
|mc = true
|plaintext = true
|rle = true
}}
The '''Thessalonic Demonoid''' is a [[Thessalonic]] [[macro-spaceship]] with a [[speed]] of 511c/1677216d made by [[PK22]] on October 19, {{year|2025}}. It is the first [[self-constructing]] spaceship with [[circuitry]] made up of only [[block]]s and [[fishhook]]s. It uses single [[channel]] construction.<ref name="post219897" />
== See also ==
* [[Demonoid]]
==References==
<references>
<ref name="post219897">{{LinkForumThread
|format = ref
|p = 219897
|title = Re: Construction Challenges and Ideas
|author = PK22
|date = October 19, 2025
}}</ref>
</references>
[[Category:Macro-spaceships]]

Thessalonic Demonoid

2025-10-18T13:58:38Z

TYCF:

{{Spaceship
|name = Thessalonic Demonoid
|pname = thessalonicdemonoid
|c = 328699
|bx = 1688769
|by = 1688326
|dir = Diagonal
|p = 1677216
|m = 1677216
|s = 511c/1677216
|z = 511c/1677216
|symmetry = n
|discoverer = PK22
|discoveryear = 2025
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23
|rulespecial = [[Conway's Game of Life]]
|mc = true
|plaintext = true
|rle = true
}}
The '''Thessalonic Demonoid''' is a [[Thessalonic]] [[spaceship]] with a [[speed]] of 511c/1677216d made by [[PK22]] on October 19, {{year|2025}}. It is the first [[self-constructing]] spaceship with [[circuitry]] made up of only [[block]]s and [[fishhook]]s. It uses single [[channel]] construction.<ref name="post219897" />
== See also ==
* [[Demonoid]]
==References==
<references>
<ref name="post219897">{{LinkForumThread
|format = ref
|p = 219897
|title = Re: Construction Challenges and Ideas
|author = PK22
|date = October 19, 2025
}}</ref>
</references>
[[Category:Macro-spaceships]]

Thessalonic Demonoid

2025-10-18T13:56:27Z

TYCF:

{{Spaceship
|name = Thessalonic Demonoid
|pname = thessalonicdemonoid
|c = 328699
|bx = 1688769
|by = 1688326
|dir = Diagonal
|p = 1677216
|m = 1677216
|s = 511c/1677216
|z = 511c/1677216
|symmetry = n
|discoverer = PK22
|discoveryear = 2025
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23
|rulespecial = [[Conway's Game of Life]]
|mc = true
|plaintext = true
|rle = true
}}
The '''Thessalonic Demonoid''' is a [[Thessalonic]] [[spaceship]] with a [[speed]] of 511c/1677216d made by [[PK22]] on October 19, {{year|2025}}. It uses single [[channel]] construction.<ref name="post219897" />
== See also ==
* [[Demonoid]]
==References==
<references>
<ref name="post219897">{{LinkForumThread
|format = ref
|p = 219897
|title = Re: Construction Challenges and Ideas
|author = PK22
|date = October 19, 2025
}}</ref>
</references>

Thessalonic Demonoid

2025-10-18T13:54:55Z

TYCF:

Thessalonic Demonoid

2025-10-18T13:53:20Z

TYCF:

Demonoid

2025-10-18T13:52:13Z

TYCF: /* See also */

{{Spaceship
|name = Demonoid
|pname = demonoid
|c = 27250
|bx = 55010
|by = 54964
|dir = Diagonal
|p = 438852
|m = 219426
|s = 65c/438852
|z = 65c/438852
|symmetry = n/e
|discoverer = Chris Cain
|discoverer2 = Dave Greene
|discoveryear = 2015
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|synthesis = 12016
|synthesisRLE = true
|mc = true
}}
'''Demonoid''' is the first type of self-constructing diagonal spaceship in the B3/S23 rule. A small "0hd Demonoid" was completed by [[Chris Cain]] in December 2015, shortly after a much larger 10hd version constructed in November<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1469&p=25716#p25702|title=Re: Demonoid (diagonal Geminoid) completed!|date=December 6, 2015|work=ConwayLife.com forums|author=Chris Cain|accessdate=December 7, 2015}}</ref> in collaboration with [[Dave Greene]]. The 0hd spaceship displaces itself by 65 cells diagonally every 438,852 generations. {{AS OF|2024}}, it is the only case where a spaceship gun pattern was completed before the actual spaceship -- the first 0hd Demonoid was fired by a gun.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1469&start=175#p25716|title=
Re: Demonoid (diagonal Geminoid) completed!|date=December 7, 2015|work=ConwayLife.com forums|author=Chris Cain|accessdate=January 4, 2016}}</ref>

The name "Demonoid" is an accidental portmanteau of "diagonal" and "Geminoid" by [[Paul Chapman]] in February 2013. "0hd" and "10hd" refer to the number of [[half-diagonal]]s separating the two glider lanes in the spaceships' construction arms.

{{POTY|name=The Demonoids|year=2015|rank=3|behind=the [[Simkin glider gun]] and the [[syringe]]}}

== Design ==
Similar to the original Gemini spaceship, the Demonoid consists of two identical halves. Where the Gemini's halves are simple translations of each other, each half of the Demonoid is a glide-reflected mirror image of the other. A ''tape'' of gliders continually relays between the two halves, instructing each to construct a daughter configuration.

In the 0hd Demonoid, each half is itself made up of two identical parts. Each part consists of a [[syringe]]-based 180-degree reflector combined with an [[edge shooter]], plus a scattering of self-destruct circuitry. A cycle is completed when one of these parts is constructed ahead of the spaceship and an identical reflector/edge shooter is destroyed at the back end as soon as its construction work is done.

== Self-destruct mechanism ==
The self-destruct sequence is triggered by a glider that follows the construction recipe on a slightly different lane. The only output of the cleanup reaction is another trigger glider, which appears in the exact same location as the original trigger glider, relative to the end of the recipe stream.

== Statistics ==
Demonoids are the smallest known self-constructing or self-supporting spaceships in terms of population, but the [[bounding box]] of the [[centipede]] is about half the size of the smallest Demonoid's bounding box, and the [[waterbear]] is considerably smaller in both longest diameter and bounding box.

Demonoid variants make up the nineteenth and twentieth explicitly-constructed spaceship velocities, but as with previous self-constructing spaceships they actually represent an infinite family of related velocities. If the two halves of the Demonoid are moved N cells farther away from each other, the 0hd Demonoid travels diagonally at a speed of 65c/(438852+8N).

== Speed limit ==
Theoretically speaking, a Demonoid spaceship using the 0hd elbow-move library could be designed with any velocity slower but not equal to 17c/792 diagonally, or roughly c/47 -- much faster than the old Gemini limit of c/580<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&p=2405#p2397 |title=Re: Universal Constructor Based Spaceship|work=ConwayLife.com forums|author=Adam P. Goucher|date=May 21, 2010|accessdate=December 9, 2015}}</ref>. A 0hd elbow can be programmed to move much faster than a Gemini elbow's speed limit of one diagonal cell per coded instruction, and signals in syringe-based Herschel circuitry can be compressed to within 90 ticks of each other. However, any speed faster than 65c/438852 would require the 0hd Demonoid's circuitry and construction recipes to be completely redesigned, with a much larger total size and population in most cases.

[[Single-channel]] Demonoids have since been created that move a block to the next construction site by creating and triggering a [[seed]] for a spaceship -- e.g., a [[Cordership]] or a [[58P5H1V1]] -- and then shooting it down later with a small [[salvo]] of gliders to produce a faraway target for the [[construction arm]]. Demonoids using Corderships to move a target can approach [[c/12 diagonal|c/12]] in speed, but never quite reach that limit, and 58P5H1V1-based Demonoids can be built with any rational speed below [[c/5 diagonal|c/5]]. A [[crab]]-based [[wickstretcher]] seed discovered by [[Tanner Jacobi]] allows a Demonoid to reach any rational speed slower than [[c/4 diagonal|c/4]], which is the absolute speed limit for any diagonal spaceship in Life.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=101555#p101555 |title= One Glider Seeds|work=ConwayLife.com forums|author=Tanner Jacobi|date=August 2, 2020|accessdate=August 12, 2020}} </ref> The first such "[[Speed Demonoid]]" to use the crabstretcher in this way was made on September 18, 2020 by Dave Greene and Pavel Grankovskiy.

== History ==
The first Demonoid designs were significantly larger and more complicated than the final 10hd or 0hd models. Some early designs required all elbow operations to be made from pairs of gliders, with no singleton gliders allowed.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1006#p7339|title=Re: Geminoid Challenge|date=December 22, 2012|work=ConwayLife.com forums|author=Dave Greene|accessdate=December 8, 2015}}</ref>

This allowed the gliders in each pair to be coded on a single tape, one directly after the other. However, it greatly increased the amount of timing circuitry needed. It also cut the allowable signal density in half. The signal density was already low because in 2012 the repeat rate for stable Spartan circuitry was 497 ticks or more.

A sizable improvement involved moving to a design with the two halves of the recipe encoded in series instead of interleaved. This allowed for better signal density, and also any combination of singleton gliders and glider pairs.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1006#p7447|title=Re: Geminoid Challenge|date=February 15, 2013|work=ConwayLife.com forums|author=Dave Greene|accessdate=December 8, 2015}}</ref>

These early designs were all 9hd -- the two construction lanes were separated by 9 half diagonals, and a block centered between the lanes served as the elbow. This allowed all elbow operations to be used either directly or in mirror-image, which meant that gliders could be fired either left or right from the elbow, and elbow moves could be mirrored if there was limited space available and the move recipe had a larger spark on one side than on the other.

After the 9hd [[linear propagator]] was completed, it became clear that 10hd was significantly more efficient, in part because it allowed for two block elbows in slightly different positions between the construction lanes.

The 10hd and 0hd Demonoid both use a much larger number of elbow locations. A library of thousands of elbow operations allows easy switching between different elbow types, and gliders can be output on any nearby lane by stringing recipes together.

The 10hd Demonoid was the first complete self-constructing diagonal spaceship.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1469&start=150#p25401|title=Re: Demonoid (diagonal Geminoid) completed!|date=November 25, 2015|work=ConwayLife.com forums|author=Dave Greene|accessdate=December 8, 2015}}</ref> Its construction recipe encoded two complete 180-degree reflector/edge shooter components, which were mostly identical to each other but had significant differences near the construction lanes. It included complex machinery that blocked the construction lanes during the half of the Demonoid's cycle when the recipe gliders intended for one circuit were passing through the other circuit's reflector.

The 0hd Demonoid improved on the 10hd model by removing the blocking mechanisms and the resulting long pause in construction. Instead, the two reflector/edge shooter components were designed to be completely identical. Each newly constructed component would first produce the trailing halves of the glider pairs in the next construction recipe. Then the same edge shooter would fire the leading halves of the glider pairs for the following construction.

In June 2017 Dave Greene completed a much simpler [[single-channel]] Demonoid using a temporary [[lossless elbow]], which displaces itself 79 cells diagonally every 1,183,842 ticks.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=45264#p45264|title=Re: Demonoid (diagonal Geminoid) completed!|date=June 26, 2017|work=ConwayLife.com forums|author=Dave Greene|accessdate=June 3, 2018}}</ref> This was an improvement in terms of design complexity, but not in terms of speed, population, or bounding box. However, all of these could be further optimized. "Scorbie's Demonoid", a single-channel Demonoid design with much more compact stable circuitry suggested by Dongook Lee, was completed in October 2018.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=60370#p64321|title=Re: Demonoid (diagonal Geminoid) completed!|date=October 3, 2018|work=ConwayLife.com forums|author=Dave Greene|accessdate=October 3, 2018}}</ref> A week later this was followed by a larger but more Hashlife-friendly version traveling 32 times faster, using somewhat different construction methods.<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?p=64590#p64590|title=Re: Demonoid (diagonal Geminoid) completed!|date=October 10, 2018|work=ConwayLife.com forums|author=Dave Greene|accessdate=October 10, 2018}}</ref>

On September 18, {{year|2020}}, [[Pavel Grankovskiy]] constructed the [[Speed Demonoid]]. It goes at 3492022/17833792=1746011/8916896 ≈ 0.1958c, very close to [[c/5]], making it the fastest Demonoid. It uses double [[crabstretcher]]s to accelerate a self-constructing spaceship to the aforementioned speed. It can be changed to any rational speed below 2c/9. Eight days later, Speed Demonoid version 2 was completed, removing the 2c/9 barrier and enabling the creation of any Demonoid with a speed of less than c/4.

== Pattern files ==
* [https://conwaylife.com/patterns/demonoid.mc Demonoid]
* [https://conwaylife.com/patterns/demonoid10hd.mc Demonoid 10hd]

== See also ==
* [[Orthogonoid]]
* [[Gemini]]
* [[Caterloopillar]]
* [[Centipede]]
* [[Waterbear]]
* [[Half-baked knightship]]
* [[Replicator]]
* [[Thessalonic Demonoid]]

== References ==
<references />

== External links ==
{{LinkLexicon|lex_d.htm#demonoid}}

[[Category:Non-monotonic spaceships]]
[[Category:Adjustable spaceships]]
[[Category:Macro-spaceships]]

File:Thessalonicdemonoid.png

2025-10-18T12:31:01Z

TYCF: TYCF uploaded a new version of File:Thessalonicdemonoid.png

== Summary ==
Image showing the universal constructor of the recently completed Thessalonic Demonoid.

User:Resu/Rules

2025-09-27T13:31:47Z

TYCF:

*B3/S23-a5
*B38/S23-a578
*B3678/S23-a678 ([[User:Resu/Rules/Heights|Heights]]) [https://catagolue.hatsya.com/census/b3678s23-a678]
*B34c/S237e
*B37c8/S23-a57c8 (Nigh-explosive?)(HighT 1) [https://catagolue.hatsya.com/census/b37c8s23-a57c8]
*B37e8/S23-a57e8 (HighT 2) Apgsearched [https://catagolue.hatsya.com/census/b37e8s23-a57e8]
*B37c8/S23-a57e8 (HighT 3) More stable [https://catagolue.hatsya.com/census/b37c8s23-a57e8]
*B37e8/S23-a57c8 (HighT 4)(Explosive)[https://catagolue.hatsya.com/census/b37e8s23-a57c8]
*B34c678/S23-a4c5cik67 [https://catagolue.hatsya.com/census/b34c678s23-a4c5cik67]
*B38/S23-a5-y78 [https://catagolue.hatsya.com/census/b38s23-a5-y78]

List of period-2 oscillators with 18 cells

2025-09-19T15:32:25Z

TYCF: Undo revision 164454 by TYCF (talk)

There are a total of 484 {{period|2}} [[oscillator]]s with 18 cells.<ref name="niemiec" />{{refn|name="oeis_a056614"|{{cite web
|url = https://oeis.org/A056614
|title = A056614: Number of n-celled P2-oscillators in Conway's game of Life
|work = The On-Line Encyclopedia of Integer Sequences
|author = N. J. A. Sloane
|date = August 28, 2000
}} (note that terms 20-21 are from Niemiec's exhaustive search<ref name="objcount" />)}} Here are the 20 most common, and others of interest:

{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[apgcode]]
! [[Frequency class]]
! [[Glider synthesis|Cost in gliders]]
|-
! 1
! [[File:Greatonoff.png|64px]]
! [[Great on-off]]
| {{LinkCatagolue|xp2_g8gid1e8z1226|style=raw}}
| 22.4
| 5
|-
! 2
! [[File:Sparkcoil.png|64px]]
! [[Spark coil]]
| {{LinkCatagolue|xp2_rhewehr|style=raw}}
| 24.0
| 4
|-
! 3
! [[File:1beacon.png|64px]]
! [[1 beacon]]
| {{LinkCatagolue|xp2_ca9baiczw32|style=raw}}
| 29.4
| 5
|-
! 4
! [[File:xp2_og2t1e8z6221.png|64px]]
! xp2_og2t1e8z6221
| {{LinkCatagolue|xp2_og2t1e8z6221|style=raw}}
| 33.9
| 5
|-
! 5
! [[File:xp2_caabaiczw32.png|64px]]
! [[xp2_caabaiczw32]]
| {{LinkCatagolue|xp2_caabaiczw32|style=raw}}
| 34.0
| 5
|-
! 6
! [[File:xp2_6a88baiczx32.png|64px]]
! [[xp2_6a88baiczx32]]
| {{LinkCatagolue|xp2_6a88baiczx32|style=raw}}
| 35.4
| 5
|-
! 7
! [[File:Racetrackandorthobeacon.png|64px]]
! [[Racetrack and ortho-beacon]]
| {{LinkCatagolue|xp2_04aab96zc813|style=raw}}
| 35.5
| 5
|-
! 8
! [[File:Cisbipoleondock.png|64px]]
! Cis-bipole on dock
| {{LinkCatagolue|xp2_31agozca22ac|style=raw}}
| 35.6
| 5
|-
! 9
! [[File:Cisbeaconuponracetrack.png|64px]]
! Cis-beacon up on racetrack
| {{LinkCatagolue|xp2_0318cz69d552|style=raw}}
| 36.0
| 6{{cn}}
|-
! 10
! [[File:xp2_og2t1acz6221.png|64px]]
! xp2_og2t1acz6221
| {{LinkCatagolue|xp2_og2t1acz6221|style=raw}}
| 36.2
| 8
|-
! 11
! [[File:Loafongriddle.png|64px]]
! [[Loaf on griddle]]
| {{LinkCatagolue|xp2_04a96z31d153|style=raw}}
| 36.2
| 5
|-
! 12
! [[File:Cisbeacondownonracetrack.png|64px]]
! Cis-beacon down on racetrack
| {{LinkCatagolue|xp2_0318cz255d96|style=raw}}
| 36.8
| 6
|-
! 13
! [[File:xp2_c8b8q4oz33x1.png|64px]]
! xp2_c8b8q4oz33x1
| {{LinkCatagolue|xp2_c8b8q4oz33x1|style=raw}}
| 36.9
| 6
|-
! 14
! [[File:xp2_c813z39d1e8.png|64px]]
! xp2_c813z39d1e8
| {{LinkCatagolue|xp2_c813z39d1e8|style=raw}}
| 36.9
| 8
|-
! 15
! [[File:Transloaftesttubebaby.png|64px]]
! [[Trans-loaf test tube baby]]
| {{LinkCatagolue|xp2_0ggm952z344ko|style=raw}}
| 37.2
| 6
|-
! 16
! [[File:Cisbeaconuponcisloafwithlongleg.png|64px]]
! Cis-beacon up on cis-loaf-with-long-leg
| {{LinkCatagolue|xp2_c813z319lic|style=raw}}
| 37.7
| 7
|-
! 17
! [[File:xp2_caab9iczw32.png|64px]]
! xp2_caab9iczw32
| {{LinkCatagolue|xp2_caab9iczw32|style=raw}}
| 37.8
| 8
|-
! 18
! [[File:Transbipoleondock.png|64px]]
! Trans-bipole on dock
| {{LinkCatagolue|xp2_31agozwca22ac|style=raw}}
| 38.3
| 9
|-
! 19
! [[File:Transbeaconuponracetrack.png|64px]]
! Trans-beacon up on racetrack
| {{LinkCatagolue|xp2_069baa4zc813|style=raw}}
| 38.3
| 8
|-
! 20
! [[File:xp2_253gv1og26.png|64px]]
! xp2_253gv1og26
| {{LinkCatagolue|xp2_253gv1og26|style=raw}}
| 38.6
| 8
|-
! N/A
! [[File:Duodecapole.png|64px]]
! [[Duodecapole]]
| {{LinkCatagolue|xp2_31a08zy01050k0gzy620ago|style=raw}}
| [No natural occurrences]
| 14
|}

== Other period-2 oscillator lists ==

* [[List of oscillators with 3 to 16 cells]] (complete; mostly but not all period 2)
* [[List of period-2 oscillators with 17 cells]] (will be complete but isn't yet)
* [[Larger period-2 oscillators]] (notable ones only)
* {{CategoryLink|Oscillators with period 2}} (notable only but regardless of cell count)

== References ==
<references>
<ref name="niemiec">{{LinkNiemiec|p2-18.htm|Life Eighteen-Bit Period-2 Oscillators|nobullet=nobullet}}</ref>
<ref name="objcount">{{LinkNiemiec|objcount.htm|Life Object Counts|nobullet=nobullet}}</ref>
</references>

[[Category:Oscillators with period 2| ]]
[[Category:Lists of oscillators with specific period|2_18]]
[[Category:Lists of patterns with synthesis costs]]

List of period-2 oscillators with 18 cells

2025-09-19T15:32:17Z

TYCF:

List of oscillators with subperiod combinations

2025-09-19T15:31:24Z

TYCF: link

This page intends to list all known [[oscillators]] of [[period]]s up to 144 containing each combination of subperiods. Only non-[[trivial]], non-[[pseudo]]-object cases are counted; a page for trivial cases may be created in future.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
! style="background-color:#dfdfff" | Blue
| This oscillator is the smallest possible example for the subperiod combination of this period.
|-
! style="background-color:#c6efce" | Green
| This oscillator is the smallest known example for the subperiod combination of this period.
|-
! style="background-color:#ffffdd" | Yellow
| This oscillator ''may'' be the smallest known example for the subperiod combination of this period; checking of other pattern collections may be advisable.
|-
! style="background-color:#ffaa00" | Orange
| Whether this subperiod combination is known for this period is unknown; checking of pattern collections advisable.
|-
! style="background-color:#ffc7ce" | Red
| This subperiod combination is currently unknown for this period.
|-
! style="background-color:#888888" | Gray
| This subperiod combination is provably impossible for this period.
|}

== Prime periods ==
Oscillators of prime period can either be fully strictly volatile or have stator cells; trivial cases cannot exist. Period 1 is included here for completeness, despite 1 not being a prime number.
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, p
! SV
|-
! 1
| colspan=2 style="background-color:#dfdfff" | [[Block|4]]
|-
! 2
| style="background-color:#dfdfff" | [[Blinker|3]]
| style="background-color:#dfdfff" | [[Phoenix 1|12]]
|-
! 3
| style="background-color:#dfdfff" | [[Caterer|12]]
| style="background-color:#dfdfff" | [[Statorless p3|140]]
|-
! 5
| style="background-color:#c6efce" | [[Pseudo-barberpole|15]]
| style="background-color:#c6efce" | [[Statorless p5|68]]
|-
! 7
| style="background-color:#c6efce" | [[28P7|28]]
| style="background-color:#ffc7ce" | none known
|-
! 11
| style="background-color:#c6efce" | [[Rattlesnake|33]]
| style="background-color:#ffc7ce" | none known
|-
! 13
| style="background-color:#c6efce" | [[Beluchenko's p13|34]]
| style="background-color:#c6efce" | [[Beluchenko's p13#Variants|128]]
|-
! 17
| style="background-color:#c6efce" | [[Honey thieves|36]]
| style="background-color:#ffc7ce" | none known
|-
! 19
| style="background-color:#c6efce" | [[Cribbage|92]]
| style="background-color:#ffc7ce" | none known
|-
! 23
| style="background-color:#c6efce" | [[54P23|54]]
| style="background-color:#ffc7ce" | none known
|-
! 29
| style="background-color:#c6efce" | [[p29 pre-pulsar shuttle|54]]
| style="background-color:#ffc7ce" | none known
|-
! 31
| style="background-color:#c6efce" | [[Merzenich's p31|48]]
| style="background-color:#ffc7ce" | none known
|-
! 37
| style="background-color:#c6efce" | [[58P37|58]]
| style="background-color:#ffc7ce" | none known
|-
! 41
| style="background-color:#c6efce" | [[p41 pi-heptomino hassler|170]]
| style="background-color:#ffc7ce" | none known
|-
! 43
| style="background-color:#c6efce" | [[p43 pi-heptomino hassler|70]]
| style="background-color:#ffc7ce" | none known
|-
! 47
| style="background-color:#c6efce" | [[p47 pre-pulsar shuttle|84]]
| style="background-color:#ffc7ce" | none known
|-
! 53
| style="background-color:#c6efce" | [[94P53|94]]
| style="background-color:#ffc7ce" | none known
|-
! 59
| style="background-color:#c6efce" | [[p59 pi-heptomino hassler|86]]
| style="background-color:#ffc7ce" | none known
|-
! 61
| style="background-color:#c6efce" | [[p61 pi-heptomino hassler|134]]
| style="background-color:#ffc7ce" | none known
|-
! 67
| style="background-color:#c6efce" | [[p67 Snark loop|228]]
| style="background-color:#ffc7ce" | none known
|-
! 71
| style="background-color:#c6efce" | [[p71 dependent reflector loop|92]]
| style="background-color:#ffc7ce" | none known
|-
! 73
| style="background-color:#c6efce" | [[p73 lumps of muck hassler|68]]
| style="background-color:#ffc7ce" | none known
|-
! 79
| style="background-color:#c6efce" | [[p79 pi-heptomino hassler|80]]
| style="background-color:#ffc7ce" | none known
|-
! 83
| style="background-color:#c6efce" | [[62P83|62]]
| style="background-color:#ffc7ce" | none known
|-
! 89
| style="background-color:#c6efce" | {{LinkCatagolue|xp89_yzy833y58e1e88gzyzyj330311ybckzyzyd3224e6y725acy165lozyzwgs2552ypggzyzy2gcoy1o8a6xca8y911zzzzysgy1g0gzy4ooy9153x6511y113xggzggyx4aa43z1qa6y135a4y767244cz023yag88c0cczye117871y5cc|patternname=164|style=raw}}
| style="background-color:#ffc7ce" | none known
|-
! 97
| style="background-color:#c6efce" | {{LinkCatagolue|xp97_ydg88e1u8y533z0kcyb11313kzol56y1ca52y6115137zy4ggyp2552sgzy411y94ocx6a8ozyzxe24zzzzyzy448ezyzyg32acx634y9ggzyzy4178kk8yp11zyzyksogkggy68ka6y1ckl3zyzyp5ogoggyb65zyzyeooy52fge221|patternname=164|style=raw}}
| style="background-color:#ffc7ce" | none known
|-
! 101
| style="background-color:#c6efce" | [[116P101|116]]
| style="background-color:#ffc7ce" | none known
|-
! 103
| style="background-color:#c6efce" | {{LinkCatagolue|xp103_yzyzyv33y58e1e88gzyzyzyzy3330311ybckzyzyzyz03224e6y725acy165lozyzyzylgs2552ypggzyzyzyxo8a6yf11zyzyzyma64y8742zzzzzyzyz4kcy86c2zzzzzyzy9gcoy8ca8zzzzzymg8oy88okzyo1ok46zy433ypg88ge2z6a8oy1ck8gy7os8gggy611z0bdy41y4g0ggy11zyd255t0t5y5ggzyh1y711|patternname=180|style=raw}}
| style="background-color:#ffc7ce" | none known
|-
! 107
| style="background-color:#c6efce" | [[86P107|86]]
| style="background-color:#ffc7ce" | none known
|-
! 109
| style="background-color:#c6efce" | [[rectifier|156]]
| style="background-color:#ffc7ce" | none known
|-
! 113
| style="background-color:#c6efce" | [[86P113|86]]
| style="background-color:#ffc7ce" | none known
|-
! 127
| style="background-color:#c6efce" | [[74P127|74]]
| style="background-color:#ffc7ce" | none known
|-
! 131
| style="background-color:#ffffdd" | [[rectifier|?]]
| style="background-color:#ffc7ce" | none known
|-
! 137
| style="background-color:#ffffdd" | [[rectifier|?]]
| style="background-color:#ffc7ce" | none known
|-
! 139
| style="background-color:#ffffdd" | [[rectifier|?]]
| style="background-color:#ffc7ce" | none known
|}

== Squares of primes ==
These are the only numbers which have exactly three divisors; only one subperiod is possible other than 1, and trivial cases cannot exist. Here, q represents sqrt(p).
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, q, p
! 1, p
! q, p
! SV
|-
! 4
| style="background-color:#dfdfff" | [[Mold|12]]
| style="background-color:#c6efce" | [[Monogram|18]]
| style="background-color:#dfdfff" | [[Mazing|12]]
| style="background-color:#c6efce" | [[Strictly volatile p4|416]]
|-
! 9
| style="background-color:#ffffdd" | {{LinkCatagolue|xp9_wg88b5kk8gz4v0lhlc221zw56|patternname=37|style=raw}}
| style="background-color:#c6efce" | [[29P9|29]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 25
| style="background-color:#ffffdd" | [[88P25|88]]
| style="background-color:#c6efce" | [[30P25|30]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#c6efce" | [[Charity's p25|128]]
|-
! 49
| style="background-color:#ffffdd" | [[p49 R-pentomino hassler|158]]
| style="background-color:#c6efce" | [[44P49|44]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 121
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | {{LinkCatagolue|xp121_yzyzyzyzymgiligzyzyzyzyzy0178cydg9g0641u08k8zyzyzyzyu4s0gym1221w11zyzyzyzyw11y7eaazzzyzyzyzymco4yb696zzzyzyzyzyh2a6zzzyzyzyvsg8zzzyzyzyqa64zzzyzyzy08okzzzyzyy42ezzzyzy9okgzzzypo4oyb86czyq1zzykkkszy5ggyn31e8z4a40v18o1243ydc4ozy112iai3yg11zy41|patternname=156|style=raw}}
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|}

== Four divisors ==
This includes oscillators whose periods are a product of two primes, and those whose periods are a cube of a prime. q1 represents the greater of the two divisors, and q2 the lesser.

{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, q1, q2, p
! 1, q1, p
! 1, q2, p
! 1, p
! q1, q2, p
! q1, p
! q2, p
! SV
|-
! 6
| style="background-color:#ffffdd" | [[p6 domino fountain|56]]
| style="background-color:#ffffdd" | [[Four blinkers around four blocks|24]]
| style="background-color:#ffffdd" | [[p6 honey farm hassler|121]]
| style="background-color:#c6efce" | [[Unix|16]]
| style="background-color:#ffffdd" | [[Statorless p6#Other statorless p6|58]]
| style="background-color:#ffffdd" | [[Jason's p6|28]]
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[Strictly volatile p6|52]]
|-
! 8
| style="background-color:#ffffdd" | {{LinkCatagolue|xp8_3520gji0253zxmxmzok78d1d87ko|patternname=45|style=raw}}
| style="background-color:#c6efce" | [[Achim's p8|18]]
| style="background-color:#ffffdd" | {{LinkCatagolue|xp8_0gk2gb3zg11y1sssz3y0777|patternname=32|style=raw}}
| style="background-color:#c6efce" | [[Blocker|15]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | {{LinkCatagolue|xp8_y9mm1ozya3c6wgzgw8808og137y1233xggo0ooz0330311xoo8y1sog132022w1zy61wc6ozy93gdd|patternname=84|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp8_xooow80e704wssszeee111y9777|patternname=34|style=raw}}
| style="background-color:#c6efce" | [[Figure eight|12]]
|-
! 10
| style="background-color:#ffffdd" | [[46P10|46]]
| style="background-color:#ffffdd" | [[37P10.1|37]]
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[24P10|24]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 14
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp14_0g886p6k48gz6b8lkl55pa9ozx1w73|patternname=47|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp14_ggw3p686k48gz1aq5howh9lkbagzw1245c3cjow11|patternname=62|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp14_8oy045a2wca23xgs2sggz0123y1skicy22606221zybg88ozw4aar0ray1gh211gy062sgzy1121y06221w2251|patternname=94|style=raw}}
| style="background-color:#ffffdd" | [[44P14|44]]
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[Tumbler|16]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
|-
! 15
| style="background-color:#ffffdd" | {{LinkCatagolue|xp15_03pmwmp3zxg11z332blic|patternname=31|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp15_8kkm1vgkczwgh26wg8ehraa4z6221xcb98gczy532|patternname=58|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp15_0oy1k70c8z1u1x675z161|patternname=27|style=raw}}
| style="background-color:#c6efce" | [[Eater eating pentadecathlon|19]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | {{LinkCatagolue|xp15_231jri22irj132zxr0hhhh0rz8ogpr9889rpgo8x4r4zyd4r4|patternname=84|style=raw}}
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[Pentadecathlon|12]]
|-
! 21
| style="background-color:#ffffdd" | [[Caterer on 42P7.1|54]]
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp21_gadicc4wccz8lldlgxggz025211h0g11xjjy1jjzy23e3xefmh3u0u3hmfezyc1x1|patternname=83|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp21_y54koy2oe1ng07gg8k8z8kkm4sk201y3771w3w3zx343y3354c|patternname=62|style=raw}}
| style="background-color:#c6efce" | [[32P21|32]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 22
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp22_gggy2g53xooz0hhhx3346y78cc4z111y2ooy03966x4cc8zya65|patternname=52|style=raw}}
| style="background-color:#ffffdd" | [[Champagne glass|45]]
|
| style="background-color:#c6efce" | [[Jason's p22|36]]
|
|
|
| style="background-color:#c6efce" | [[48P22.1|48]]
|-
! 26
| style="background-color:#ffffdd" | [[70P26|70]]
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp26_0gs2ibaa4y8o8zlm0mlkn3wssssksx32hgy7ggoggz25s168bbgy8ddy6juaacg7k8zx11311y8g8ox27y078ongld0dlzyf23y86baq9871|patternname=150|style=raw}}
| style="background-color:#c6efce" | [[p26 honey farm hassler|60]]
| style="background-color:#c6efce" |
{{LinkCatagolue|xp26_y7g33xexex33gzy6121w464x464w121zccw252y5ggxggy5252wccz0444w27y26401x1046y272w444z0222w4ey262goxog26y2e4w222z33w4a4yl4a4w33zy68k8w262x262w8k8zy8ccx7x7xcc|patternname=144|style=raw}}
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 27
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp27_mkid1e80g8gz1qaaw5l5kjcidicggzx1no3cjk44nkjgjkv0fpzy23452gv0sg624611|patternname=120|style=raw}}
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp27_c9b88g0s26xggz3h4u0t4vonkkn8a52z011w32h8imipzy414|patternname=73|style=raw}}
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp27_gya66y0s112ogggz1pl208k8y36952xo9zy0sy4a9imk80321zychzy07y4ai9d520o8gzgjl80252y3cik8x3iz1yaccy07gg83111|patternname=118|style=raw}}
| style="background-color:#c6efce" | [[56P27|56]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 33
| style="background-color:#c6efce" | [[Caterer on rattlesnake|46]]
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp33_8k4ra1vgc48cz1168711xk2s0ggzwc4go2egnkld221zy065w66|patternname=72|style=raw}}
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp33_ybgoy3i52z0gy812g1xot1046z7ery7278f6zsuby4cu2s8zwkuey3g18gzw7soy431zx121|patternname=77|style=raw}}
| style="background-color:#c6efce" | [[Jason's p33|60]]
|
|
|
| style="background-color:#ffffdd" | {{LinkCatagolue|xp33_yn46f01y520uc8zyo4rcy7om8zylocgyb1wogzymrggyc1m1zyl111yc13704zxgy58ck8808ooayr7e2022532wgg8gg0gsogz0a332022562y51yzy211y22zz8y2ggyzy2gy58ck8808ooaz1371011211w8ok8808esyra332022562y51zym40sogycgggzyngdgyc11rzyn13wgyb163zyq2d3y76r4zyp26f08y5g0uc4|patternname=236|style=raw}}
|-
! 34
| style="background-color:#ffffdd" | {{LinkCatagolue|xp34_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|patternname=620|style=raw}}
|
|
| style="background-color:#c6efce" | [[74P34|74]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 35
| style="background-color:#ffffdd" | {{LinkCatagolue|xp35_0ojaq3c4o0ooz0gwgw1162acggz9m99m9xc970121|patternname=58|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp35_6604epz8c3n9ec31zx972066zy4o4oz8k8y0o8pzy3111x8o1vg4czy18oy223zx311|patternname=74|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp35_y73pmwmp3zxgy611z0gjkl2y2ee4z320146yb6iogkczy8277y24aiczy5gg88ggzy4c96w69c|patternname=84|style=raw}}
| style="background-color:#c6efce" | [[p35 honey farm hassler|44]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 38
|
|
| style="background-color:#c6efce" | [[42P38|42]]
| style="background-color:#c6efce" | [[44P38|44]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 39
| style="background-color:#c6efce" | [[Caterer on Beluchenko's p13|46]]
| style="background-color:#ffffdd" | {{LinkCatagolue|xp39_yco44mhar0rahm44ozyb17870123232107871zytg88czyggh37310o0ox1108oy84aabi2sgzy84s0gw6221y11221y212308suy4ullm0mlzwg88c88gy111wgg8gybo4kkw1y2g89a61s52zkq3omlp1y3og02221yc1y0o8gy111311zamg6qa7y47310c4oy28k4oy1ok46y032zw344d552y81108ox10108cec8zyi311zyn8u1ego4s4s4oge1u8zyo122685d0d586221|patternname=340|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp39_ye8kc871zya6a8qili0a4z2egoy6gggzy4232y01y162sgz08k0iaim4kozwo4cb4z011|patternname=78|style=raw}}
| style="background-color:#c6efce" | [[Pi-heptomino hasslers#p39|82]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 46
|
| style="background-color:#c6efce" | [[Twin bees shuttle|28]]
|
| style="background-color:#c6efce" | [[Tanner's p46|41]]
|
| style="background-color:#ffffdd" | {{LinkCatagolue|xp46_y74ep7zwo4oy28s6ozx1y511y9gs19ezs6jic0cij6sz11y311y9ggy3ggzyk7cp96069pc7zweig71y9ggy5gzyg3c72y2343zygsje4|patternname=114|style=raw}}
|
|
|-
! 51
| style="background-color:#ffffdd" | [[90P51|90]]
|
| style="background-color:#ffffdd" | {{LinkCatagolue|xp51_x2dugxccy7o0oy5ok46zg0sce054ccoy51w111y3ez11xsyi6cc880sce13zo8a6y5717w1y4ccx3ucgzyu1|patternname=86|style=raw}}
| style="background-color:#c6efce" | [[Period-51 glider gun|84]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 55
| style="background-color:#c6efce" | [[Pseudo-barberpole on rattlesnake|49]]
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp55_gy4ca23z11da88rcwgy0ggozwc871x121w32zy8go8y4ca23zy911zy58oy4ae4zy3311yfg8ozycc453w2520ocab8ozyj8ow3w1226zyh311|patternname=108|style=raw}}
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp55_xggy4ca23zy0346y0o448y28k8wo8ggo4a6zy711y76488gdx7zoxc2448ozpk863246w4a4y24897y0o8gzydggkcy432zyd1|patternname=98|style=raw}}
| style="background-color:#c6efce" | [[p55 pre-pulsar shuttle|134]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 57
|
|
| style="background-color:#c6efce" | [[112P57|112]]
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 58
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp58_y2g8o6pb8oyqo8bp6o8gz0ggcaa9o74y233xoge2y42egox33y247o9aacggz320f9y1373x373y2oogwgooy2373x373y19f023zy6gy3gy211y011y2gy3gzy51218k8w1218k8y12664y21218k8w1218k8zyooogwgoozxckgf9wgwcecxcecwggw11y011wggwcecxcecwgw9fgkczy2355p1u2gwgwccx1074y44701xccwgwg2u1p553zy61169d11yq11d9611|patternname=310|style=raw}}
| style="background-color:#ffffdd" | [[Pi-heptomino hasslers#p58|68]]
|
| style="background-color:#c6efce" | [[p58 pi-heptomino hassler|54]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 62
| style="background-color:#ffffdd" | [[110P62|110]]
| style="background-color:#c6efce" | [[66P62|66]]
| style="background-color:#ffffdd" | [[Century hasslers#p62|78]]
| style="background-color:#c6efce" | [[Lumps of muck hasslers#p62|92]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 65
| style="background-color:#c6efce" | [[Fumarole on Beluchenko's p13|52]]
|
| style="background-color:#ffffdd" | [[Honey farm hasslers#p65|138]]
| style="background-color:#c6efce" | [[Honey farm hasslers#p65|176]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 69
| style="background-color:#c6efce" | {{LinkCatagolue|xp69_y42egoy1ca23zybsgox4acga6zwgy0gs26y01y239czw1p5ao488ggwccx6a8oz8p78bhc870728cz012521|patternname=103|style=raw}}
|
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp69_n8ggxggy3ggowckggz01iuw3ip8y1122695dioajoz4b7xpje0218ogycoge2zydeiczyk69ezy58e13yc132g80epjxsq4zyd3pa39mkic88gy12j9owf9gzyf1156w311y311x112t|patternname=184|style=raw}}
| style="background-color:#c6efce" | {{LinkCatagolue|xp69_y2g8o6pb8oy039e0u2ggz0ggcaa9o74x8o8x355t2i1z320f9y53211y111y0o4oz0g88c0ccygdd0d552zw117871y8ggy54s0ggzy7jhe88g011474x8o64kld221zy632gv1t5gy064k6o743zyc11y211|patternname=196|style=raw}}
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 74
|
| style="background-color:#c6efce" | [[Raucci's p74|84]]
|
| style="background-color:#c6efce" | [[Honey farm hasslers#p74|96]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 77
| style="background-color:#c6efce" | [[34P7 on rattlesnake|67]]
|
|
| style="background-color:#c6efce" | [[Pi-heptomino hasslers#p77|78]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 82
|
|
| style="background-color:#c6efce" | [[p82 lumps of muck hassler|48]]
| style="background-color:#c6efce" | [[Pi-heptomino hasslers#p82|116]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 85
|
|
| style="background-color:#c6efce" | [[p85 R-pentomino hassler|68]]
| style="background-color:#c6efce" | {{LinkCatagolue|xp85_yeca23y1178cwooy2gzggy6cqikgyikn0ncz1cr0rby51y82bimcy2110123zw121y166wc4oy2ggkczyc11y11|patternname=96|style=raw}}
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 86
|
|
|
| style="background-color:#c6efce" | [[76P86|76]]
|
|
|
| style="background-color:#ffffdd" | [[Strictly volatile p86|168]]
|-
! 87
|
|
|
| style="background-color:#c6efce" | [[84P87|84]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 91
| style="background-color:#c6efce" | [[34P7 on Beluchenko's p13|68]]
|
|
| style="background-color:#c6efce" | [[R-pentomino hasslers#p91|84]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 93
| style="background-color:#c6efce" | [[Caterer on Merzenich's p31|60]]
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 94
|
|
|
| style="background-color:#c6efce" | [[54P94|54]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 95
| style="background-color:#c6efce" | [[Cribbage#LCM oscillators|141]]
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 106
|
|
| style="background-color:#c6efce" | [[66P106|66]]
| style="background-color:#c6efce" | [[115P106|115]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 111
| style="background-color:#c6efce" | [[Fire-spitting on p37 lumps of muck hassler|91]]
|
|
| style="background-color:#c6efce" | [[R-pentomino hasslers#p111|292]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 115
| style="background-color:#c6efce" | {{LinkCatagolue|xp115_y032acx66zw6ioy2gy0c871zca16a4x317zy2o8a6y0gbbgn1e808ozya11mq0v5kk8zye343|patternname=93|style=raw}}
|
|
| style="background-color:#c6efce" | [[Lumps of muck hasslers#115|96]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 118
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp118_0c4o0u93y1dbzca2t452y3ggzx11y5d87zxggc2sgyagggzx254ragv164koy332023y16426zypgwg08ozyl64k7o55lp1zyn11|patternname=119|style=raw}}
|
| style="background-color:#ffffdd" | [[snark loop|208]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 119
|
|
|
| style="background-color:#c6efce" | [[72P119|72]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 122
|
|
|
| style="background-color:#c6efce" | [[R-pentomino hasslers#p122|102]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 123
|
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 125
|
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 129
|
|
|
| style="background-color:#c6efce" | [[p129 R-pentomino hassler|38]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 133
|
|
|
| style="background-color:#c6efce" | [[B-heptomino hasslers#p133|84]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 134
|
|
|
| style="background-color:#ffffdd" | [[snark loop|208]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 141
| style="background-color:#c6efce" | [[Fire-spitting on p47 pre-pulsar shuttle|103]]
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 142
|
|
|
| style="background-color:#ffffdd" | [[snark loop|208]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 143
| style="background-color:#c6efce" | {{LinkCatagolue|xp143_xgbb88gzy1cd3gv04aczc4530gy1gr3zy1d5a64210g8c4066zy7kr6og|patternname=69|style=raw}}
|
|
| style="background-color:#c6efce" | [[p143 Bandersnatch loop|122]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|}

== Tesseracts of primes ==
These are the only numbers which have exactly five divisors. q1 represents the prime cubed, q2 the prime squared and q3 the prime itself.
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, q1, q2, q3, p
! 1, q1, q2, p
! 1, q1, q3, p
! 1, q2, q3, p
! 1, q1, p
! 1, q2, p
! 1, q3, p
! 1, p
! q1, q2, q3, p
! q1, q2, p
! q1, q3, p
! q2, q3, p
! q1, p
! q2, p
! q3, p
! SV
|-
! 16
| style="background-color:#ffffdd" | {{LinkCatagolue|xp16_gfnz1op1zxg8093731zy034a96|patternname=35|style=raw}}
| style="background-color:#ffffdd" | [[Ship in a bottle|86]]
| style="background-color:#c6efce" | [[p16 century shuttle|27]]
| style="background-color:#ffffdd" | {{LinkCatagolue|xp16_697o4cy8c4o796zxvvuw4a8cc4k8wuvvzo4o79cy8c97o4oz011ye11|patternname=78|style=raw}}
| style="background-color:#ffffdd" | [[Charity's p16|28]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | [[Achim's other p16|96]]
| style="background-color:#ffffdd" | [[Rich's p16|34]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | [[Achim's p16|32]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[Rob's p16|21]]
|-
! 81
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | {{LinkCatagolue|xp81_yzx8g33ykg8gzybo4oy6gxggy41xo80gy03pege1u0okcwgcabch6qzy9dj8m5l6ow6as0v07onc1y9323y1mfvwv6pgxv090fg9gzy9o48ngkgfwg8s3v0gfnry1e2moy8c9707870123x35t3o65zy923che21x11w3430346xggys1zyrgx4701x23jgw66zyr1156y4j20hzyzy1111y6cczzyccczyo31hiy4o8zyloo012ihgy1o80113zyq11y0321wo8g0g8gy4gs2cggz8o6he8gxggwo4o0o4cy86qgsy1mrs30vge53ws3a2r496z342t151uw127ov01utry1gggyadr7o0v1ekow7oa8r4iczmp2dklc3wca70v0s3t6gy03056y83210121y4178611zw343y61x11y4gg25zyp11|patternname=550|style=raw}}
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | {{LinkCatagolue|xp81_yzyzwca23zyzyy33y2eu80gswsg0gzyzyw2a6y4178ewew121zyzyz0o4ozyzyugs26x1zyzyzxco4zyzyca64zzzyzyisg8zyu42ezzzyz08okzya86czyhoge2zyc696z0gxsws4oy5okgz1212ewe205vsy2ggzyaggkc011zya1|patternname=146|style=raw}}
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|}

== Six divisors ==
12, 18, 20, 28, 32, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99, 116, 117, 124

For the square number the period is divisible by, a1 is that number, and a2 is its square root. b is the remaining factor, and ab is a times b.

For fifth powers, a1, a2, ab, and b represent x^4, x^3, x^2, and x respectively.

=== Has stator cells ===
wait where did 18 go
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, a1, a2, ab, b, p
! 1, a1, a2, ab, p
! 1, a1, a2, b, p
! 1, a1, a2, p
! 1, a1, ab, b, p
! 1, a1, ab, p
! 1, a1, b, p
! 1, a1, p
! 1, a2, ab, b, p
! 1, a2, ab, p
! 1, a2, b, p
! 1, a2, p
! 1, ab, b, p
! 1, ab, p
! 1, b, p
! 1, p
|-
! 12
|
|
| style="background-color:#c6efce" | [[mold on fire-spitting|31]]
|
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp12_xoq93xgz176eix7gg83111zy133|patternname=33|style=raw}}
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[dinner table|33]]
|
|
|-
! 20
|
|
| style="background-color:#c6efce" | [[mold on fumarole|30]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 28
| style="background-color:#c6efce" | [[mold on 34P14 shuttle|46]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 32
|
|
|
|
|
|
|
| style="background-color:#ffffdd" | [[68P32|68]]
| style="background-color:#c6efce" | [[p32 honey farm hassler|45]]
|
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp32_y2gk2gb3zy211y0g0s4zy2kbkx11zoozxooozeee111|patternname=48|style=raw}}
|
|
|
| style="background-color:#ffffdd" | [[gourmet|66]]
|-
! 44
|
|
| style="background-color:#c6efce" | [[mold on rattlesnake|45]]
|
|
|
|
|
|
|
|
|
|
|
| style="background-color:#ffffdd" | [[Pi-heptomino hasslers#p44|70]]
| style="background-color:#ffffdd" | [[p44 pi-heptomino hassler|72]]
|-
! 45
|
|
|
|
|
| style="background-color:#ffffdd" | [[pentadecathlon on snacker|52]]
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[p45 pi-heptomino hassler|29]]
|
|
|-
! 50
|
|
|
| style="background-color:#ffffdd" | [[p50 glider shuttle|188]]
|
| style="background-color:#c6efce" | [[24P10 on 30P25|58]]
|
|
|
|
|
|
|
|
|
|
|-
! 52
|
|
|
| style="background-color:#ffffdd" | [[Four molds hassling eight blocks|83]]
|
|
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[Four eaters hassling lumps of muck|35]]
|
|
|-
! 63
|
|
|
|
|
|
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[32P21 phase-shifting p5|64]]
|
|
|-
! 68
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[p68 century hassler|38]]
|-
! 75
|
|
|
|
|
| style="background-color:#c6efce" | [[Pentadecathlon on 30P25|42]]
|
|
|
|
|
|
|
| style="background-color:#ffffdd" | [[6 bits|49]]
|
|
|-
| 76
|
|
|
| style="background-color:#c6efce" | [[p76 pi-heptomino hassler|57]]
|
|
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[p76 pi-heptomino shuttle|52]]
|
|
|-
! 92
| style="background-color:#c6efce" | [[mold on twin bees shuttle|44]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 98
|
| style="background-color:#c6efce" | [[Gallus|105]]
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp98_660g0fmy64a4x62z0cqb0t53y8ca8x66w66zw6fx66ydccxuczxccwccyeokn0qb6zy6ccx4a4y6du010cc|patternname=105|style=raw}}
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 99
|
|
|
|
|
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp99_wg8o696o8a6zg1aq1qr6wccx6ioz11074wo80gxeqaa4ozy511y217871|patternname=75|style=raw}}
|
|
|
|
|
|
|
|
|
|-
! 116
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp116_y6o4an7zy711zy166y5ok4kozym31e8zx32acyc6a8oz2egozy535453y5cc|patternname=68|style=raw}}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 117
|
|
|
|
|
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp117_wg8o696o8a6zg1aq1qr6wccz11074wgy1gr3zy3d5a64210g8c4066zy9kr6og|patternname=76|style=raw}}
|
|
|
|
|
|
|
|
|
|-
! 124
|
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| style="background-color:#c6efce" | [[mold on Merzenich's p31|60]]
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|}

=== Volatility 1 ===
If a period is not listed (e.g. 75), no volatility 1 oscillators of that period are known.
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! a1, a2, ab, b, p
! a1, a2, ab, p
! a1, a2, b, p
! a1, a2, p
! a1, ab, b, p
! a1, ab, p
! a1, b, p
! a1, p
! a2, ab, b, p
! a2, ab, p
! a2, b, p
! a2, p
! ab, b, p
! ab, p
! b, p
! p
|-
! 12
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|-
! 20
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|-
! 32
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|-
! 45
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|-
! 92
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|-
! 99
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|}

== Hexeracts of primes ==
64

== Eight divisors ==
24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 128, 130, 135, 136, 138

== Nine divisors ==
36, 100

== Ten divisors ==
48, 80, 112

== Twelve divisors ==
60, 72, 84, 90, 96, 108, 126, 132, 140

== Fifteen divisors ==
144

== Sixteen divisors ==
120
[[Category:Lists of oscillators]]

List of oscillators with subperiod combinations

2025-09-19T15:30:48Z

TYCF: /* Sixteen divisors */

This page intends to list all known oscillators of periods up to 144 containing each combination of subperiods. Only non-trivial, non-pseudo-object cases are counted; a page for trivial cases may be created in future.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
! style="background-color:#dfdfff" | Blue
| This oscillator is the smallest possible example for the subperiod combination of this period.
|-
! style="background-color:#c6efce" | Green
| This oscillator is the smallest known example for the subperiod combination of this period.
|-
! style="background-color:#ffffdd" | Yellow
| This oscillator ''may'' be the smallest known example for the subperiod combination of this period; checking of other pattern collections may be advisable.
|-
! style="background-color:#ffaa00" | Orange
| Whether this subperiod combination is known for this period is unknown; checking of pattern collections advisable.
|-
! style="background-color:#ffc7ce" | Red
| This subperiod combination is currently unknown for this period.
|-
! style="background-color:#888888" | Gray
| This subperiod combination is provably impossible for this period.
|}

== Prime periods ==
Oscillators of prime period can either be fully strictly volatile or have stator cells; trivial cases cannot exist. Period 1 is included here for completeness, despite 1 not being a prime number.
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, p
! SV
|-
! 1
| colspan=2 style="background-color:#dfdfff" | [[Block|4]]
|-
! 2
| style="background-color:#dfdfff" | [[Blinker|3]]
| style="background-color:#dfdfff" | [[Phoenix 1|12]]
|-
! 3
| style="background-color:#dfdfff" | [[Caterer|12]]
| style="background-color:#dfdfff" | [[Statorless p3|140]]
|-
! 5
| style="background-color:#c6efce" | [[Pseudo-barberpole|15]]
| style="background-color:#c6efce" | [[Statorless p5|68]]
|-
! 7
| style="background-color:#c6efce" | [[28P7|28]]
| style="background-color:#ffc7ce" | none known
|-
! 11
| style="background-color:#c6efce" | [[Rattlesnake|33]]
| style="background-color:#ffc7ce" | none known
|-
! 13
| style="background-color:#c6efce" | [[Beluchenko's p13|34]]
| style="background-color:#c6efce" | [[Beluchenko's p13#Variants|128]]
|-
! 17
| style="background-color:#c6efce" | [[Honey thieves|36]]
| style="background-color:#ffc7ce" | none known
|-
! 19
| style="background-color:#c6efce" | [[Cribbage|92]]
| style="background-color:#ffc7ce" | none known
|-
! 23
| style="background-color:#c6efce" | [[54P23|54]]
| style="background-color:#ffc7ce" | none known
|-
! 29
| style="background-color:#c6efce" | [[p29 pre-pulsar shuttle|54]]
| style="background-color:#ffc7ce" | none known
|-
! 31
| style="background-color:#c6efce" | [[Merzenich's p31|48]]
| style="background-color:#ffc7ce" | none known
|-
! 37
| style="background-color:#c6efce" | [[58P37|58]]
| style="background-color:#ffc7ce" | none known
|-
! 41
| style="background-color:#c6efce" | [[p41 pi-heptomino hassler|170]]
| style="background-color:#ffc7ce" | none known
|-
! 43
| style="background-color:#c6efce" | [[p43 pi-heptomino hassler|70]]
| style="background-color:#ffc7ce" | none known
|-
! 47
| style="background-color:#c6efce" | [[p47 pre-pulsar shuttle|84]]
| style="background-color:#ffc7ce" | none known
|-
! 53
| style="background-color:#c6efce" | [[94P53|94]]
| style="background-color:#ffc7ce" | none known
|-
! 59
| style="background-color:#c6efce" | [[p59 pi-heptomino hassler|86]]
| style="background-color:#ffc7ce" | none known
|-
! 61
| style="background-color:#c6efce" | [[p61 pi-heptomino hassler|134]]
| style="background-color:#ffc7ce" | none known
|-
! 67
| style="background-color:#c6efce" | [[p67 Snark loop|228]]
| style="background-color:#ffc7ce" | none known
|-
! 71
| style="background-color:#c6efce" | [[p71 dependent reflector loop|92]]
| style="background-color:#ffc7ce" | none known
|-
! 73
| style="background-color:#c6efce" | [[p73 lumps of muck hassler|68]]
| style="background-color:#ffc7ce" | none known
|-
! 79
| style="background-color:#c6efce" | [[p79 pi-heptomino hassler|80]]
| style="background-color:#ffc7ce" | none known
|-
! 83
| style="background-color:#c6efce" | [[62P83|62]]
| style="background-color:#ffc7ce" | none known
|-
! 89
| style="background-color:#c6efce" | {{LinkCatagolue|xp89_yzy833y58e1e88gzyzyj330311ybckzyzyd3224e6y725acy165lozyzwgs2552ypggzyzy2gcoy1o8a6xca8y911zzzzysgy1g0gzy4ooy9153x6511y113xggzggyx4aa43z1qa6y135a4y767244cz023yag88c0cczye117871y5cc|patternname=164|style=raw}}
| style="background-color:#ffc7ce" | none known
|-
! 97
| style="background-color:#c6efce" | {{LinkCatagolue|xp97_ydg88e1u8y533z0kcyb11313kzol56y1ca52y6115137zy4ggyp2552sgzy411y94ocx6a8ozyzxe24zzzzyzy448ezyzyg32acx634y9ggzyzy4178kk8yp11zyzyksogkggy68ka6y1ckl3zyzyp5ogoggyb65zyzyeooy52fge221|patternname=164|style=raw}}
| style="background-color:#ffc7ce" | none known
|-
! 101
| style="background-color:#c6efce" | [[116P101|116]]
| style="background-color:#ffc7ce" | none known
|-
! 103
| style="background-color:#c6efce" | {{LinkCatagolue|xp103_yzyzyv33y58e1e88gzyzyzyzy3330311ybckzyzyzyz03224e6y725acy165lozyzyzylgs2552ypggzyzyzyxo8a6yf11zyzyzyma64y8742zzzzzyzyz4kcy86c2zzzzzyzy9gcoy8ca8zzzzzymg8oy88okzyo1ok46zy433ypg88ge2z6a8oy1ck8gy7os8gggy611z0bdy41y4g0ggy11zyd255t0t5y5ggzyh1y711|patternname=180|style=raw}}
| style="background-color:#ffc7ce" | none known
|-
! 107
| style="background-color:#c6efce" | [[86P107|86]]
| style="background-color:#ffc7ce" | none known
|-
! 109
| style="background-color:#c6efce" | [[rectifier|156]]
| style="background-color:#ffc7ce" | none known
|-
! 113
| style="background-color:#c6efce" | [[86P113|86]]
| style="background-color:#ffc7ce" | none known
|-
! 127
| style="background-color:#c6efce" | [[74P127|74]]
| style="background-color:#ffc7ce" | none known
|-
! 131
| style="background-color:#ffffdd" | [[rectifier|?]]
| style="background-color:#ffc7ce" | none known
|-
! 137
| style="background-color:#ffffdd" | [[rectifier|?]]
| style="background-color:#ffc7ce" | none known
|-
! 139
| style="background-color:#ffffdd" | [[rectifier|?]]
| style="background-color:#ffc7ce" | none known
|}

== Squares of primes ==
These are the only numbers which have exactly three divisors; only one subperiod is possible other than 1, and trivial cases cannot exist. Here, q represents sqrt(p).
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, q, p
! 1, p
! q, p
! SV
|-
! 4
| style="background-color:#dfdfff" | [[Mold|12]]
| style="background-color:#c6efce" | [[Monogram|18]]
| style="background-color:#dfdfff" | [[Mazing|12]]
| style="background-color:#c6efce" | [[Strictly volatile p4|416]]
|-
! 9
| style="background-color:#ffffdd" | {{LinkCatagolue|xp9_wg88b5kk8gz4v0lhlc221zw56|patternname=37|style=raw}}
| style="background-color:#c6efce" | [[29P9|29]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 25
| style="background-color:#ffffdd" | [[88P25|88]]
| style="background-color:#c6efce" | [[30P25|30]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#c6efce" | [[Charity's p25|128]]
|-
! 49
| style="background-color:#ffffdd" | [[p49 R-pentomino hassler|158]]
| style="background-color:#c6efce" | [[44P49|44]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 121
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | {{LinkCatagolue|xp121_yzyzyzyzymgiligzyzyzyzyzy0178cydg9g0641u08k8zyzyzyzyu4s0gym1221w11zyzyzyzyw11y7eaazzzyzyzyzymco4yb696zzzyzyzyzyh2a6zzzyzyzyvsg8zzzyzyzyqa64zzzyzyzy08okzzzyzyy42ezzzyzy9okgzzzypo4oyb86czyq1zzykkkszy5ggyn31e8z4a40v18o1243ydc4ozy112iai3yg11zy41|patternname=156|style=raw}}
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|}

== Four divisors ==
This includes oscillators whose periods are a product of two primes, and those whose periods are a cube of a prime. q1 represents the greater of the two divisors, and q2 the lesser.

{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, q1, q2, p
! 1, q1, p
! 1, q2, p
! 1, p
! q1, q2, p
! q1, p
! q2, p
! SV
|-
! 6
| style="background-color:#ffffdd" | [[p6 domino fountain|56]]
| style="background-color:#ffffdd" | [[Four blinkers around four blocks|24]]
| style="background-color:#ffffdd" | [[p6 honey farm hassler|121]]
| style="background-color:#c6efce" | [[Unix|16]]
| style="background-color:#ffffdd" | [[Statorless p6#Other statorless p6|58]]
| style="background-color:#ffffdd" | [[Jason's p6|28]]
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[Strictly volatile p6|52]]
|-
! 8
| style="background-color:#ffffdd" | {{LinkCatagolue|xp8_3520gji0253zxmxmzok78d1d87ko|patternname=45|style=raw}}
| style="background-color:#c6efce" | [[Achim's p8|18]]
| style="background-color:#ffffdd" | {{LinkCatagolue|xp8_0gk2gb3zg11y1sssz3y0777|patternname=32|style=raw}}
| style="background-color:#c6efce" | [[Blocker|15]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | {{LinkCatagolue|xp8_y9mm1ozya3c6wgzgw8808og137y1233xggo0ooz0330311xoo8y1sog132022w1zy61wc6ozy93gdd|patternname=84|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp8_xooow80e704wssszeee111y9777|patternname=34|style=raw}}
| style="background-color:#c6efce" | [[Figure eight|12]]
|-
! 10
| style="background-color:#ffffdd" | [[46P10|46]]
| style="background-color:#ffffdd" | [[37P10.1|37]]
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[24P10|24]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 14
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp14_0g886p6k48gz6b8lkl55pa9ozx1w73|patternname=47|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp14_ggw3p686k48gz1aq5howh9lkbagzw1245c3cjow11|patternname=62|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp14_8oy045a2wca23xgs2sggz0123y1skicy22606221zybg88ozw4aar0ray1gh211gy062sgzy1121y06221w2251|patternname=94|style=raw}}
| style="background-color:#ffffdd" | [[44P14|44]]
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[Tumbler|16]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
|-
! 15
| style="background-color:#ffffdd" | {{LinkCatagolue|xp15_03pmwmp3zxg11z332blic|patternname=31|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp15_8kkm1vgkczwgh26wg8ehraa4z6221xcb98gczy532|patternname=58|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp15_0oy1k70c8z1u1x675z161|patternname=27|style=raw}}
| style="background-color:#c6efce" | [[Eater eating pentadecathlon|19]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | {{LinkCatagolue|xp15_231jri22irj132zxr0hhhh0rz8ogpr9889rpgo8x4r4zyd4r4|patternname=84|style=raw}}
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[Pentadecathlon|12]]
|-
! 21
| style="background-color:#ffffdd" | [[Caterer on 42P7.1|54]]
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp21_gadicc4wccz8lldlgxggz025211h0g11xjjy1jjzy23e3xefmh3u0u3hmfezyc1x1|patternname=83|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp21_y54koy2oe1ng07gg8k8z8kkm4sk201y3771w3w3zx343y3354c|patternname=62|style=raw}}
| style="background-color:#c6efce" | [[32P21|32]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 22
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp22_gggy2g53xooz0hhhx3346y78cc4z111y2ooy03966x4cc8zya65|patternname=52|style=raw}}
| style="background-color:#ffffdd" | [[Champagne glass|45]]
|
| style="background-color:#c6efce" | [[Jason's p22|36]]
|
|
|
| style="background-color:#c6efce" | [[48P22.1|48]]
|-
! 26
| style="background-color:#ffffdd" | [[70P26|70]]
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp26_0gs2ibaa4y8o8zlm0mlkn3wssssksx32hgy7ggoggz25s168bbgy8ddy6juaacg7k8zx11311y8g8ox27y078ongld0dlzyf23y86baq9871|patternname=150|style=raw}}
| style="background-color:#c6efce" | [[p26 honey farm hassler|60]]
| style="background-color:#c6efce" |
{{LinkCatagolue|xp26_y7g33xexex33gzy6121w464x464w121zccw252y5ggxggy5252wccz0444w27y26401x1046y272w444z0222w4ey262goxog26y2e4w222z33w4a4yl4a4w33zy68k8w262x262w8k8zy8ccx7x7xcc|patternname=144|style=raw}}
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 27
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp27_mkid1e80g8gz1qaaw5l5kjcidicggzx1no3cjk44nkjgjkv0fpzy23452gv0sg624611|patternname=120|style=raw}}
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp27_c9b88g0s26xggz3h4u0t4vonkkn8a52z011w32h8imipzy414|patternname=73|style=raw}}
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp27_gya66y0s112ogggz1pl208k8y36952xo9zy0sy4a9imk80321zychzy07y4ai9d520o8gzgjl80252y3cik8x3iz1yaccy07gg83111|patternname=118|style=raw}}
| style="background-color:#c6efce" | [[56P27|56]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 33
| style="background-color:#c6efce" | [[Caterer on rattlesnake|46]]
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp33_8k4ra1vgc48cz1168711xk2s0ggzwc4go2egnkld221zy065w66|patternname=72|style=raw}}
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp33_ybgoy3i52z0gy812g1xot1046z7ery7278f6zsuby4cu2s8zwkuey3g18gzw7soy431zx121|patternname=77|style=raw}}
| style="background-color:#c6efce" | [[Jason's p33|60]]
|
|
|
| style="background-color:#ffffdd" | {{LinkCatagolue|xp33_yn46f01y520uc8zyo4rcy7om8zylocgyb1wogzymrggyc1m1zyl111yc13704zxgy58ck8808ooayr7e2022532wgg8gg0gsogz0a332022562y51yzy211y22zz8y2ggyzy2gy58ck8808ooaz1371011211w8ok8808esyra332022562y51zym40sogycgggzyngdgyc11rzyn13wgyb163zyq2d3y76r4zyp26f08y5g0uc4|patternname=236|style=raw}}
|-
! 34
| style="background-color:#ffffdd" | {{LinkCatagolue|xp34_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|patternname=620|style=raw}}
|
|
| style="background-color:#c6efce" | [[74P34|74]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 35
| style="background-color:#ffffdd" | {{LinkCatagolue|xp35_0ojaq3c4o0ooz0gwgw1162acggz9m99m9xc970121|patternname=58|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp35_6604epz8c3n9ec31zx972066zy4o4oz8k8y0o8pzy3111x8o1vg4czy18oy223zx311|patternname=74|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp35_y73pmwmp3zxgy611z0gjkl2y2ee4z320146yb6iogkczy8277y24aiczy5gg88ggzy4c96w69c|patternname=84|style=raw}}
| style="background-color:#c6efce" | [[p35 honey farm hassler|44]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 38
|
|
| style="background-color:#c6efce" | [[42P38|42]]
| style="background-color:#c6efce" | [[44P38|44]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 39
| style="background-color:#c6efce" | [[Caterer on Beluchenko's p13|46]]
| style="background-color:#ffffdd" | {{LinkCatagolue|xp39_yco44mhar0rahm44ozyb17870123232107871zytg88czyggh37310o0ox1108oy84aabi2sgzy84s0gw6221y11221y212308suy4ullm0mlzwg88c88gy111wgg8gybo4kkw1y2g89a61s52zkq3omlp1y3og02221yc1y0o8gy111311zamg6qa7y47310c4oy28k4oy1ok46y032zw344d552y81108ox10108cec8zyi311zyn8u1ego4s4s4oge1u8zyo122685d0d586221|patternname=340|style=raw}}
| style="background-color:#ffffdd" | {{LinkCatagolue|xp39_ye8kc871zya6a8qili0a4z2egoy6gggzy4232y01y162sgz08k0iaim4kozwo4cb4z011|patternname=78|style=raw}}
| style="background-color:#c6efce" | [[Pi-heptomino hasslers#p39|82]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 46
|
| style="background-color:#c6efce" | [[Twin bees shuttle|28]]
|
| style="background-color:#c6efce" | [[Tanner's p46|41]]
|
| style="background-color:#ffffdd" | {{LinkCatagolue|xp46_y74ep7zwo4oy28s6ozx1y511y9gs19ezs6jic0cij6sz11y311y9ggy3ggzyk7cp96069pc7zweig71y9ggy5gzyg3c72y2343zygsje4|patternname=114|style=raw}}
|
|
|-
! 51
| style="background-color:#ffffdd" | [[90P51|90]]
|
| style="background-color:#ffffdd" | {{LinkCatagolue|xp51_x2dugxccy7o0oy5ok46zg0sce054ccoy51w111y3ez11xsyi6cc880sce13zo8a6y5717w1y4ccx3ucgzyu1|patternname=86|style=raw}}
| style="background-color:#c6efce" | [[Period-51 glider gun|84]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 55
| style="background-color:#c6efce" | [[Pseudo-barberpole on rattlesnake|49]]
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp55_gy4ca23z11da88rcwgy0ggozwc871x121w32zy8go8y4ca23zy911zy58oy4ae4zy3311yfg8ozycc453w2520ocab8ozyj8ow3w1226zyh311|patternname=108|style=raw}}
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp55_xggy4ca23zy0346y0o448y28k8wo8ggo4a6zy711y76488gdx7zoxc2448ozpk863246w4a4y24897y0o8gzydggkcy432zyd1|patternname=98|style=raw}}
| style="background-color:#c6efce" | [[p55 pre-pulsar shuttle|134]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 57
|
|
| style="background-color:#c6efce" | [[112P57|112]]
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 58
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp58_y2g8o6pb8oyqo8bp6o8gz0ggcaa9o74y233xoge2y42egox33y247o9aacggz320f9y1373x373y2oogwgooy2373x373y19f023zy6gy3gy211y011y2gy3gzy51218k8w1218k8y12664y21218k8w1218k8zyooogwgoozxckgf9wgwcecxcecwggw11y011wggwcecxcecwgw9fgkczy2355p1u2gwgwccx1074y44701xccwgwg2u1p553zy61169d11yq11d9611|patternname=310|style=raw}}
| style="background-color:#ffffdd" | [[Pi-heptomino hasslers#p58|68]]
|
| style="background-color:#c6efce" | [[p58 pi-heptomino hassler|54]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 62
| style="background-color:#ffffdd" | [[110P62|110]]
| style="background-color:#c6efce" | [[66P62|66]]
| style="background-color:#ffffdd" | [[Century hasslers#p62|78]]
| style="background-color:#c6efce" | [[Lumps of muck hasslers#p62|92]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 65
| style="background-color:#c6efce" | [[Fumarole on Beluchenko's p13|52]]
|
| style="background-color:#ffffdd" | [[Honey farm hasslers#p65|138]]
| style="background-color:#c6efce" | [[Honey farm hasslers#p65|176]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 69
| style="background-color:#c6efce" | {{LinkCatagolue|xp69_y42egoy1ca23zybsgox4acga6zwgy0gs26y01y239czw1p5ao488ggwccx6a8oz8p78bhc870728cz012521|patternname=103|style=raw}}
|
| style="background-color:#ffffdd" |
{{LinkCatagolue|xp69_n8ggxggy3ggowckggz01iuw3ip8y1122695dioajoz4b7xpje0218ogycoge2zydeiczyk69ezy58e13yc132g80epjxsq4zyd3pa39mkic88gy12j9owf9gzyf1156w311y311x112t|patternname=184|style=raw}}
| style="background-color:#c6efce" | {{LinkCatagolue|xp69_y2g8o6pb8oy039e0u2ggz0ggcaa9o74x8o8x355t2i1z320f9y53211y111y0o4oz0g88c0ccygdd0d552zw117871y8ggy54s0ggzy7jhe88g011474x8o64kld221zy632gv1t5gy064k6o743zyc11y211|patternname=196|style=raw}}
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 74
|
| style="background-color:#c6efce" | [[Raucci's p74|84]]
|
| style="background-color:#c6efce" | [[Honey farm hasslers#p74|96]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 77
| style="background-color:#c6efce" | [[34P7 on rattlesnake|67]]
|
|
| style="background-color:#c6efce" | [[Pi-heptomino hasslers#p77|78]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 82
|
|
| style="background-color:#c6efce" | [[p82 lumps of muck hassler|48]]
| style="background-color:#c6efce" | [[Pi-heptomino hasslers#p82|116]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 85
|
|
| style="background-color:#c6efce" | [[p85 R-pentomino hassler|68]]
| style="background-color:#c6efce" | {{LinkCatagolue|xp85_yeca23y1178cwooy2gzggy6cqikgyikn0ncz1cr0rby51y82bimcy2110123zw121y166wc4oy2ggkczyc11y11|patternname=96|style=raw}}
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 86
|
|
|
| style="background-color:#c6efce" | [[76P86|76]]
|
|
|
| style="background-color:#ffffdd" | [[Strictly volatile p86|168]]
|-
! 87
|
|
|
| style="background-color:#c6efce" | [[84P87|84]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 91
| style="background-color:#c6efce" | [[34P7 on Beluchenko's p13|68]]
|
|
| style="background-color:#c6efce" | [[R-pentomino hasslers#p91|84]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 93
| style="background-color:#c6efce" | [[Caterer on Merzenich's p31|60]]
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 94
|
|
|
| style="background-color:#c6efce" | [[54P94|54]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 95
| style="background-color:#c6efce" | [[Cribbage#LCM oscillators|141]]
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 106
|
|
| style="background-color:#c6efce" | [[66P106|66]]
| style="background-color:#c6efce" | [[115P106|115]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 111
| style="background-color:#c6efce" | [[Fire-spitting on p37 lumps of muck hassler|91]]
|
|
| style="background-color:#c6efce" | [[R-pentomino hasslers#p111|292]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 115
| style="background-color:#c6efce" | {{LinkCatagolue|xp115_y032acx66zw6ioy2gy0c871zca16a4x317zy2o8a6y0gbbgn1e808ozya11mq0v5kk8zye343|patternname=93|style=raw}}
|
|
| style="background-color:#c6efce" | [[Lumps of muck hasslers#115|96]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 118
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp118_0c4o0u93y1dbzca2t452y3ggzx11y5d87zxggc2sgyagggzx254ragv164koy332023y16426zypgwg08ozyl64k7o55lp1zyn11|patternname=119|style=raw}}
|
| style="background-color:#ffffdd" | [[snark loop|208]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 119
|
|
|
| style="background-color:#c6efce" | [[72P119|72]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 122
|
|
|
| style="background-color:#c6efce" | [[R-pentomino hasslers#p122|102]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 123
|
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 125
|
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 129
|
|
|
| style="background-color:#c6efce" | [[p129 R-pentomino hassler|38]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 133
|
|
|
| style="background-color:#c6efce" | [[B-heptomino hasslers#p133|84]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 134
|
|
|
| style="background-color:#ffffdd" | [[snark loop|208]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 141
| style="background-color:#c6efce" | [[Fire-spitting on p47 pre-pulsar shuttle|103]]
|
|
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 142
|
|
|
| style="background-color:#ffffdd" | [[snark loop|208]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|-
! 143
| style="background-color:#c6efce" | {{LinkCatagolue|xp143_xgbb88gzy1cd3gv04aczc4530gy1gr3zy1d5a64210g8c4066zy7kr6og|patternname=69|style=raw}}
|
|
| style="background-color:#c6efce" | [[p143 Bandersnatch loop|122]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|}

== Tesseracts of primes ==
These are the only numbers which have exactly five divisors. q1 represents the prime cubed, q2 the prime squared and q3 the prime itself.
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, q1, q2, q3, p
! 1, q1, q2, p
! 1, q1, q3, p
! 1, q2, q3, p
! 1, q1, p
! 1, q2, p
! 1, q3, p
! 1, p
! q1, q2, q3, p
! q1, q2, p
! q1, q3, p
! q2, q3, p
! q1, p
! q2, p
! q3, p
! SV
|-
! 16
| style="background-color:#ffffdd" | {{LinkCatagolue|xp16_gfnz1op1zxg8093731zy034a96|patternname=35|style=raw}}
| style="background-color:#ffffdd" | [[Ship in a bottle|86]]
| style="background-color:#c6efce" | [[p16 century shuttle|27]]
| style="background-color:#ffffdd" | {{LinkCatagolue|xp16_697o4cy8c4o796zxvvuw4a8cc4k8wuvvzo4o79cy8c97o4oz011ye11|patternname=78|style=raw}}
| style="background-color:#ffffdd" | [[Charity's p16|28]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | [[Achim's other p16|96]]
| style="background-color:#ffffdd" | [[Rich's p16|34]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | [[Achim's p16|32]]
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#c6efce" | [[Rob's p16|21]]
|-
! 81
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | {{LinkCatagolue|xp81_yzx8g33ykg8gzybo4oy6gxggy41xo80gy03pege1u0okcwgcabch6qzy9dj8m5l6ow6as0v07onc1y9323y1mfvwv6pgxv090fg9gzy9o48ngkgfwg8s3v0gfnry1e2moy8c9707870123x35t3o65zy923che21x11w3430346xggys1zyrgx4701x23jgw66zyr1156y4j20hzyzy1111y6cczzyccczyo31hiy4o8zyloo012ihgy1o80113zyq11y0321wo8g0g8gy4gs2cggz8o6he8gxggwo4o0o4cy86qgsy1mrs30vge53ws3a2r496z342t151uw127ov01utry1gggyadr7o0v1ekow7oa8r4iczmp2dklc3wca70v0s3t6gy03056y83210121y4178611zw343y61x11y4gg25zyp11|patternname=550|style=raw}}
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffaa00" | check
| style="background-color:#ffffdd" | {{LinkCatagolue|xp81_yzyzwca23zyzyy33y2eu80gswsg0gzyzyw2a6y4178ewew121zyzyz0o4ozyzyugs26x1zyzyzxco4zyzyca64zzzyzyisg8zyu42ezzzyz08okzya86czyhoge2zyc696z0gxsws4oy5okgz1212ewe205vsy2ggzyaggkc011zya1|patternname=146|style=raw}}
| style="background-color:#ffffdd" | [[snark loop|228]]
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
| style="background-color:#ffc7ce" | none known
|}

== Six divisors ==
12, 18, 20, 28, 32, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99, 116, 117, 124

For the square number the period is divisible by, a1 is that number, and a2 is its square root. b is the remaining factor, and ab is a times b.

For fifth powers, a1, a2, ab, and b represent x^4, x^3, x^2, and x respectively.

=== Has stator cells ===
wait where did 18 go
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! 1, a1, a2, ab, b, p
! 1, a1, a2, ab, p
! 1, a1, a2, b, p
! 1, a1, a2, p
! 1, a1, ab, b, p
! 1, a1, ab, p
! 1, a1, b, p
! 1, a1, p
! 1, a2, ab, b, p
! 1, a2, ab, p
! 1, a2, b, p
! 1, a2, p
! 1, ab, b, p
! 1, ab, p
! 1, b, p
! 1, p
|-
! 12
|
|
| style="background-color:#c6efce" | [[mold on fire-spitting|31]]
|
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp12_xoq93xgz176eix7gg83111zy133|patternname=33|style=raw}}
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[dinner table|33]]
|
|
|-
! 20
|
|
| style="background-color:#c6efce" | [[mold on fumarole|30]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 28
| style="background-color:#c6efce" | [[mold on 34P14 shuttle|46]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 32
|
|
|
|
|
|
|
| style="background-color:#ffffdd" | [[68P32|68]]
| style="background-color:#c6efce" | [[p32 honey farm hassler|45]]
|
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp32_y2gk2gb3zy211y0g0s4zy2kbkx11zoozxooozeee111|patternname=48|style=raw}}
|
|
|
| style="background-color:#ffffdd" | [[gourmet|66]]
|-
! 44
|
|
| style="background-color:#c6efce" | [[mold on rattlesnake|45]]
|
|
|
|
|
|
|
|
|
|
|
| style="background-color:#ffffdd" | [[Pi-heptomino hasslers#p44|70]]
| style="background-color:#ffffdd" | [[p44 pi-heptomino hassler|72]]
|-
! 45
|
|
|
|
|
| style="background-color:#ffffdd" | [[pentadecathlon on snacker|52]]
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[p45 pi-heptomino hassler|29]]
|
|
|-
! 50
|
|
|
| style="background-color:#ffffdd" | [[p50 glider shuttle|188]]
|
| style="background-color:#c6efce" | [[24P10 on 30P25|58]]
|
|
|
|
|
|
|
|
|
|
|-
! 52
|
|
|
| style="background-color:#ffffdd" | [[Four molds hassling eight blocks|83]]
|
|
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[Four eaters hassling lumps of muck|35]]
|
|
|-
! 63
|
|
|
|
|
|
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[32P21 phase-shifting p5|64]]
|
|
|-
! 68
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[p68 century hassler|38]]
|-
! 75
|
|
|
|
|
| style="background-color:#c6efce" | [[Pentadecathlon on 30P25|42]]
|
|
|
|
|
|
|
| style="background-color:#ffffdd" | [[6 bits|49]]
|
|
|-
| 76
|
|
|
| style="background-color:#c6efce" | [[p76 pi-heptomino hassler|57]]
|
|
|
|
|
|
|
|
|
| style="background-color:#c6efce" | [[p76 pi-heptomino shuttle|52]]
|
|
|-
! 92
| style="background-color:#c6efce" | [[mold on twin bees shuttle|44]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 98
|
| style="background-color:#c6efce" | [[Gallus|105]]
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp98_660g0fmy64a4x62z0cqb0t53y8ca8x66w66zw6fx66ydccxuczxccwccyeokn0qb6zy6ccx4a4y6du010cc|patternname=105|style=raw}}
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 99
|
|
|
|
|
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp99_wg8o696o8a6zg1aq1qr6wccx6ioz11074wo80gxeqaa4ozy511y217871|patternname=75|style=raw}}
|
|
|
|
|
|
|
|
|
|-
! 116
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp116_y6o4an7zy711zy166y5ok4kozym31e8zx32acyc6a8oz2egozy535453y5cc|patternname=68|style=raw}}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 117
|
|
|
|
|
|
| style="background-color:#c6efce" | {{LinkCatagolue|xp117_wg8o696o8a6zg1aq1qr6wccz11074wgy1gr3zy3d5a64210g8c4066zy9kr6og|patternname=76|style=raw}}
|
|
|
|
|
|
|
|
|
|-
! 124
|
|
| style="background-color:#c6efce" | [[mold on Merzenich's p31|60]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|}

=== Volatility 1 ===
If a period is not listed (e.g. 75), no volatility 1 oscillators of that period are known.
{| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;"
! p
! a1, a2, ab, b, p
! a1, a2, ab, p
! a1, a2, b, p
! a1, a2, p
! a1, ab, b, p
! a1, ab, p
! a1, b, p
! a1, p
! a2, ab, b, p
! a2, ab, p
! a2, b, p
! a2, p
! ab, b, p
! ab, p
! b, p
! p
|-
! 12
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 20
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 32
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 45
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 92
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 99
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|}

== Hexeracts of primes ==
64

== Eight divisors ==
24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 128, 130, 135, 136, 138

== Nine divisors ==
36, 100

== Ten divisors ==
48, 80, 112

== Twelve divisors ==
60, 72, 84, 90, 96, 108, 126, 132, 140

== Fifteen divisors ==
144

== Sixteen divisors ==
120
[[Category:Lists of oscillators]]

List of oscillators with 3 to 16 cells

2025-09-19T15:30:29Z

TYCF:

This page lists known oscillators with a population between 3 and 16 inclusive. All oscillators up to 9 cells were enumerated by [[Nick Gotts]] except period-6 and period-12 oscillators. Oscillators of periods 6 and 12 have only been enumerated up to 8 cells.<ref name="post172725"/>
<center>
{|class="wikitable"
! colspan="7" | Contents
|-
| style="text-align:center" | [[#3 cells|3 cells]]
| style="text-align:center" | [[#4 cells|4 cells]]
| style="text-align:center" | [[#5 cells|5 cells]]
| style="text-align:center" | [[#6 cells|6 cells]]
| style="text-align:center" | [[#7 cells|7 cells]]
| style="text-align:center" | [[#8 cells|8 cells]]
| style="text-align:center" | [[#9 cells|9 cells]]
|-
| style="text-align:center" | [[#10 cells|10 cells]]
| style="text-align:center" | [[#11 cells|11 cells]]
| style="text-align:center" | [[#12 cells|12 cells]]
| style="text-align:center" | [[#13 cells|13 cells]]
| style="text-align:center" | [[#14 cells|14 cells]]
| style="text-align:center" | [[#15 cells|15 cells]]
| style="text-align:center" | [[#16 cells|16 cells]]
|}
{|class="wikitable" style="text-align:center"
! colspan="8" | Period color key !! Cost in gliders color key
|-
| style="background:#ffffdd;width:18px" | 2
| style="background:#ddffdd;width:18px" | 3
| style="background:#ffeedd;width:18px" | 4
| style="background:#ddddff;width:18px" | 5
| style="background:#bbffff;width:18px" | 6
| style="background:#ffdddd;width:18px" | 8
| style="background:#ffddcc;width:18px" | 14
| style="background:#ffddff;width:18px" | 15
| style="background:#ffffdd" | cost > # of cells
|}
</center>

== 3 cells ==
There is a total of 1 oscillator with 3 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Blinker.png|64px]]
! [[Blinker]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_7|style=tabulated}}
| 0.1
| 2
|}

== 6 cells ==
There are a total of 3 oscillators with 6 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Toad.png|64px]]
! [[Toad]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_7e|style=tabulated}}
| 7.1
| 3
|-
! 2
! [[File:Beacon.png|64px]]
! [[Beacon]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318c|style=tabulated}}
| 8.8
| 3
|-
! 3
! [[File:Clock.png|64px]]
! [[Clock]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_2a54|style=tabulated}}
| 19.4
| 4
|}

== 8 cells ==
There is a total of 1 oscillator with 8 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Bipole.png|64px]]
! [[Bipole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31ago|style=tabulated}}
| 21.7
| 4
|}

== 9 cells ==
There is 1 known oscillator with 9 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Tripole.png|64px]]
! [[Tripole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_g0k053z11|style=tabulated}}
| 26.6
| 5
|}

== 10 cells ==
There is 1 known oscillator with 10 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Quadpole.png|64px]]
! [[Quadpole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0g0k053z32|style=tabulated}}
| 21.8
| 5
|}

== 11 cells ==
There is 1 known oscillator with 11 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Pentapole.png|64px]]
! [[Pentapole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_wg0k053z642|style=tabulated}}
| 38.3
| 8
|}

== 12 cells ==
There are 11 known oscillators with 12 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Pentadecathlon.png|64px]]
! [[Pentadecathlon]]
| style="background-color:#ffddff" | {{period|15|brief}}
| {{LinkCatagolue|xp15_4r4z4r4|style=tabulated}}
| 18.6
| 3
|-
! 2
! [[File:Figureeight.png|64px]]
! [[Figure eight]]
| style="background-color:#ffdddd" | {{period|8|brief}}
| {{LinkCatagolue|xp8_gk2gb3z11|style=tabulated}}
| 23.4
| 4
|-
! 3
! [[File:Mold.png|64px]]
! [[Mold]]
| style="background-color:#ffeedd" | {{period|4|brief}}
| {{LinkCatagolue|xp4_37bkic|style=tabulated}}
| 24.2
| 5
|-
! 4
! [[File:Mazing.png|64px]]
! [[Mazing]]
| style="background-color:#ffeedd" | {{period|4|brief}}
| {{LinkCatagolue|xp4_ssj3744zw3|style=tabulated}}
| 26.6
| 5
|-
! 5
! [[File:Transbeaconontable.png|64px]]
! [[Trans-beacon on table]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_wbq23z32|style=tabulated}}
| 28.6
| 5
|-
! 6
! [[File:Cisbeaconontable.png|64px]]
! [[Cis-beacon on table]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318c0f9|style=tabulated}}
| 28.7
| 5
|-
! 7
! [[File:Caterer.png|64px]]
! [[Caterer]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_4hh186z07|style=tabulated}}
| 32.0
| 5
|-
! 8
! [[File:Fox.png|64px]]
! [[Fox]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_g45h1sz03|style=tabulated}}
| 35.6
| 6
|-
! 9
! [[File:Lei.png|64px]]
! [[Lei]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_s0i0j0ezw1|style=tabulated}}
| 39.5
| 6
|-
! 10
! [[File:Hexapole.png|64px]]
! [[Hexapole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_xg0k053zca02|style=tabulated}}
| 39.5
| 7
|-
! 11
! [[File:Phoenix1.png|64px]]
! [[Phoenix 1]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_882030kgz010602|style=tabulated}}
| 41.4
| 6
|}

== 13 cells ==
There are 4 known oscillators with 13 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Jam.png|64px]]
! [[Jam]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_695qc8zx33|style=tabulated}}
| 27.6
| 5
|-
! 2
! [[File:Boattiebipole.png|64px]]
! [[Boat tie bipole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_xoga13z253|style=tabulated}}
| 33.0
| 5
|-
! 3
! [[File:Byflops.png|64px]]
! [[By flops]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_4k1u1k4zx1|style=tabulated}}
| 38.6
| 6
|-
! 4
! [[File:Heptapole.png|64px]]
! [[Heptapole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31a08zy01050ko|style=tabulated}}
| '''?'''
| 11
|}

== 14 cells ==
There are 21 known oscillators with 14 cells.

{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Testtubebaby.png|64px]]
! [[Test tube baby]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31egge13|style=tabulated}}
| 29.0
| 5
|-
! 2
! [[File:Cisbeaconuponlongbookend.png|64px]]
! style="background-color:#dddddd" | [[Cis-beacon up on long bookend]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_3hu0og26|style=tabulated}}
| 30.6
| 5
|-
! 3
! [[File:Cisbeacononcap.png|64px]]
! style="background-color:#dddddd" | [[Cis-beacon on cap]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318c0f96|style=tabulated}}
| 30.7
| 5
|-
! 4
! [[File:Cisbeacondownonlongbookend.png|64px]]
! style="background-color:#dddddd" | [[Cis-beacon down on long bookend]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318c0fho|style=tabulated}}
| 30.9
| 5
|-
! 5
! [[File:Transbeacondownonlongbookend.png|64px]]
! style="background-color:#dddddd" | [[Trans-beacon down on long bookend]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_w8o0uh3z32|style=tabulated}}
| 31.9
| 5
|-
! 6
! [[File:Transbeacononcap.png|64px]]
! style="background-color:#dddddd" | [[Trans-beacon on cap]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318czw3553|style=tabulated}}
| 32.3
| 5
|-
! 7
! [[File:Transbeaconuponlongbookend.png|64px]]
! style="background-color:#dddddd" | [[Trans-beacon up on long bookend]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_03lk46z6401|style=tabulated}}
| 32.6
| 5
|-
! 8
! [[File:Bipoletieship.png|64px]]
! [[Bipole tie ship]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_xoga13z653|style=tabulated}}
| 32.8
| 5
|-
! 9
! [[File:Eaterplug.png|64px]]
! [[Eater plug]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_wo44871z6221|style=tabulated}}
| 34.1
| 6
|-
! 10
! [[File:Beacononcover.png|64px]]
! style="background-color:#dddddd" | [[Beacon on cover]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_wbq2sgz32|style=tabulated}}
| 34.8
| 6
|-
! 11
! [[File:Cisbipoleontable.png|64px]]
! [[Cis-bipole on table]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31ago0ui|style=tabulated}}
| 37.4
| 7
|-
! 12
! [[File:Twoeaters.png|64px]]
! [[Two eaters]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_32aczy0354c|style=tabulated}}
| 38.8
| 6
|-
! 13
! [[File:Transbipoleontable.png|64px]]
! [[Trans-bipole on table]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_32qbzx1056|style=tabulated}}
| 38.8
| 6
|-
! 14
! [[File:xp2_3lgh1lo.png|64px]]
! [[14P2.1]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_3lgh1lo|style=tabulated}}
| 39.6
| 6
|-
! 15
! [[File:Whynot.png|64px]]
! [[Why not]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_4k1u1k4zw121|style=tabulated}}
| 39.9
| 7
|-
! 16
! [[File:Boattietripole.png|64px]]
! [[Boat tie tripole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_xg8o652zca02|style=tabulated}}
| 40.4
| 8
|-
! 17
! [[File:Bipoletiesnake.png|64px]]
! [[Bipole tie snake]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_woga13zdb|style=tabulated}}
| 42.1
| 6
|-
! 18
! [[File:Carriertiebipole.png|64px]]
! [[Carrier tie bipole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_xoga13zc93|style=tabulated}}
| 43.1
| 9
|-
! 19
! [[File:xp2_62k0l51z032.png|64px]]
! [[14P2.3]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_62k0l51z032|style=tabulated}}
| 44.2
| 8
|-
! N/A
! [[File:xp2_4l1148kgzx302.png|64px]]
! [[14P2.4]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_4l1148kgzx302|style=tabulated}}
| [No natural{{br}}occurrences]
| style="background-color:#ffffdd" | 28
|-
! N/A
! [[File:Octapole.png|64px]]
! style="background-color:#dddddd" | [[Octapole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_y1g0k053zg80a02z11|style=tabulated}}
| [No natural{{br}}occurrences]
| 12
|}

== 15 cells ==
There are 31 known oscillators with 15 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Blocker.png|64px]]
! [[Blocker]]
| style="background-color:#ffdddd" | {{period|8|brief}}
| {{LinkCatagolue|xp8_g3jgz1ut|style=tabulated}}
| 27.2
| 5
|-
! 2
! [[File:Blockongriddle.png|64px]]
! [[Block on griddle]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_c8b8aczw33|style=tabulated}}
| 30.0
| 5
|-
! 3
! [[File:Boattiequadpole.png|64px]]
! [[Boat tie quadpole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_256o8gzy120ago|style=tabulated}}
| 33.5
| 6
|-
! 4
! [[File:Oddtesttubebaby.png|64px]]
! [[Odd test tube baby]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_03544oz4a511|style=tabulated}}
| 34.1
| 6
|-
! 5
! [[File:Cisbeaconupontubwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon up on tub-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_c813z3115a4|style=tabulated}}
| 37.4
| 6
|-
! 6
! [[File:Cisbeacondownontubwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon down on tub-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318cz3115a4|style=tabulated}}
| 37.4
| 8
|-
! 7
! [[File:Transbeacondownontubwithlongleg.png|64px]]
! style="background-color:#dddddd" | Trans-beacon down on tub-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318czw3115a4|style=tabulated}}
| 38.2
| 8
|-
! 8
! [[File:Tripoletieship.png|64px]]
! [[Tripole tie ship]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_xg8o653zca02|style=tabulated}}
| 38.5
| 6
|-
! 9
! [[File:Cisbeaconuponhookwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon up on hook-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_32hu0og26|style=tabulated}}
| 39.1
| 8
|-
! 10
! [[File:Hooktesttubebaby.png|64px]]
! style="background-color:#dddddd" | [[Hook test tube baby]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31egge123|style=tabulated}}
| 39.4
| 8
|-
! 11
! [[File:Transbeaconupontubwithlongleg.png|64px]]
! style="background-color:#dddddd" | Trans-beacon up on tub-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_25a88czc813|style=tabulated}}
| 39.7
| 6
|-
! 12
! [[File:Longboattiebipole.png|64px]]
! style="background-color:#dddddd" | Long boat tie bipole
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozy135a4|style=tabulated}}
| 40.3
| 7
|-
! 13
! [[File:Transbeacondownonhookwithlongleg.png|64px]]
! style="background-color:#dddddd" | Trans-beacon down on hook-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318czw311da|style=tabulated}}
| 40.6
| 9
|-
! 14
! [[File:Transbeaconuponhookwithlongleg.png|64px]]
! style="background-color:#dddddd" | Trans-beacon up on hook-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_05b88czc813|style=tabulated}}
| 41.3
| 9
|-
! 15
! [[File:Bipoletieeatertail.png|64px]]
! style="background-color:#dddddd" | Bipole tie eater tail
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozxc871|style=tabulated}}
| 41.4
| 6
|-
! 16
! [[File:Cisbeacondownonhookwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon down on hook-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318c0fh8o|style=tabulated}}
| 41.9
| 9
|-
! 17
! [[File:Cistripoleontable.png|64px]]
! style="background-color:#dddddd" | Cis-tripole on table
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_rai3zw20ac|style=tabulated}}
| 43.6
| 8
|-
! 18
! [[File:Bipoletieeaterhead.png|64px]]
! style="background-color:#dddddd" | Bipole tie eater head
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozy131e8|style=tabulated}}
| 43.7
| 8
|-
! 19
! [[File:Transtripoleontable.png|64px]]
! style="background-color:#dddddd" | Trans-tripole on table
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_32qbzx1058c|style=tabulated}}
| 44.2
| 8
|-
! 20
! [[File:xp2_jlg4glj.png|64px]]
! [[15P2.1]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_jlg4glj|style=tabulated}}
| 45
| 8
|-
! 21
! [[File:Mutteringmoat1.png|64px]]
! [[Muttering moat 1]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0m24gl3z3201|style=tabulated}}
| 45
| 10
|-
! 22
! [[File:xp2_g0l1hgl3z11.png|64px]]
! [[xp2_g0l1hgl3z11]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_g0l1hgl3z11|style=tabulated}}
| 46
| 9
|-
! 23
! [[File:Bipoletielongsnake.png|64px]]
! style="background-color:#dddddd" | Bipole tie long snake
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_3lozx31ago|style=tabulated}}
| 47
| 10
|-
! 24
! [[File:xp2_62k0l51z642.png|64px]]
! [[xp2_62k0l51z642]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_62k0l51z642|style=tabulated}}
| '''?'''
| 10
|-
! 25
! [[File:Blinkersbitpole.png|64px]]
! [[Blinkers bit pole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_k3g4gljz11|style=tabulated}}
| '''?'''
| 10
|-
! 26
! [[File:Carriertietripole.png|64px]]
! style="background-color:#dddddd" | Carrier tie tripole
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_39cggzx1050ko|style=tabulated}}
| '''?'''
| 11
|-
! 27
! [[File:Phoenixwithcavity.png|64px]]
! [[Phoenix with cavity]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_882030kgz014a86|style=tabulated}}
| '''?'''
| 10
|-
! 28
! [[File:xp2_350k0l51zw32.png|64px]]
! [[xp2_350k0l51zw32]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_350k0l51zw32|style=tabulated}}
| '''?'''
| 14
|-
! 29
! [[File:Tripoletiesnake.png|64px]]
! style="background-color:#dddddd" | Tripole tie snake
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_bdggzw1050ko|style=tabulated}}
| '''?'''
| 10
|-
! N/A
! [[File:Nonapole.png|64px]]
! style="background-color:#dddddd" | [[Nonapole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_y2g0k053zw80a02z321|style=tabulated}}
| [No natural{{br}}occurrences]
| 14
|-
! N/A
! [[File:Pseudobarberpole.png|64px]]
! [[Pseudo-barberpole]]
| style="background-color:#ddddff" | {{period|5|brief}}
| {{LinkCatagolue|xp5_y2g0k413zwo0a02z32|style=tabulated}}
| [No natural{{br}}occurrences]
| 9
|}

== 16 cells ==
There are 108 known oscillators with 16 cells.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Oscillator
! [[Period]]
! [[apgcode]]
! [[Frequency class|FC]]
! [[Glider synthesis|Synth.{{br}}cost]]
|-
! 1
! [[File:Quadpoletieship.png|64px]]
! [[Quadpole tie ship]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31a08zy0123cko|style=tabulated}}
| 25.5
| 5
|-
! 2
! [[File:Octagon2.png|64px]]
! [[Octagon 2]]
| style="background-color:#ddddff" | {{period|5|brief}}
| {{LinkCatagolue|xp5_idiidiz01w1|style=tabulated}}
| 29.3
| 5
|-
! 3
! [[File:Cisbeaconondock.png|64px]]
! style="background-color:#dddddd" | [[Cis-beacon on dock]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_j1u062goz11|style=tabulated}}
| 28.7
| 4
|-
! 4
! [[File:Tubtesttubebaby.png|64px]]
! [[Tub test tube baby]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_25a88gz8ka221|style=tabulated}}
| 29.4
| 6
|-
! 5
! [[File:Transbeaconondock.png|64px]]
! style="background-color:#dddddd" | [[Trans-beacon on dock]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_03lk453z6401|style=tabulated}}
| 29.9
| 5
|-
! 6
! [[File:Tumbler.png|64px]]
! [[Tumbler]]
| style="background-color:#ffddcc" | {{period|14|brief}}
| {{LinkCatagolue|xp14_j9d0d9j|style=tabulated}}
| 29.9
| 5
|-
! 7
! [[File:Unix.png|64px]]
! [[Unix]]
| style="background-color:#bbffff" | {{period|6|brief}}
| {{LinkCatagolue|xp6_ccb7w66z066|style=tabulated}}
| 29.3
| 5
|-
! 8
! [[File:Transblockoncandlefrobra.png|64px]]
! [[Trans-block on candlefrobra]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_025qzrq221|style=tabulated}}
| 31.0
| 5
|-
! 9
! [[File:xp2_8e1t2gozw23.png|64px]]
! style="background-color:#dddddd" | [[xp2_8e1t2gozw23]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_8e1t2gozw23|style=tabulated}}
| 32.5
| 5
|-
! 10
! [[File:Cisblockoncandlefrobra.png|64px]]
! [[Cis-block on candlefrobra]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_025qz32qq1|style=tabulated}}
| 32.5
| 5
|-
! 11
! [[File:Boatongriddle.png|64px]]
! style="background-color:#dddddd" | [[Boat on griddle]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_c8b8acz0253|style=tabulated}}
| 33.5
| 6
|-
! 12
! [[File:Fourboats.png|64px]]
! [[Four boats]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_8ki1688gzx3421|style=tabulated}}
| 33.5
| 6
|-
! 13
! [[File:xp2_gk2t2sgzw23.png|64px]]
! style="background-color:#dddddd" | xp2_gk2t2sgzw23
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_gk2t2sgzw23|style=tabulated}}
| 35.5
| 6
|-
! 14
! [[File:Transboattesttubebaby.png|64px]]
! style="background-color:#dddddd" | [[Trans-boat test tube baby]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_03544ozca511|style=tabulated}}
| 36.3
| 8
|-
! 15
! [[File:Transbipoleuponlongbookend.png|64px]]
! style="background-color:#dddddd" | Trans-bipole up on long bookend
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0g0kc0fhoz32|style=tabulated}}
| 37.1
| 6
|-
! 16
! [[File:Mangled1beacon.png|64px]]
! style="background-color:#dddddd" | [[Mangled 1 beacon]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_c88b9iczw32|style=tabulated}}
| 37.2
| 6
|-
! 17
! [[File:xp2_ciabgzx254c.png|64px]]
! style="background-color:#dddddd" | xp2_ciabgzx254c
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_ciabgzx254c|style=tabulated}}
| 37.3
| 6
|-
! 18
! [[File:Transbeacondownontransboatwithlongleg.png|64px]]
! style="background-color:#dddddd" | Trans-beacon down on trans-boat-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318czw3115ac|style=tabulated}}
| 37.3
| 6
|-
! 19
! [[File:Cisbeaconupontransboatwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon up on trans-boat-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_c813z3115ac|style=tabulated}}
| 37.6
| 8
|-
! 20
! [[File:xp2_c813z31178c.png|64px]]
! style="background-color:#dddddd" | xp2_c813z31178c
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_c813z31178c|style=tabulated}}
| 37.7
| 7
|-
! 21
! [[File:Cisbipoletie.png|64px]]
! style="background-color:#dddddd" | Cis-bipole-tie
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozy1350ko|style=tabulated}}
| 37.7
| 6
|-
! 22
! [[File:Bipoleoncover.png|64px]]
! style="background-color:#dddddd" | Bipole on cover
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_wgbq2sgz642|style=tabulated}}
| 37.8
| 6
|-
! 23
! [[File:Cisbeacondownontransboatwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon down on trans-boat-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318cz3115ac|style=tabulated}}
| 37.8
| 8
|-
! 24
! [[File:Cisbeaconuponcisboatwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon up on cis-boat-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_c813z311da4|style=tabulated}}
| 38.5
| 7
|-
! 25
! [[File:Transbeacondownoncisboatwithlongleg.png|64px]]
! style="background-color:#dddddd" | Trans-beacon down on cis-boat-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318czw311da4|style=tabulated}}
| 38.6
| 7
|-
! 26
! [[File:xp2_318czc87113.png|64px]]
! style="background-color:#dddddd" | xp2_318czc87113
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318czc87113|style=tabulated}}
| 38.8
| 7
|-
! 27
! [[File:Cisboattesttubebaby.png|64px]]
! style="background-color:#dddddd" | [[Cis-boat test tube baby]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_03544oz4ad11|style=tabulated}}
| 38.8
| 7
|-
! 28
! [[File:Ponytailtesttubebaby.png|64px]]
! style="background-color:#dddddd" | Ponytail test tube baby
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_2ege11ego|style=tabulated}}
| 38.9
| 8
|-
! 29
! [[File:Cisbeacondownoncisboatwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon down on cis-boat-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318cz311da4|style=tabulated}}
| 38.9
| 7
|-
! 30
! [[File:xp2_318c0s26zw311.png|64px]]
! style="background-color:#dddddd" | xp2_318c0s26zw311
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318c0s26zw311|style=tabulated}}
| 39.0
| 6
|-
! 31
! [[File:xp2_318cz31178c.png|64px]]
! style="background-color:#dddddd" | xp2_318cz31178c
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318cz31178c|style=tabulated}}
| 39.1
| 7
|-
! 32
! [[File:Cisbeacononcarriersiamesetable.png|64px]]
! style="background-color:#dddddd" | Cis-beacon on carrier-siamese-table
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_64132arzx32|style=tabulated}}
| 39.1
| 9
|-
! 33
! [[File:xp2_gk2t2kozw23.png|64px]]
! style="background-color:#dddddd" | xp2_gk2t2kozw23
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_gk2t2kozw23|style=tabulated}}
| 39.1
| 6
|-
! 34
! [[File:Bentkeys.png|64px]]
! [[Bent keys]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_2524sws4252|style=tabulated}}
| 39.2
| 7
|-
! 35
! [[File:xp2_62go1vg4c.png|64px]]
! style="background-color:#dddddd" | xp2_62go1vg4c
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_62go1vg4c|style=tabulated}}
| 39.8
| 9
|-
! 36
! [[File:xp2_354k8zx1221e8.png|64px]]
! style="background-color:#dddddd" | xp2_354k8zx1221e8
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_354k8zx1221e8|style=tabulated}}
| 39.8
| 7
|-
! 37
! [[File:Cisbipoleoncap.png|64px]]
! style="background-color:#dddddd" | Cis-bipole on cap
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31ago0uic|style=tabulated}}
| 40.0
| 7
|-
! 38
! [[File:Transbeaconupontransboatwithlongleg.png|64px]]
! style="background-color:#dddddd" | [[Trans-beacon up on trans-boat-with-long-leg]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318czca5113|style=tabulated}}
| 40.0
| 8
|-
! 39
! [[File:Transbipoledownonlongbookend.png|64px]]
! style="background-color:#dddddd" | Trans-bipole down on long bookend
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozx622ac|style=tabulated}}
| 40.3
| 9
|-
! 40
! [[File:xp2_318czw31178c.png|64px]]
! style="background-color:#dddddd" | xp2_318czw31178c
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318czw31178c|style=tabulated}}
| 40.4
| 6
|-
! 41
! [[File:Eatereatingintegral.png|64px]]
! style="background-color:#dddddd" | [[Eater eating integral]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_31egozy231e8|style=tabulated}}
| 40.5
| 7
|-
! 42
! [[File:Skewedquad.png|64px]]
! [[Skewed quad]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_g3l0k26z11w23|style=tabulated}}
| 40.6
| 8
|-
! 43
! [[File:Tricetongs.png|64px]]
! [[Trice tongs]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_04qi3s4z33w1|style=tabulated}}
| 40.6
| 8
|-
! 44
! [[File:Transbeacononcarriersiamesetable.png|64px]]
! style="background-color:#dddddd" | Trans-beacon on carrier-siamese-table
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_4s0c813z39c|style=tabulated}}
| 40.7
| 10
|-
! 45
! [[File:Oddkeys.png|64px]]
! [[Odd keys]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_2524sws44a4|style=tabulated}}
| 40.7
| 7
|-
! 46
! [[File:Transbeaconuponcisboatwithlongleg.png|64px]]
! style="background-color:#dddddd" | Trans-beacon up on cis-boat-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_25b88czc813|style=tabulated}}
| 40.9
| 7
|-
! 47
! [[File:Hooktubtesttubebaby.png|64px]]
! style="background-color:#dddddd" | Hook tub test tube baby
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_g88a52z122qk|style=tabulated}}
| 41.0
| 9
|-
! 48
! [[File:Cisbipoledownonlongbookend.png|64px]]
! style="background-color:#dddddd" | Cis-bipole down on long bookend
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_064kl3zc8501|style=tabulated}}
| 41.1
| 9
|-
! 49
! [[File:Transquadpoleontable.png|64px]]
! style="background-color:#dddddd" | Trans-quadpole on table
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_32qbzx1050ko|style=tabulated}}
| 41.1
| 7
|-
! 50
! [[File:Shortkeys.png|64px]]
! [[Short keys]]
| style="background-color:#ddffdd" | {{period|3|brief}}
| {{LinkCatagolue|xp3_2522ewe2252|style=tabulated}}
| 41.1
| 6
|-
! 51
! [[File:Cisbipoleuponlongbookend.png|64px]]
! style="background-color:#dddddd" | Cis-bipole up on long bookend
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31ago0uh3|style=tabulated}}
| 41.2
| 9
|-
! 52
! [[File:Cisquadpoleontable.png|64px]]
! style="background-color:#dddddd" | Cis-quadpole on table
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31a08zxo9ar|style=tabulated}}
| 41.3
| 7
|-
! 53
! [[File:Antiphasewhybother.png|64px]]
! [[Antiphase why bother]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_882t2kgz01252|style=tabulated}}
| 41.4
| 7
|-
! 54
! [[File:Longhooktesttubebaby.png|64px]]
! [[Long hook test tube baby]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31egge1246|style=tabulated}}
| 41.4
| 9
|-
! 55
! [[File:xp2_o8b9czx318c.png|64px]]
! style="background-color:#dddddd" | xp2_o8b9czx318c
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_o8b9czx318c|style=tabulated}}
| 41.7
| 9
|-
! 56
! [[File:Transbipoleoncap.png|64px]]
! style="background-color:#dddddd" | Trans-bipole on cap
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozx6aa6|style=tabulated}}
| 41.7
| 7
|-
! 57
! [[File:Quadpoletiesnake.png|64px]]
! style="background-color:#dddddd" | Quadpole tie snake
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_xg0kc3213zca02|style=tabulated}}
| 41.9
| 8
|-
! 58
! [[File:Bipoletielongship.png|64px]]
! style="background-color:#dddddd" | Bipole tie long ship
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozy135ac|style=tabulated}}
| 42.2
| 8
|-
! 59
! [[File:Cisbeacononsnakesiamesetable.png|64px]]
! style="background-color:#dddddd" | Cis-beacon on snake-siamese-table
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_pf0318cz23|style=tabulated}}
| 42.4
| 6
|-
! 60
! [[File:xp2_0318czc93123.png|64px]]
! style="background-color:#dddddd" | xp2_0318czc93123
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0318czc93123|style=tabulated}}
| 43.0
| 9
|-
! 61
! [[File:Cisbeaconuponlonghookwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon up on long-hook-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_62go0uh246|style=tabulated}}
| 43.6
| 9
|-
! 62
! [[File:Whybother.png|64px]]
! [[Why bother]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_gk2t2kgzw252|style=tabulated}}
| 43.5
| 6
|-
! 63
! [[File:Cisbeacondownonlonghookwithlongleg.png|64px]]
! style="background-color:#dddddd" | Cis-beacon down on long-hook-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318c0fh84c|style=tabulated}}
| 43.5
| 9
|-
! 64
! [[File:Transbeacondownonlonghookwithlongleg.png|64px]]
! style="background-color:#dddddd" | Trans-beacon down on long-hook-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_318czw31pl2|style=tabulated}}
| 44.5
| 9
|-
! 65
! [[File:Transbeacononsnakesiamesetable.png|64px]]
! style="background-color:#dddddd" | Trans-beacon on snake-siamese-table
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_4s0c813zbd|style=tabulated}}
| 44.5
| 11
|-
! 66
! [[File:Byflopswithcavity.png|64px]]
! style="background-color:#dddddd" | By flops with cavity
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_4k1u1kiczx1|style=tabulated}}
| 45
| 11
|-
! 67
! [[File:Transbeaconuponlonghookwithlongleg.png|64px]]
! style="background-color:#dddddd" | Trans-beacon up on long-hook-with-long-leg
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_08ljgozog26|style=tabulated}}
| 45
| 9
|-
! 68
! [[File:xp2_bt062goz32.png|64px]]
! style="background-color:#dddddd" | xp2_bt062goz32
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_bt062goz32|style=tabulated}}
| 45
| 12
|-
! 69
! [[File:Tripoletieeatertail.png|64px]]
! style="background-color:#dddddd" | Tripole tie eater tail
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_8ehjzw1050ko|style=tabulated}}
| 45
| 10
|-
! 70
! [[File:Quad.png|64px]]
! [[Quad]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_j5g29jz11w11|style=tabulated}}
| 46 
| 8
|-
! 71
! [[File:Longboattietripole.png|64px]]
! style="background-color:#dddddd" | Long boat tie tripole
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_25acggzy01050ko|style=tabulated}}
| 46
| 10
|-
! 72
! [[File:Carriertiequadpole.png|64px]]
! style="background-color:#dddddd" | Carrier tie quadpole
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_3146o8gzy220ago|style=tabulated}}
| 46
| 8
|-
! 73
! [[File:xp2_3l04gl3z3201.png|64px]]
! style="background-color:#dddddd" | xp2_3l04gl3z3201
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_3l04gl3z3201|style=tabulated}}
| 46
| 9
|-
! 74
! [[File:Bipoletieshillelaghhead.png|64px]]
! style="background-color:#dddddd" | Bipole tie shillelagh head
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_djozx31ago|style=tabulated}}
| 46
| 8
|-
! 75
! [[File:xp2_0bt062goz32.png|64px]]
! style="background-color:#dddddd" | xp2_0bt062goz32
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0bt062goz32|style=tabulated}}
| 47
| 9
|-
! 76
! [[File:xp2_g1l141lpz11.png|64px]]
! style="background-color:#dddddd" | xp2_g1l141lpz11
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_g1l141lpz11|style=tabulated}}
| 47
| 11
|-
! 77
! [[File:xp2_jlg44glj.png|64px]]
! style="background-color:#dddddd" | xp2_jlg44glj
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_jlg44glj|style=tabulated}}
| 47
| 8
|-
! 78
! [[File:xp2_0mq0c813z641.png|64px]]
! style="background-color:#dddddd" | xp2_0mq0c813z641
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0mq0c813z641|style=tabulated}}
| 47
| 11
|-
! 79
! [[File:xp2_mq0c813z65.png|64px]]
! style="background-color:#dddddd" | xp2_mq0c813z65
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_mq0c813z65|style=tabulated}}
| '''?'''
| 11
|-
! 80
! [[File:Bipoletietubwithtail.png|64px]]
! style="background-color:#dddddd" | Bipole tie tub with tail
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozw8k871|style=tabulated}}
| '''?'''
| 9
|-
! 81
! [[File:xp2_0c48c93zc813.png|64px]]
! style="background-color:#dddddd" | xp2_0c48c93zc813
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0c48c93zc813|style=tabulated}}
| '''?'''
| 9
|-
! 82
! [[File:xp2_k3g441lpz11.png|64px]]
! style="background-color:#dddddd" | xp2_k3g441lpz11
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_k3g441lpz11|style=tabulated}}
| '''?'''
| 11
|-
! 83
! [[File:Bipoletiehookwithtailtail.png|64px]]
! style="background-color:#dddddd" | Bipole tie hook-with-tail tail
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0g0kc32qkz32|style=tabulated}}
| '''?'''
| 9
|-
! 84
! [[File:xp2_0k3g4gljz32.png|64px]]
! style="background-color:#dddddd" | xp2_0k3g4gljz32
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0k3g4gljz32|style=tabulated}}
| '''?'''
| 14
|-
! 85
! [[File:Hookstesttubebaby.png|64px]]
! style="background-color:#dddddd" | [[Hooks test tube baby]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_321egge123|style=tabulated}}
| '''?'''
| 8
|-
! 86
! [[File:Bipoletieverylongsnake.png|64px]]
! style="background-color:#dddddd" | Bipole tie very long snake
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozy131248c|style=tabulated}}
| '''?'''
| 9
|-
! 87
! [[File:Bipoletiecanoe.png|64px]]
! style="background-color:#dddddd" | Bipole tie canoe
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_312kozy131ago|style=tabulated}}
| '''?'''
| 10
|-
! 88
! [[File:xp2_jlg441lp.png|64px]]
! style="background-color:#dddddd" | xp2_jlg441lp
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_jlg441lp|style=tabulated}}
| '''?'''
| 12
|-
! 89
! [[File:Bipoletiehookwithtailhook.png|64px]]
! style="background-color:#dddddd" | Bipole tie hook-with-tail hook
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozxo8b5|style=tabulated}}
| '''?'''
| 11
|-
! 90
! [[File:xp2_0g0l1hgl3z32.png|64px]]
! style="background-color:#dddddd" | xp2_0g0l1hgl3z32
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0g0l1hgl3z32|style=tabulated}}
| '''?'''
| 10
|-
! 91
! [[File:Bipoletieshillelaghtail.png|64px]]
! style="background-color:#dddddd" | Bipole tie shillelagh tail
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_mp3zw31ago|style=tabulated}}
| '''?'''
| 10
|-
! 92
! [[File:Boattiepentapole.png|64px]]
! style="background-color:#dddddd" | Boat tie pentapole
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_y1g0k053zg8o642z01|style=tabulated}}
| '''?'''
| 10
|-
! 93
! [[File:Chacha.png|64px]]
! [[Cha cha]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_4o6o7o68zx1|style=tabulated}}
| '''?'''
| 10
|-
! 94
! [[File:Transbipoletie.png|64px]]
! style="background-color:#dddddd" | Trans-bipole-tie
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_31agozy131ago|style=tabulated}}
| '''?'''
| 8
|-
! 95
! [[File:Tripoletieeaterhead.png|64px]]
! style="background-color:#dddddd" | Tripole tie eater head
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_178cggzy01050ko|style=tabulated}}
| '''?'''
| 12
|-
! N/A
! [[File:xp2_0g4j04g53z32x3.png|64px]]
! style="background-color:#dddddd" | xp2_0g4j04g53z32x3
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_0g4j04g53z32x3|style=tabulated}}
| '''?'''<ref group=note>This object has not occurred in the official [[Catagolue]] C1 census, but it has {{cata|hashsoup/C1/c_SfyMzmFOb8PA71481176/b3s23|a C2_2 occurrence}} that works as {{cata|hashsoup/C1/c_SfyMzmFOb8PA71481176/b3s23|a C1 soup}}</ref>
| 16
|-
! N/A
! [[File:2.3.3.png|64px]]
! [[2.3.3]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_k3g44gljz11|style=tabulated}}
| [No natural{{br}}occurrences]
| 13
|-
! N/A
! [[File:Decapole.png|64px]]
! style="background-color:#dddddd" | [[Decapole]]
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_y3g0k053zx80a02z6501|style=tabulated}}
| [No natural{{br}}occurrences]
| 12
|-
! N/A
! [[File:xp2_kg34azwa4o15.png|64px]]
! style="background-color:#dddddd" | xp2_kg34azwa4o15
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_kg34azwa4o15|style=tabulated}}
| [No natural{{br}}occurrences]
| 13
|-
! N/A
! [[File:xp2_8a2543gkz010602.png|64px]]
! style="background-color:#dddddd" | xp2_8a2543gkz010602
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_8a2543gkz010602|style=tabulated}}
| [No natural{{br}}occurrences]
| style="background-color:#ffffdd" | 56
|-
! N/A
! [[File:Tripoletielongsnake.png|64px]]
! style="background-color:#dddddd" | Tripole tie long snake
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_xg8o64213zca02|style=tabulated}}
| [No natural{{br}}occurrences]
| 14
|-
! N/A
! [[File:xp2_ia284gljz11.png|64px]]
! style="background-color:#dddddd" | xp2_ia284gljz11
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_ia284gljz11|style=tabulated}}
| [No natural{{br}}occurrences]
| 8
|-
! N/A
! [[File:xp2_4k4g4gljz32.png|64px]]
! style="background-color:#dddddd" | xp2_4k4g4gljz32
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_4k4g4gljz32|style=tabulated}}
| [No natural{{br}}occurrences]
| 12
|-
! N/A
! [[File:xp2_350k0l51z0642.png|64px]]
! style="background-color:#dddddd" | xp2_350k0l51z0642
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_350k0l51z0642|style=tabulated}}
| [No natural{{br}}occurrences]
| style="background-color:#ffffdd" | 18
|-
! N/A
! [[File:xp2_3lg42mzx10246.png|64px]]
! style="background-color:#dddddd" | xp2_3lg42mzx10246
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_3lg42mzx10246|style=tabulated}}
| [No natural{{br}}occurrences]
| 16
|-
! N/A
! [[File:xp2_062k0l51zca02.png|64px]]
! style="background-color:#dddddd" | xp2_062k0l51zca02
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_062k0l51zca02|style=tabulated}}
| [No natural{{br}}occurrences]
| 14
|-
! N/A
! [[File:xp2_350k04gj4zx642.png|64px]]
! style="background-color:#dddddd" | xp2_350k04gj4zx642
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_350k04gj4zx642|style=tabulated}}
| [No natural{{br}}occurrences]
| style="background-color:#ffffdd" | 18
|-
! N/A
! [[File:xp2_bh284gljz01.png|64px]]
! style="background-color:#dddddd" | xp2_bh284gljz01
| style="background-color:#ffffdd" | {{period|2|brief}}
| {{LinkCatagolue|xp2_bh284gljz01|style=tabulated}}
| [No natural{{br}}occurrences]
| style="background-color:#ffffdd" | 30
|}

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

== References ==
<references>
<ref name="post172725">{{LinkForumThread
|format = ref
|p = 172725
|title = Re: Thread for basic questions
|author = Matthias Merzenich
|date = February 3, 2025
}}</ref>
</references>

[[Category:Lists of patterns]]
[[Category:Lists of patterns with synthesis costs]]
[[Category:Lists of oscillators]]
__NOTOC__

List of oscillators by present frequencies

2025-09-19T15:30:02Z

TYCF: /* References */

Oscillators of each period by which cell frequency values are present. Frequency-0 cells are not counted as part of the oscillator.

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
! style="background-color:#dfdfff" | Blue
| This oscillator is the smallest possible example for the subperiod combination of this period.
|-
! style="background-color:#c6efce" | Green
| This oscillator is the smallest known example for the subperiod combination of this period.
|-
! style="background-color:#ffffdd" | Yellow
| This oscillator ''may'' be the smallest known example for the subperiod combination of this period; checking of other pattern collections may be advisable.
|-
! style="background-color:#ffaa00" | Orange
| Whether this subperiod combination is known for this period is unknown; checking of pattern collections advisable.
|-
! style="background-color:#ffc7ce" | Red
| This subperiod combination is currently unknown for this period.
|-
! style="background-color:#aaaaaa" | Gray
| This subperiod combination is provably impossible for this period.
|}

== p2 ==
{| class="wikitable"
! Freqs.
! Oscillator
! Cells
|-
! 1 only
| [[phoenix 1]]
| style="background-color:#dfdfff" | 12
|-
! 1, 2
| [[blinker]]
| style="background-color:#dfdfff" | 3
|}

== p3 ==
{| class="wikitable"
! Freqs.
! Oscillator
! Cells
|-
! 1 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="phoenix_problem_proof" />
|-
! 1,2
| [[Statorless p3]]
| style="background-color:#dfdfff" | 140<ref name="post191044" />
|-
! 1,3
| [[open cuphook]]
| style="background-color:#dfdfff" | 18<ref name="post217909" />
|-
! 1,2,3
| [[caterer]]
| style="background-color:#dfdfff" | 12
|-
! 2 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217886" />
|-
! 2,3
| [[stillater]] (stator variant)
| style="background-color:#dfdfff" | 20<ref name="post217909" />
|}

== p4 ==
{| class="wikitable"
! Freqs.
! Oscillator
! Cells
|-
! 1 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="phoenix_problem_proof" />
|-
! 1,2
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,3
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217886" />
|-
! 1,2,3
| [[mazing]]
| style="background-color:#dfdfff" | 12
|-
! 1,4
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217886" />
|-
! 1,2,4
| [[lightweight emulator]]
| style="background-color:#ffffdd" | 30
|-
! 1,3,4
| [[boss]]
| style="background-color:#ffffdd" | 42
|-
! 1,2,3,4
| [[mold]]
| style="background-color:#dfdfff" | 12
|-
! 2 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217886" />
|-
! 2,3
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post218088" />
|-
! 2,4
| {{LinkCatagolue|xp4_ckgggmld2kozx66|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 25
|-
! 2,3,4
| [[1-2-3-4]]
| style="background-color:#ffffdd" | 25
|-
! 3 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217886" />
|-
! 3,4
| {{LinkCatagolue|xp4_g8eh6kkmz9f0fio023|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 33
|}

== p5 ==
{| class="wikitable"
! Freqs.
! Oscillator
! Cells
|-
! 1 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="phoenix_problem_proof" />
|-
! 1,2
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 1,3
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 1,2,3
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,4
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 1,2,4
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,3,4
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,3,4
| [[statorless p5]]
| style="background-color:#c6efce" | 68
|-
! 1,5
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 1,2,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,3,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,3,5
| [[pseudo-barberpole]]
| style="background-color:#c6efce" | 15
|-
! 1,4,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,4,5
| [[hooks]]
| style="background-color:#c6efce" | 21
|-
! 1,3,4,5
| {{LinkCatagolue|xp5_4s0ci2r88cggz11622r896074|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 38
|-
! 1,2,3,4,5
| [[Silver's p5]]
| style="background-color:#c6efce" | 17
|-
! 2 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 2,3
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 2,4
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 2,3,4
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 2,5
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post218088" />
|-
! 2,3,5
| [[mathematician]]
| style="background-color:#ffffdd" | 35
|-
! 2,4,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 2,3,4,5
| [[Elkies' p5]]
| style="background-color:#c6efce" | 20
|-
! 3 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 3,4
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 3,5
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217944" />
|-
! 3,4,5
| {{LinkCatagolue|xp5_y1pf0c4ozwca2qdl3mpe1bq23z311321ehr2qd11zy632|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 72
|-
! 4 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|-
! 4,5
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="post217916" />
|}

== p6 ==
{| class="wikitable"
! Freqs.
! Oscillator
! Cells
! rowspan="32" |
! Freqs.
! Oscillator
! Cells
|-
! 1 only
| colspan="2" style="background-color:#aaaaaa" | '''proven impossible'''<ref name="phoenix_problem_proof" />
! 1,3,4,5,6
| {{LinkCatagolue|xp6_g88e1d248gz1259gc0t543zy111|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 34
|-
! 1,2
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 1,2,3,4,5,6
| [[blonker]]
| style="background-color:#c6efce" | 20
|-
! 1,3
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2 only
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,3
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,3
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,4
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,4
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,4
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,3,4
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,3,4
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,3,4
| [[statorless p6]]
| style="background-color:#ffffdd" | 36
! 2,3,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,4,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,3,4,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,3,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,3,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,3,6
| {{LinkCatagolue|xp6_xo44m9icz3p69klge123zw121|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 38
|-
! 1,4,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,4,6
| {{LinkCatagolue|xp6_06a84sjqajozc871|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 28
|-
! 1,2,4,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,3,4,6
| {{LinkCatagolue|xp6_gs2qb1e0u9arzxrage0fiqb871|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 52
|-
! 1,3,4,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,5,6
| {{LinkCatagolue|xp6_ok4m92sgz2eg6r8a6zx1|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 32
|-
! 1,2,3,4,5
| [[Jason's p6]]
| style="background-color:#ffffdd" | 28
! 2,3,5,6
| {{LinkCatagolue|xp6_c48c487p8a6z0bdhejpzw23|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 38
|-
! 1,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 2,3,4,5,6
| {{LinkCatagolue|xp6_kc0v1i4lb8oz11da268f032|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 40
|-
! 2,4,5,6
| {{LinkCatagolue|xp6_0g84kraak8z230fi871|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 28
! 3 only
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 3,4
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,3,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 3,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,3,6
| {{LinkCatagolue|xp6_xj9abgz25552325552z255dimid552zx6426|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 56
! 3,4,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,4,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 3,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,4,6
| {{LinkCatagolue|xp6_0c48c4o7p8a6z8e1t7p9zx121|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 38
! 3,4,6
| {{LinkCatagolue|xp6_466t186z0i6o32z3045331|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 32
|-
! 1,3,4,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 3,5,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,3,4,6
| [[p6 thumb]]
| style="background-color:#ffffdd" | 27
! 3,4,5,6
| {{LinkCatagolue|xp6_0g88c1f0b9icz349d0f8311|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 36
|-
! 1,5,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 4 only
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,5,6
| [[A for all]]
| style="background-color:#ffffdd" | 28
! 4,5
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,3,5,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
! 4,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,3,5,6
| [[unix]]
| style="background-color:#c6efce" | 16
! 4,5,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,4,5,6
| {{LinkCatagolue|xp6_o4p7871u0ooz01470743|patternname=unnamed|style=raw}}
| style="background-color:#ffffdd" | 33
! 5 only
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|-
! 1,2,4,5,6
| [[30P6.1]]
| style="background-color:#ffffdd" | 30
! 5,6
| colspan="2" style="background-color:#ffc7ce" | ''none known''
|}

{| class="wikitable" style="text-align:center;"
!rowspan=3, colspan=3|
!!!1!!!!1!!!!1!!!!1
|-
!!!!!2!!2!!!!!!2!!2
|-
!!!!!!!!!3!!3!!3!!3
|-
!!!!!
|style="background-color:#cccccc"|-
|style="background-color:#cccccc"|<ref name="phoenix_problem_proof" />
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|-
!4!!!!
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffffdd"|[[statorless p6|36]]
|-
!!!5!!
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|-
!4!!5!!
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffffdd"|[[Jason's p6|28]]
|-
!!!!!6
|style="background-color:#cccccc"|-
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_xo44m9icz3p69klge123zw121|patternname=38|style=raw}}
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_xj9abgz25552325552z255dimid552zx6426|patternname=56|style=raw}}
|-
!4!!!!6
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_06a84sjqajozc871|patternname=28|style=raw}}
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_0c48c4o7p8a6z8e1t7p9zx121|patternname=38|style=raw}}
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_466t186z0i6o32z3045331|patternname=32|style=raw}}
|style="background-color:#ffc7ce"|?
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_gs2qb1e0u9arzxrage0fiqb871|patternname=52|style=raw}}
|style="background-color:#ffffdd"|[[p6 thumb|27]]
|-
!!!5!!6
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_ok4m92sgz2eg6r8a6zx1|patternname=32|style=raw}}
|style="background-color:#ffffdd"|[[A for all|28]]
|style="background-color:#ffc7ce"|?
|style="background-color:#ffc7ce"|?
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_c48c487p8a6z0bdhejpzw23|patternname=38|style=raw}}
|style="background-color:#c6efce"|[[unix|16]]
|-
!4!!5!!6
|style="background-color:#ffc7ce"|?
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_o4p7871u0ooz01470743|patternname=33|style=raw}}
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_0g84kraak8z230fi871|patternname=28|style=raw}}
|style="background-color:#ffffdd"|[[30P6.1|30]]
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_0g88c1f0b9icz349d0f8311|patternname=36|style=raw}}
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_g88e1d248gz1259gc0t543zy111|patternname=34|style=raw}}
|style="background-color:#ffffdd"|{{LinkCatagolue|xp6_kc0v1i4lb8oz11da268f032|patternname=40|style=raw}}
|style="background-color:#c6efce"|[[blonker|20]]
|}

== References ==
<references>
<ref name="phoenix_problem_proof">{{cite web
|url = https://cp4space.hatsya.com/2024/01/20/every-finite-phoenix-has-period-2/
|title = Every finite phoenix has period 2
|work = Complex Projective 4-Space
|accessdate = January 20, 2024
}}</ref>
<ref name="post191044">{{LinkForumThread
|format = ref
|p = 191044
|title = Re: LLSSS min pop search results spam
|author = Keith Amling
|date = July 31, 2024
}}</ref>
<ref name="post217886">{{LinkForumThread
|format = ref
|p = 217886
|title = Re: amling search program principles discussion / brain dump
|author = Keith Amling
|date = September 14, 2025
}}</ref>
<ref name="post217909">{{LinkForumThread
|format = ref
|p = 217909
|title = Re: amling search program principles discussion / brain dump
|author = Keith Amling
|date = September 14, 2025
}}</ref>
<ref name="post217916">{{LinkForumThread
|format = ref
|p = 217916
|title = Re: amling search program principles discussion / brain dump
|author = Matthias Merzenich
|date = September 15, 2025
}}</ref>
<ref name="post217944">{{LinkForumThread
|format = ref
|p = 217944
|title = Re: amling search program principles discussion / brain dump
|author = Keith Amling
|date = September 15, 2025
}}</ref>
<ref name="post218088">{{LinkForumThread
|format = ref
|p = 218088
|title = Re: Oscillator Discussion Thread
|author = Matthias Merzenich
|date = September 18, 2025
}}</ref>
</references>

[[Category:Lists of patterns]]
[[Category:Lists of oscillators]]

Category:Lists of oscillators with specific period

2025-09-19T15:29:28Z

TYCF:

{{CategoryTools}}
This is a category for list pages describing oscillators with a specific period.
Templates {{tl|OscListP/HF}}, {{tl|OscListP/P}}, {{tl|OscListP/R}}, {{tl|OscListP/LoM}}, {{tl|OscListP/sparkers}}, {{tl|OscListP/volatile}} automatically add pages to this category.
{{CatRel|Oscillators with specific period}}

[[Category:Lists of patterns]]
[[Category:Lists of oscillators]]

Category:Lists of oscillators

2025-09-19T15:28:48Z

TYCF: Created page with "{{CategoryTools}} This is a category for pages containing lists of oscillatorss. See also {{CategoryLink|Pattern collections and databases|style=inline}} for pages about collections of patterns which are maintained externally (i.e. not on the LifeWiki). Category:Patterns Category:Lists of patterns"

{{CategoryTools}}
This is a category for pages containing lists of [[oscillators]]s.

See also {{CategoryLink|Pattern collections and databases|style=inline}} for pages about collections of patterns which are maintained externally (i.e. not on the LifeWiki).

[[Category:Patterns]]
[[Category:Lists of patterns]]

Leaf bug 2

2025-09-08T16:24:00Z

TYCF: /* Gun */

{{Spaceship
|name = Leaf bug 2
|pname = leafbug2
|c = 24460
|bx = 12415
|by = 6315
|dir = Orthogonal
|p = 240
|m = 240
|s = 31c/240
|z = 31c/240
|h = 16724.9
|symmetry = n
|discoverer = Gustone
|discoveryear = 2025
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 850 HEIGHT 500 ]]
|mc = true
|plaintext = true
|rle = true
}}

'''Leaf bug 2''' is a [[31c/240 orthogonal]] [[spaceship]] using the [[31c/240 Herschel-pair climber]] that was constructed on June 4, {{year|2025}}, by [[Gustone]],<ref name="post212878"/> as an improvement over the earlier [[leaf bug]]. The first version, known as '''leaf bug 2a''', had a [[population]] of 29591 cells and a {{times|15129|7988}} [[bounding box]].<ref name="post212878"/> The following form, known as '''leaf bug 2a.1''', was created on June 7 with a population of 27507 cells and a bounding box of {{times|14285|7576}}.<ref name="post212983"/> On June 14, it was reduced to '''leaf bug 2c''', with a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213261"/> On June 22, it was finally reduced to '''leaf bug 2e''', with a population of 24861, and a bounding box of {{times|13179|6698}}.<ref name="post213595"/> On June 24, a variant of leaf bug 2c was created by Gustone, with a bounding box of {{times|12927|6576}}, and a population of 24814.<ref name="post213623"/> It is the smallest [[macro-spaceship]] constructed, both in bounding box, and in population.

A comparison with the original leaf bug can be seen below:
{{gallery top}}
{{gallery item|{{ThumbEnlarge|Leafbugandleafbug2.png}}}}
{{gallery bottom}}

==Synthesis==
On June 2, 2025, a [[dirty]] [[synthesis]] of a Leaf bug 2 variant was created by Gustone, based on earlier partial synthesis of the central pair, [[track]] builder, first [[LWSS]] [[rake]], and small diamond, also by Gustone.<ref name="post213923"/><ref name="post213982"/> A clean version of the synthesis was created by [[Entity Valkyrie]] on the same day, using 2988 [[glider]]s, 644 LWSSes, and 2 [[HWSS]]es (4926 gliders in total).<ref name="post214022"/> It was then reduced by 2 gliders by [[rabbit]].<ref name="post214023"/> On June 3, 2025, a smaller synthesis was created by [[EvinZL]].<ref name="post214048"/>
{{gallery top}}
{{gallery item|[[image:Leafbug2synth.png‎|thumb|left|EvinZL's synthesis of a variant of Leaf bug 2]]}}
{{gallery item|[[image:Leafbug2EVsynth.png‎|thumb|left|Entity Valkyrie's synthesis of a variant of Leaf bug 2]]}}
{{gallery bottom}}

==Gun==
A period 131072 [[gun]] was created by [[Entity Valkyrie]] on August 14, {{year|2025}}, to fire a variant of Leaf bug 2. It was the first gun created to fire a [[31c/240 orthogonal]] spaceship. The population of the gun is 16,225,032 cells, and it has a bounding box of {{times|1,097,252|829,150}}.<ref name="post216063"/>
{|class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
|[[image:Leafbug2EVgun.png‎|400px]]
|-
|Entity Valkyrie's p131072 gun of a variant of Leaf bug 2
|}
It was later reduced by [[Hippo.69]] twice to a bounding box of {{times|124,834|117,922}} and a population of 1,054,677.
{|class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
|[[image:Leafbug2Hippo.69gun.png‎|500px]]
|-
|Hippo.69's reduced p131072 gun
|}

== Versions ==
=== Leaf bug 2a ===
'''Leaf bug 2a''', which was constructed on June 4, 2025, was designed to minimize the amount of possible points of failure.<ref name="post212878"/> It was later reduced to '''leaf bug 2a.1'''.<ref name="post212983"/>
{{EmbedViewer
|pname = leafbug2a
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2a
}}

=== Leaf bug 2a.1 ===
'''Leaf bug 2a.1''', which was constructed on June 7, 2025, decreased the population to 27507 and the bounding box to {{times|14285|7576}}.<ref name="post212983"/> It was later reduced to '''leaf bug 2c'''.<ref name="post213261"/>
{{EmbedViewer
|pname = leafbug2a1
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 500 ]]
|position = center
|caption = Leaf bug 2a.1
}}
=== Leaf bug 2c ===
'''Leaf bug 2c''', which was constructed on June 14, 2025, was the first version that broke the record of the smallest macro-spaceship by both population and bounding box. It had a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213595"/> It was later reduced to '''leaf bug 2e''', which is displayed in the infobox.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2c
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2c
}}
==== Bounding box variant ====
A bounding box-optimised variant of Leaf bug c, was created by Gustone on June 24, 2025. It had a bounding box of {{times|12927|6576}}, and a population of 24814. It was however based on Leaf bug e.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2cbb
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Bounding box-optimised variant of Leaf bug 2c
}}

== References ==
<references>
<ref name="post212878">{{LinkForumThread
|format = ref
|p = 212878
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 4, 2025
}}</ref>
<ref name="post212983">{{LinkForumThread
|format = ref
|p = 212983
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 7, 2025
}}</ref>
<ref name="post213923">{{LinkForumThread
|format = ref
|p = 213923
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = June 30, 2025
}}</ref>
<ref name="post213982">{{LinkForumThread
|format = ref
|p = 213982
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = July 2, 2025
}}</ref>
<ref name="post214022">{{LinkForumThread
|format = ref
|p = 214022
|title = Re: Small Spaceship Syntheses
|author = Entity Valkyrie 2
|date = July 2, 2025
}}</ref>
<ref name="post213261">{{LinkForumThread
|format = ref
|p = 213261
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 14, 2025
}}</ref>
<ref name="post213595">{{LinkForumThread
|format = ref
|p = 213595
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 22, 2025
}}</ref>
<ref name="post213623">{{LinkForumThread
|format = ref
|p = 213623
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 24, 2025
}}</ref>
<ref name="post214023">{{LinkForumThread
|format = ref
|p = 214023
|title = Re: Small Spaceship Syntheses
|author = rabbit
|date = July 2, 2025
}}</ref>
<ref name="post214048">{{LinkForumThread
|format = ref
|p = 214048
|title = Re: Small Spaceship Syntheses
|author = EvinZL
|date = July 3, 2025
}}</ref>
<ref name="post216063">{{LinkForumThread
|format = ref
|p = 216063
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Entity Valkyrie 2
|date = August 14, 2025
}}</ref>
</references>

== External links ==
* [https://en.wikipedia.org/wiki/Phylliidae Leaf insect] at Wikipedia

[[Category:Engineered spaceships]]
[[Category:Macro-spaceships]]

File:Leafbug2Hippo.69gun.png

2025-09-08T16:23:23Z

TYCF: TYCF uploaded a new version of File:Leafbug2Hippo.69gun.png

== Summary ==
Hippo.69's Leaf bug 2 gun from [https://conwaylife.com/forums/viewtopic.php?p=216920#p217616]

File:Leafbug2Hippo.69gun.png

2025-09-08T16:21:12Z

TYCF: Hippo.69's Leaf bug 2 gun from [https://conwaylife.com/forums/viewtopic.php?p=216920#p217616]

== Summary ==
Hippo.69's Leaf bug 2 gun from [https://conwaylife.com/forums/viewtopic.php?p=216920#p217616]

Leaf bug 2

2025-09-08T16:15:51Z

TYCF: /* Gun */

{{Spaceship
|name = Leaf bug 2
|pname = leafbug2
|c = 24460
|bx = 12415
|by = 6315
|dir = Orthogonal
|p = 240
|m = 240
|s = 31c/240
|z = 31c/240
|h = 16724.9
|symmetry = n
|discoverer = Gustone
|discoveryear = 2025
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 850 HEIGHT 500 ]]
|mc = true
|plaintext = true
|rle = true
}}

'''Leaf bug 2''' is a [[31c/240 orthogonal]] [[spaceship]] using the [[31c/240 Herschel-pair climber]] that was constructed on June 4, {{year|2025}}, by [[Gustone]],<ref name="post212878"/> as an improvement over the earlier [[leaf bug]]. The first version, known as '''leaf bug 2a''', had a [[population]] of 29591 cells and a {{times|15129|7988}} [[bounding box]].<ref name="post212878"/> The following form, known as '''leaf bug 2a.1''', was created on June 7 with a population of 27507 cells and a bounding box of {{times|14285|7576}}.<ref name="post212983"/> On June 14, it was reduced to '''leaf bug 2c''', with a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213261"/> On June 22, it was finally reduced to '''leaf bug 2e''', with a population of 24861, and a bounding box of {{times|13179|6698}}.<ref name="post213595"/> On June 24, a variant of leaf bug 2c was created by Gustone, with a bounding box of {{times|12927|6576}}, and a population of 24814.<ref name="post213623"/> It is the smallest [[macro-spaceship]] constructed, both in bounding box, and in population.

A comparison with the original leaf bug can be seen below:
{{gallery top}}
{{gallery item|{{ThumbEnlarge|Leafbugandleafbug2.png}}}}
{{gallery bottom}}

==Synthesis==
On June 2, 2025, a [[dirty]] [[synthesis]] of a Leaf bug 2 variant was created by Gustone, based on earlier partial synthesis of the central pair, [[track]] builder, first [[LWSS]] [[rake]], and small diamond, also by Gustone.<ref name="post213923"/><ref name="post213982"/> A clean version of the synthesis was created by [[Entity Valkyrie]] on the same day, using 2988 [[glider]]s, 644 LWSSes, and 2 [[HWSS]]es (4926 gliders in total).<ref name="post214022"/> It was then reduced by 2 gliders by [[rabbit]].<ref name="post214023"/> On June 3, 2025, a smaller synthesis was created by [[EvinZL]].<ref name="post214048"/>
{{gallery top}}
{{gallery item|[[image:Leafbug2synth.png‎|thumb|left|EvinZL's synthesis of a variant of Leaf bug 2]]}}
{{gallery item|[[image:Leafbug2EVsynth.png‎|thumb|left|Entity Valkyrie's synthesis of a variant of Leaf bug 2]]}}
{{gallery bottom}}

==Gun==
A period 131072 [[gun]] was created by [[Entity Valkyrie]] on August 14, {{year|2025}}, to fire a variant of Leaf bug 2. It was the first gun created to fire a [[31c/240 orthogonal]] spaceship. The population of the gun is 16,225,032 cells, and it has a bounding box of {{times|1,097,252|829,150}}.<ref name="post216063"/>
{|class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
|[[image:Leafbug2EVgun.png‎|400px]]
|-
|Entity Valkyrie's p131072 gun of a variant of Leaf bug 2
|}
It was later reduced by [[Hippo.69]] twice to a bounding box of {{times|124,834|117,922}} and a population of 1,054,677.

== Versions ==
=== Leaf bug 2a ===
'''Leaf bug 2a''', which was constructed on June 4, 2025, was designed to minimize the amount of possible points of failure.<ref name="post212878"/> It was later reduced to '''leaf bug 2a.1'''.<ref name="post212983"/>
{{EmbedViewer
|pname = leafbug2a
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2a
}}

=== Leaf bug 2a.1 ===
'''Leaf bug 2a.1''', which was constructed on June 7, 2025, decreased the population to 27507 and the bounding box to {{times|14285|7576}}.<ref name="post212983"/> It was later reduced to '''leaf bug 2c'''.<ref name="post213261"/>
{{EmbedViewer
|pname = leafbug2a1
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 500 ]]
|position = center
|caption = Leaf bug 2a.1
}}
=== Leaf bug 2c ===
'''Leaf bug 2c''', which was constructed on June 14, 2025, was the first version that broke the record of the smallest macro-spaceship by both population and bounding box. It had a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213595"/> It was later reduced to '''leaf bug 2e''', which is displayed in the infobox.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2c
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2c
}}
==== Bounding box variant ====
A bounding box-optimised variant of Leaf bug c, was created by Gustone on June 24, 2025. It had a bounding box of {{times|12927|6576}}, and a population of 24814. It was however based on Leaf bug e.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2cbb
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Bounding box-optimised variant of Leaf bug 2c
}}

== References ==
<references>
<ref name="post212878">{{LinkForumThread
|format = ref
|p = 212878
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 4, 2025
}}</ref>
<ref name="post212983">{{LinkForumThread
|format = ref
|p = 212983
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 7, 2025
}}</ref>
<ref name="post213923">{{LinkForumThread
|format = ref
|p = 213923
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = June 30, 2025
}}</ref>
<ref name="post213982">{{LinkForumThread
|format = ref
|p = 213982
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = July 2, 2025
}}</ref>
<ref name="post214022">{{LinkForumThread
|format = ref
|p = 214022
|title = Re: Small Spaceship Syntheses
|author = Entity Valkyrie 2
|date = July 2, 2025
}}</ref>
<ref name="post213261">{{LinkForumThread
|format = ref
|p = 213261
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 14, 2025
}}</ref>
<ref name="post213595">{{LinkForumThread
|format = ref
|p = 213595
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 22, 2025
}}</ref>
<ref name="post213623">{{LinkForumThread
|format = ref
|p = 213623
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 24, 2025
}}</ref>
<ref name="post214023">{{LinkForumThread
|format = ref
|p = 214023
|title = Re: Small Spaceship Syntheses
|author = rabbit
|date = July 2, 2025
}}</ref>
<ref name="post214048">{{LinkForumThread
|format = ref
|p = 214048
|title = Re: Small Spaceship Syntheses
|author = EvinZL
|date = July 3, 2025
}}</ref>
<ref name="post216063">{{LinkForumThread
|format = ref
|p = 216063
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Entity Valkyrie 2
|date = August 14, 2025
}}</ref>
</references>

== External links ==
* [https://en.wikipedia.org/wiki/Phylliidae Leaf insect] at Wikipedia

[[Category:Engineered spaceships]]
[[Category:Macro-spaceships]]

Leaf bug 2

2025-08-29T12:02:44Z

TYCF: /* Gun */

{{Spaceship
|name = Leaf bug 2
|pname = leafbug2
|c = 24460
|bx = 12415
|by = 6315
|dir = Orthogonal
|p = 240
|m = 240
|s = 31c/240
|z = 31c/240
|h = 16724.9
|symmetry = n
|discoverer = Gustone
|discoveryear = 2025
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 850 HEIGHT 500 ]]
|mc = true
|plaintext = true
|rle = true
}}

'''Leaf bug 2''' is a [[31c/240 orthogonal]] [[spaceship]] using the [[31c/240 Herschel-pair climber]] that was constructed on June 4, {{year|2025}}, by [[Gustone]],<ref name="post212878"/> as an improvement over the earlier [[leaf bug]]. The first version, known as '''leaf bug 2a''', had a [[population]] of 29591 cells and a {{times|15129|7988}} [[bounding box]].<ref name="post212878"/> The following form, known as '''leaf bug 2a.1''', was created on June 7 with a population of 27507 cells and a bounding box of {{times|14285|7576}}.<ref name="post212983"/> On June 14, it was reduced to '''leaf bug 2c''', with a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213261"/> On June 22, it was finally reduced to '''leaf bug 2e''', with a population of 24861, and a bounding box of {{times|13179|6698}}.<ref name="post213595"/> On June 24, a variant of leaf bug 2c was created by Gustone, with a bounding box of {{times|12927|6576}}, and a population of 24814.<ref name="post213623"/> It is the smallest [[macro-spaceship]] constructed, both in bounding box, and in population.

A comparison with the original leaf bug can be seen below:
{{gallery top}}
{{gallery item|{{ThumbEnlarge|Leafbugandleafbug2.png}}}}
{{gallery bottom}}

==Synthesis==
On June 2, 2025, a [[dirty]] [[synthesis]] of a Leaf bug 2 variant was created by Gustone, based on earlier partial synthesis of the central pair, [[track]] builder, first [[LWSS]] [[rake]], and small diamond, also by Gustone.<ref name="post213923"/><ref name="post213982"/> A clean version of the synthesis was created by [[Entity Valkyrie]] on the same day, using 2988 [[glider]]s, 644 LWSSes, and 2 [[HWSS]]es (4926 gliders in total).<ref name="post214022"/> It was then reduced by 2 gliders by [[rabbit]].<ref name="post214023"/> On June 3, 2025, a smaller synthesis was created by [[EvinZL]].<ref name="post214048"/>
{{gallery top}}
{{gallery item|[[image:Leafbug2synth.png‎|thumb|left|EvinZL's synthesis of a variant of Leaf bug 2]]}}
{{gallery item|[[image:Leafbug2EVsynth.png‎|thumb|left|Entity Valkyrie's synthesis of a variant of Leaf bug 2]]}}
{{gallery bottom}}

==Gun==
A period 131072 [[gun]] was created by [[Entity Valkyrie]] on August 14, {{year|2025}}, to fire a variant of Leaf bug 2. It was the first gun created to fire a [[31c/240 orthogonal]] spaceship. The population of the gun is 16,225,032 cells, and it has a bounding box of {{times|1,097,252|829,150}}.<ref name="post216063"/>
{|class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
|[[image:Leafbug2EVgun.png‎|400px]]
|-
|Entity Valkyrie's p131072 gun of a variant of Leaf bug 2
|}
It was later reduced by [[Hippo.69]] to a bounding box of {{times|124834|117922}} and a population of 1394,125.

== Versions ==
=== Leaf bug 2a ===
'''Leaf bug 2a''', which was constructed on June 4, 2025, was designed to minimize the amount of possible points of failure.<ref name="post212878"/> It was later reduced to '''leaf bug 2a.1'''.<ref name="post212983"/>
{{EmbedViewer
|pname = leafbug2a
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2a
}}

=== Leaf bug 2a.1 ===
'''Leaf bug 2a.1''', which was constructed on June 7, 2025, decreased the population to 27507 and the bounding box to {{times|14285|7576}}.<ref name="post212983"/> It was later reduced to '''leaf bug 2c'''.<ref name="post213261"/>
{{EmbedViewer
|pname = leafbug2a1
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 500 ]]
|position = center
|caption = Leaf bug 2a.1
}}
=== Leaf bug 2c ===
'''Leaf bug 2c''', which was constructed on June 14, 2025, was the first version that broke the record of the smallest macro-spaceship by both population and bounding box. It had a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213595"/> It was later reduced to '''leaf bug 2e''', which is displayed in the infobox.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2c
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2c
}}
==== Bounding box variant ====
A bounding box-optimised variant of Leaf bug c, was created by Gustone on June 24, 2025. It had a bounding box of {{times|12927|6576}}, and a population of 24814. It was however based on Leaf bug e.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2cbb
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Bounding box-optimised variant of Leaf bug 2c
}}

== References ==
<references>
<ref name="post212878">{{LinkForumThread
|format = ref
|p = 212878
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 4, 2025
}}</ref>
<ref name="post212983">{{LinkForumThread
|format = ref
|p = 212983
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 7, 2025
}}</ref>
<ref name="post213923">{{LinkForumThread
|format = ref
|p = 213923
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = June 30, 2025
}}</ref>
<ref name="post213982">{{LinkForumThread
|format = ref
|p = 213982
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = July 2, 2025
}}</ref>
<ref name="post214022">{{LinkForumThread
|format = ref
|p = 214022
|title = Re: Small Spaceship Syntheses
|author = Entity Valkyrie 2
|date = July 2, 2025
}}</ref>
<ref name="post213261">{{LinkForumThread
|format = ref
|p = 213261
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 14, 2025
}}</ref>
<ref name="post213595">{{LinkForumThread
|format = ref
|p = 213595
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 22, 2025
}}</ref>
<ref name="post213623">{{LinkForumThread
|format = ref
|p = 213623
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 24, 2025
}}</ref>
<ref name="post214023">{{LinkForumThread
|format = ref
|p = 214023
|title = Re: Small Spaceship Syntheses
|author = rabbit
|date = July 2, 2025
}}</ref>
<ref name="post214048">{{LinkForumThread
|format = ref
|p = 214048
|title = Re: Small Spaceship Syntheses
|author = EvinZL
|date = July 3, 2025
}}</ref>
<ref name="post216063">{{LinkForumThread
|format = ref
|p = 216063
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Entity Valkyrie 2
|date = August 14, 2025
}}</ref>
</references>

== External links ==
* [https://en.wikipedia.org/wiki/Phylliidae Leaf insect] at Wikipedia

[[Category:Engineered spaceships]]
[[Category:Macro-spaceships]]

Leaf bug 2 gun

2025-08-29T11:02:42Z

TYCF: Redirected page to Leaf bug 2#Gun

#REDIRECT [[Leaf bug 2#Gun]]

Centipede/Snippet

2025-08-28T13:39:10Z

TYCF:

<noinclude>{{Snippet}}</noinclude>
[[Image:Centipede.png|right]]
The '''centipede''' is a [[31c/240 orthogonal|31c/240]] [[spaceship]] completed in 2014. It was created by [[Chris Cain]] later on the same day as the [[shield bug]], and actually reuses most of its circuitry despite having a very different shape. Its smaller size is due to a more compact front-end that was built by Cain a day earlier.

It was the smallest 31c/240 spaceship until the appearance in 2016 of the [[caterloopillar]]'s [[Centipede caterloopillar|31c/240 variant]] — which was in turn supplanted by the [[silverfish]] in 2020, the [[leaf bug]] in 2024 and the [[water strider]] and [[leaf bug 2]] in 2025.

Rule:Conwaystones6

2025-08-23T12:39:32Z

TYCF: Created page with "@RULE conwaystones6 https://conwaylife.com/forums/viewtopic.php?p=5503#p6693 @TABLE n_states:3 neighborhood:Moore symmetries:permute var a={1,2} var b={a} var c={a} var d={a} var e={a} var f={a} var g={a} var h={a} var i={0,1,2} var j={i} var k={i} var L={i} var m={i} var n={i} var p={i} var q={i} var r={0,2} var s={r} var t={r} var v={r} var w={r} var x={r} var y={r} var z={r} # Birth 0,a,b,c,0,0,0,0,0,1 # Change 1,a,b,c,d,e,f,g,0,2 0,a,b,c,d,e,f,p,2,2 2,2,i,j,k,L..."

@RULE conwaystones6

https://conwaylife.com/forums/viewtopic.php?p=5503#p6693

@TABLE

n_states:3
neighborhood:Moore
symmetries:permute

var a={1,2}
var b={a}
var c={a}
var d={a}
var e={a}
var f={a}
var g={a}
var h={a}
var i={0,1,2}
var j={i}
var k={i}
var L={i}
var m={i}
var n={i}
var p={i}
var q={i}
var r={0,2}
var s={r}
var t={r}
var v={r}
var w={r}
var x={r}
var y={r}
var z={r}

# Birth
0,a,b,c,0,0,0,0,0,1

# Change
1,a,b,c,d,e,f,g,0,2
0,a,b,c,d,e,f,p,2,2
2,2,i,j,k,L,m,n,p,0

# Death
1,0,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,0
# 1,1,1,0,0,0,0,0,0,0
# 1,1,1,1,0,0,0,0,0,0
1,1,1,1,1,0,0,0,0,0
1,1,1,1,1,1,0,0,0,0
1,1,1,1,1,1,1,0,0,0
1,1,1,1,1,1,1,1,0,0
1,1,1,1,1,1,1,1,1,0

1,2,0,0,0,0,0,0,0,0
# 1,2,b,0,0,0,0,0,0,0
1,2,b,c,0,0,0,0,0,0
1,2,b,c,d,0,0,0,0,0
# 1,2,b,c,d,e,0,0,0,0
1,2,b,c,d,e,f,0,0,0
1,2,b,c,d,e,f,g,0,0
1,2,b,c,d,e,f,g,h,0

Rule:Conwaystones

2025-08-23T12:37:45Z

TYCF:

@RULE conwaystones

https://conwaylife.com/forums/viewtopic.php?p=5503#p5503

@TABLE

n_states:3
neighborhood:Moore
symmetries:permute

var a={1,2}
var b={a}
var c={a}
var d={a}
var e={a}
var f={a}
var g={a}
var h={a}
var i={0,1,2}
var j={i}
var k={i}
var L={i}
var m={i}
var n={i}
var p={i}
var q={i}

# Birth
0,a,b,c,0,0,0,0,0,1

# Change
0,a,b,c,d,e,f,g,h,2
0,a,b,c,d,e,f,p,2,2
2,2,i,j,k,L,m,n,p,1

# Death
1,0,0,0,0,0,0,0,0,0
1,a,0,0,0,0,0,0,0,0
1,a,2,0,0,0,0,0,0,0
1,a,b,2,0,0,0,0,0,0
1,a,b,c,d,0,0,0,0,0
1,a,b,c,d,e,0,0,0,0
1,a,b,c,d,e,f,0,0,0
1,a,b,c,d,e,f,g,0,0
1,a,b,c,d,e,f,g,h,0

Rule:Conwaystones

2025-08-23T12:35:19Z

TYCF: Not my rule

@RULE conwaystones

https://conwaylife.com/forums/viewtopic.php?p=5503#p5503

@TABLE

n_states:3
neighborhood:Moore
symmetries:permute

var a={1,2}
var b={a}
var c={a}
var d={a}
var e={a}
var f={a}
var g={a}
var h={a}
var i={0,1,2}
var j={i}
var k={i}
var L={i}
var m={i}
var n={i}
var p={i}
var q={i}

# Birth
0,a,b,c,0,0,0,0,0,1

# Change
0,a,b,c,d,e,f,g,h,2
0,a,b,c,d,e,n,p,2,2
2,2,i,j,k,L,m,n,p,1

# Death
1,0,0,0,0,0,0,0,0,0
1,a,0,0,0,0,0,0,0,0
1,a,2,0,0,0,0,0,0,0
1,a,b,2,0,0,0,0,0,0
1,a,b,c,d,0,0,0,0,0
1,a,b,c,d,e,0,0,0,0
1,a,b,c,d,e,f,0,0,0
1,a,b,c,d,e,f,g,0,0
1,a,b,c,d,e,f,g,h,0

User:TYCF/Draft/Draft 4

2025-08-20T08:52:48Z

TYCF:

<nowiki>{{Spaceship
|name = Mini silverfish
|pname = minisilverfish
|c = 180028
|bx = 6496
|by = 28134
|dir = Orthogonal
|p = 240
|m = 240
|s = 31c/240
|z = 31c/240
|symmetry = n
|discoverer = Gustone
|discoveryear = 2025
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|rle = true
}}</nowiki>
The '''mini silverfish''' is a [[31c/240 orthogonal]] [[spaceship]] that was constructed on June 26, {{year|2025}}, by [[Gustone]]. It is a narrow-[[track]] version of the [[silverfish]]. It was designed "for fun", and was designed to use as many backrakes as possible.

Mold

2025-08-19T14:22:59Z

TYCF:

{{Oscillator
|name = Mold
|pname = mold
|c = 12
|bx = 6
|by = 6
|fc = 24.2
|p = 4
|m = 2
|h = 7
|v = 0.63
|sv = 0.53
|symmetry = n/
|discoverer = Achim Flammenkamp
|discoveryear = 1988
|rulemin = B3/S23
|rulemax = B3678/S2378
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B3-kqry/S2ckn3ac
|isorulemax = B2n34-j5-ck678/S1e234-an5-ij6-c78
|synthesis = 5
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xp4_37bkic
|pentadecathlonid = 12P4.1
|animated = true
|viewerconfig = #C [[ TRACKLOOP 4 0 0 GPS 2 THUMBSIZE 2 ]]
}}
'''Mold''' is a {{period|4}} [[oscillator]] found by [[Achim Flammenkamp]] in {{year|1988}},<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> but not widely known until [[Dean Hickerson]] rediscovered it (and named it) in August {{year|1989}}. In terms of its minimum population of {{cells|12|text=12 cells}} it ties with [[mazing]] as the smallest {{period|4}} oscillator, but in terms of its {{times|6|6}} [[bounding box]] it wins outright. In fact, of all oscillators that fit in a {{times|6|7}} box it is the only one with period greater than 2.

It emits [[corner dot]]s, which can support other [[pattern]]s such as the 45-cell [[p32 honey farm hassler]], [[four molds hassling eight blocks]], [[traffic circle]], [[butter]],<ref name="post71795" /> {{LinkCatagolue|xp8_y2osq596zg8keey0g844owg88gz1221x698y1ee521zy4cikb73|patternname=an unnamed p8 oscillator|style=raw}}.

== Construction ==
Mold is known to be [[Glider synthesis|constructible]] with {{gliders|5|text=5 gliders}}.<ref name="catagolue_object" /> Several known alternate syntheses are available in [[Mark Niemiec's database]].<ref name="niemiec" />

{|style="margin:auto;width:300px;"
|{{EmbedViewer
|rle = x = 36, y = 20, rule = B3/S23
20bo$18b2o$2bo16b2o8bo$obo24b2o$b2o20bo4b2o$23bobo$23b2o2$31b2o$30bo2b
o$30bobo2bo$31bo$32b2obo$34bo4$27bo$26b2o$26bobo!
|viewerconfig = #C [[ THEME Book ZOOM 10 AUTOSTART GPS 8 T 0 PAUSE 3 T 20 PAUSE 1 T 36 PAUSE 1 T 49 PAUSE 2 LOOP 50 ]]
|position = center
|caption = A 5G synthesis<ref name="niemiec" />
}}
|-
|{{EmbedViewer
|rle = x = 51, y = 24, rule = B3/S23
16b2o28b2o$15bo2bo26bo2bo$15bobo2bo8bo15bobo2bo$16bo3bo9bo6bobo6bo$20b
o7b3o6b2o8b2obo$17bo20bo10bo$18b2o15$b2o$obo$2bo!
|viewerconfig = #C [[ THEME Book ZOOM 10 AUTOSTART GPS 8 T 0 PAUSE 3 T 59 PAUSE 1 T 104 PAUSE 2 LOOP 105 ]]
|position = center
|caption = A three-glider conversion of [[jam]] to mold<ref name="niemiec" />
}}
|}

== Occurrence ==
Mold is the twelfth [[List of common oscillators|most common]] naturally-occurring oscillator in [[Achim Flammenkamp's census]], being less common than the [[spark coil]] but more common than the [[quadpole tie ship]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> On [[Catagolue]], it is the most common period 4 oscillator, being more common than [[mazing]].<ref>{{citeCatagolue|page=census/b3s23/C1|title=Census|accessdate=October 27, 2018}}</ref>

The first natural mold [[stator]] variant, cis-mold on [[dock]], occurred in May {{year|2015}}.<ref name="post19438" />

The [[octo3obj database]] contains one collision with a mold in the ash.{{refn|The headerless RLE of the collision is {{headerlessRLE|8b2o$8b2o3$6bo$3o2bobo$5bobo$6bo2$4b2o$4bobo$4bo!}}}} There are two [[three-glider collision]]s in the [[octo3g database]] with a mold in the ash; both collisions converge to the same sequence before the mold forms.{{refn|Headerless RLEs of the collisions are {{headerlessRLE|bo$2bo$3o96$133bo$131b2o$132b2o$128bo$129bo$127b3o!}} and {{headerlessRLE|133bo$131b2o$132b2o$128bo$129bo$127b3o137$3o$2bo$bo!}}}}

== See also ==
* [[Mold on fumarole]]
* [[Jam]]
* [[Blocker]]
* [[Butter]]

== References ==
<references>
<ref name="catagolue_object">{{LinkCatagolue|xp4_37bkic|style=nobullet}}</ref>
<ref name="niemiec">{{LinkNiemiec|p4.htm#p4-12|The 2 twelve-bit period 4 oscillators|rle=12/12md.rle|nobullet=nobullet}}</ref>
<ref name="post71795">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 71795
|author = Entity Valkyrie
|date = February 26, 2019
}}</ref>
<ref name="post19438">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 19438
|author = praosylen
|date = May 7, 2015
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_m.htm#mold}}
* {{LinkCatagolue|xp4_37bkic}}
* {{LinkPentadecathlonObject|12P4.1}}

{{Sparker|p=4|type=dot|strength=moderate}}

__NOTOC__

Nontrivial

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#REDIRECT [[Non-trivial]]

File:Xp6 0go8273uoe03b28z16l1h10hts044ktb4zx2660303672.png

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File:Seveneleven.png

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Waveguide

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TYCF: Removed redirect to Superstring#Waveguides

'''Waveguide''' may either refer to:
*A '''waveguide''', tracks between which a finite section of a [[superstring]] is stabilized.
*A moving [[fencepost]] for wickes, sometimes referred to as a '''waveguide'''.
[[Category:Disambiguation pages]]

P131072 leaf bug gun

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#REDIRECT [[Leaf bug 2#Gun]]

[[Category:Patterns found by Entity Valkyrie]]
[[Category:Guns]]
[[Category:Patterns discovered by pseudonymous users]]
[[Category:Guns with period 131072]]
[[Category:Patterns with between 10,000,000 and 99,999,999 cells]]
[[Category:Patterns found in 2025]]
[[Category:Patterns]]
[[Category:Infinite growth]]
[[Category:Isotropically endemic patterns]]
[[Category:Outer-totalistically endemic patterns]]
[[Category:Linear growth]]

P131072 leaf bug gun

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#REDIRECT [[Leaf bug 2#Gun]]
[[Category:Patterns found by Entity Valkyrie]]
[[Category:Guns]]
[[Category:Patterns discovered by pseudonymous users]]
[[Category:Guns with period 131072]]
[[Category:Patterns with between 10,000,000 and 99,999,999 cells]]
[[Category:Patterns found in 2025]]
[[Category:Patterns]]
[[Category:Infinite growth]]
[[Category:Isotropically endemic patterns]]
[[Category:Outer-totalistically endemic patterns]]
[[Category:Linear growth]]

Category:Guns with period 131072

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P131072 leaf bug gun

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TYCF: Redirected page to Leaf bug 2#Gun

#REDIRECT [[Leaf bug 2#Gun]]
[[Category:Patterns found by Entity Valkyrie]]
[[Category:Guns]]
[[Category:Patterns discovered by pseudonymous users]]
[[Category:Guns with period 131072]]
[[Category:Patterns with between 10,000,000 and 99,999,999 cells]]
[[Category:Patterns found in 2025]]
[[Category:Patterns]]
[[Category:Infinite growth]]
[[Category:Isotropically endemic patterns]]
[[Category:Outer-totalistically endemic patterns]]
[[Category:Linear growth]]

Category:Guns with an unknown number of barrels

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Leaf bug 2

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TYCF: /* References */

{{Spaceship
|name = Leaf bug 2
|pname = leafbug2
|c = 24460
|bx = 12415
|by = 6315
|dir = Orthogonal
|p = 240
|m = 240
|s = 31c/240
|z = 31c/240
|h = 16724.9
|symmetry = n
|discoverer = Gustone
|discoveryear = 2025
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 850 HEIGHT 500 ]]
|mc = true
|plaintext = true
|rle = true
}}

'''Leaf bug 2''' is a [[31c/240 orthogonal]] [[spaceship]] using the [[31c/240 Herschel-pair climber]] that was constructed on June 4, {{year|2025}}, by [[Gustone]],<ref name="post212878"/> as an improvement over the earlier [[leaf bug]]. The first version, known as '''leaf bug 2a''', had a [[population]] of 29591 cells and a {{times|15129|7988}} [[bounding box]].<ref name="post212878"/> The following form, known as '''leaf bug 2a.1''', was created on June 7 with a population of 27507 cells and a bounding box of {{times|14285|7576}}.<ref name="post212983"/> On June 14, it was reduced to '''leaf bug 2c''', with a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213261"/> On June 22, it was finally reduced to '''leaf bug 2e''', with a population of 24861, and a bounding box of {{times|13179|6698}}.<ref name="post213595"/> On June 24, a variant of leaf bug 2c was created by Gustone, with a bounding box of {{times|12927|6576}}, and a population of 24814.<ref name="post213623"/> It is the smallest [[macro-spaceship]] constructed, both in bounding box, and in population.

A comparison with the original leaf bug can be seen below:
{{gallery top}}
{{gallery item|{{ThumbEnlarge|Leafbugandleafbug2.png}}}}
{{gallery bottom}}

==Synthesis==
On June 2, 2025, a [[dirty]] [[synthesis]] of a Leaf bug 2 variant was created by Gustone, based on earlier partial synthesis of the central pair, [[track]] builder, first [[LWSS]] [[rake]], and small diamond, also by Gustone.<ref name="post213923"/><ref name="post213982"/> A clean version of the synthesis was created by [[Entity Valkyrie]] on the same day, using 2988 [[glider]]s, 644 LWSSes, and 2 [[HWSS]]es (4926 gliders in total).<ref name="post214022"/> It was then reduced by 2 gliders by [[rabbit]].<ref name="post214023"/> On June 3, 2025, a smaller synthesis was created by [[EvinZL]].<ref name="post214048"/>
{{gallery top}}
{{gallery item|[[image:Leafbug2synth.png‎|thumb|left|EvinZL's synthesis of a variant of Leaf bug 2]]}}
{{gallery item|[[image:Leafbug2EVsynth.png‎|thumb|left|Entity Valkyrie's synthesis of a variant of Leaf bug 2]]}}
{{gallery bottom}}

==Gun==
A period 131072 [[gun]] was created by [[Entity Valkyrie]] on August 14, {{year|2025}}, to fire a variant of Leaf bug 2. It was the first gun created to fire a [[31c/240 orthogonal]] spaceship. The population of the gun is 16,225,032 cells, and it has a bounding box of {{times|1,097,252|829,150}}.<ref name="post216063"/>
{|class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
|[[image:Leafbug2EVgun.png‎|400px]]
|-
|Entity Valkyrie's p131072 gun of a variant of Leaf bug 2
|}

== Versions ==
=== Leaf bug 2a ===
'''Leaf bug 2a''', which was constructed on June 4, 2025, was designed to minimize the amount of possible points of failure.<ref name="post212878"/> It was later reduced to '''leaf bug 2a.1'''.<ref name="post212983"/>
{{EmbedViewer
|pname = leafbug2a
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2a
}}

=== Leaf bug 2a.1 ===
'''Leaf bug 2a.1''', which was constructed on June 7, 2025, decreased the population to 27507 and the bounding box to {{times|14285|7576}}.<ref name="post212983"/> It was later reduced to '''leaf bug 2c'''.<ref name="post213261"/>
{{EmbedViewer
|pname = leafbug2a1
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 500 ]]
|position = center
|caption = Leaf bug 2a.1
}}
=== Leaf bug 2c ===
'''Leaf bug 2c''', which was constructed on June 14, 2025, was the first version that broke the record of the smallest macro-spaceship by both population and bounding box. It had a population of 26571, and a bounding box of {{times|13339|7107}}.<ref name="post213595"/> It was later reduced to '''leaf bug 2e''', which is displayed in the infobox.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2c
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Leaf bug 2c
}}
==== Bounding box variant ====
A bounding box-optimised variant of Leaf bug c, was created by Gustone on June 24, 2025. It had a bounding box of {{times|12927|6576}}, and a population of 24814. It was however based on Leaf bug e.<ref name="post213623"/>
{{EmbedViewer
|pname = leafbug2cbb
|viewerconfig = [[ MAXGRIDSIZE 14 AUTOSTART OFF WIDTH 1000 HEIGHT 600 ]]
|position = center
|caption = Bounding box-optimised variant of Leaf bug 2c
}}

== References ==
<references>
<ref name="post212878">{{LinkForumThread
|format = ref
|p = 212878
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 4, 2025
}}</ref>
<ref name="post212983">{{LinkForumThread
|format = ref
|p = 212983
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 7, 2025
}}</ref>
<ref name="post213923">{{LinkForumThread
|format = ref
|p = 213923
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = June 30, 2025
}}</ref>
<ref name="post213982">{{LinkForumThread
|format = ref
|p = 213982
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Gustone
|date = July 2, 2025
}}</ref>
<ref name="post214022">{{LinkForumThread
|format = ref
|p = 214022
|title = Re: Small Spaceship Syntheses
|author = Entity Valkyrie 2
|date = July 2, 2025
}}</ref>
<ref name="post213261">{{LinkForumThread
|format = ref
|p = 213261
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 14, 2025
}}</ref>
<ref name="post213595">{{LinkForumThread
|format = ref
|p = 213595
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 22, 2025
}}</ref>
<ref name="post213623">{{LinkForumThread
|format = ref
|p = 213623
|title = Re: 31c/240 caterpillar working notes
|author = Gustone
|date = June 24, 2025
}}</ref>
<ref name="post214023">{{LinkForumThread
|format = ref
|p = 214023
|title = Re: Small Spaceship Syntheses
|author = rabbit
|date = July 2, 2025
}}</ref>
<ref name="post214048">{{LinkForumThread
|format = ref
|p = 214048
|title = Re: Small Spaceship Syntheses
|author = EvinZL
|date = July 3, 2025
}}</ref>
<ref name="post216063">{{LinkForumThread
|format = ref
|p = 216063
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Entity Valkyrie 2
|date = August 14, 2025
}}</ref>
</references>

== External links ==
* [https://en.wikipedia.org/wiki/Phylliidae Leaf insect] at Wikipedia

[[Category:Engineered spaceships]]
[[Category:Macro-spaceships]]

File:72p4h1v0.png

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File:66p5h2v0.png

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File:66p10h4v0.png

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44P5H2V0

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TYCF:

{{Spaceship
|name = 44P5H2V0
|pname = 44p5h2v0
|c = 44
|bx = 15
|by = 10
|dir = Orthogonal
|p = 5
|m = 5
|s = 2c/5
|z = 2c/5
|h = 47.2
|symmetry = -c
|discoverer = Dean Hickerson
|discoveryear = 1991
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-ey/S2-n3-c
|isorulemax = B34ety5aei6en7c8/S234ctz5acery6-k7e8
|synthesis = 23
|plaintext = true
|rle = true
|animated = true
|viewerconfig = #C [[ GPS 5 TRACKLOOP 5 0 -2/5 THUMBSIZE 2 ]]
|apgcode = xq5_0sg3pnxnp3gsz4s01tve0evt10s4
|pentadecathlonid = 44P5H2V0.1
|eppsteinid = 13491
}}
'''44P5H2V0''' is an unnamed [[2c/5 orthogonal]] [[spaceship]] discovered by [[Dean Hickerson]] on July 23, {{year|1991}},<ref>David Bell's article, "[[Spaceships in Conway's Life]] (Part 6)"</ref> being the first 2c/5 spaceship to be found. [[Robert Wainwright]] and [[David Bell]] then found some small [[tagalong]]s that allowed the creation of arbitrarily large 2c/5 spaceships. These were the only known 2c/5 spaceships until the discovery of [[70P5H2V0]] by [[Hartmut Holzwart]] on December 5, {{year|1992}}.<ref>David Bell's article, "[[Spaceships in Conway's Life]] (Addendum 1)"</ref> It can also be attached to a tagalong to create [[66P10H4V0]].

On February 1, 2024, Keith Amling proved that it is the unique smallest period-5, symmetric, odd-width 2c/5 spaceship in terms of its minimum population of 44 cells.<ref name="post177064" />

Goldtiger997 found a {{gliders|131}} [[Glider synthesis|synthesis]] for 44P5H2V0 on August 29, {{year|2020}}.<ref name="post103142" /> [[Tanner Jacobi]] improved the synthesis to {{gliders|41|text=41 gliders}} the same day,<ref name="message749388079902752778" /> and [[iNoMed]] improved it to {{gliders|39|text=39 gliders}} in March {{year|2021}}.<ref name="post127210" /> ENORMOUS_NAME and [[iNoMed]] constructed a 44P5H2V0 [[gun]] on October 30, 2020.<ref name="post108483" />

It is currently the only {{periodS|5}} spaceship to have occurred [[semi-natural]]ly, having first appeared in a [[soup]] found using [[Charity Engine]] on April 2, {{year|2022}}.<ref name="post143703" /> Using the recipe from this soup, a {{gliders|24}} synthesis was found by [[Goldtiger997]] and [[iNoMed]].<ref name="post143704" />

== Tagalongs ==
[[File:44p5h2v0 tagalongs.png|thumb|center|Tagalongs shown in green]]

Its backend's [[obo! spark]] is capable of supporting tagalongs that have only a single cell in their leading edge in the iteration before forwards growth.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = 44p5h2v0tagalongs
|viewerconfig = #C [[ THUMBSIZE 2 WIDTH 560 HEIGHT 650 ZOOM 8 ANGLE 90 GPS 5 AUTOSTART TRACKLOOP 5 -2/5 0 ]]
|position = center
|caption = Some tagalongs for pairs of 44P5H2V0 (first two found by Robert Wainwright, third found by David Bell)
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 115, y = 233, rule = B3/S23
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|viewerconfig = #C [[ THUMBSIZE 2 WIDTH 1120 HEIGHT 560 ZOOM 4 ANGLE 90 GPS 5 AUTOSTART TRACKLOOP 5 -2/5 0 ]]
|position = center
|caption = Some of the smallest symmetrical tagalongs for 44P5H2V0 from [[Catagolue]]'s {{cata|census/b3s23/ikpx2_stdin/xq5|<tt>ikpx2_stdin</tt> census}}
|style = width:300px;
}}}}
{{gallery bottom}}

== See also ==
* [[30P5H2V0]]
* [[60P5H2V0]]

== References ==
<references>
<ref name="message749388079902752778">{{CiteDiscord
|author = Tanner Jacobi
|date = August 29, 2020
|channel = cgol
|id = 749388079902752778
}}</ref>
<ref name="post103142">{{LinkForumThread
|format = ref
|p = 103142
|title = Re: Small Spaceship Syntheses
|author = Goldtiger997
|date = August 29, 2020
}}</ref>
<ref name="post108483">{{LinkForumThread
|format = ref
|p = 108483
|title = Re: Gun Discussion Thread
|author = ENORMOUS_NAME
|date = October 30, 2020
}}</ref>
<ref name="post127210">{{LinkForumThread
|format = ref
|p = 127210
|title = Re: Small Spaceship Syntheses
|author = iNoMed
|date = March 28, 2021
}}</ref>
<ref name="post143703">{{LinkForumThread
|format = ref
|p = 143703
|title = Re: Soup search results
|author = David Raucci
|date = April 2, 2022
}}</ref>
<ref name="post143704">{{LinkForumThread
|format = ref
|p = 143704
|title = Re: Small Spaceship Syntheses
|author = iNoMed
|date = April 2, 2022
}}</ref>
<ref name="post177064">{{LinkForumThread
|format = ref
|f = 2
|t = 6224
|p = 177064
|title = Re: LLSSS min pop search results spam
|author = Keith Amling
|date = February 1, 2024
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_1.htm#a-44p5h2v0}}

* {{LinkEppsteinRule|rule=b3s23|rulename=Life (B3/S23)|archivedate=20160309235206}} 
* {{LinkCatagolue|xq5_0sg3pnxnp3gsz4s01tve0evt10s4}}
* {{LinkPentadecathlonObject|44P5H2V0.1}}

[[Category:Unnamed periodic objects]]
{{seminatural}}

__NOTOC__

File:61p4h1v0.png

2025-08-15T15:46:46Z

TYCF:

File:57p5h2v0.png

2025-08-15T15:46:15Z

TYCF:

File:51p5h2v0.2.png

2025-08-15T15:45:50Z

TYCF: