Rules with temporal or spatial dynamics

[LuveelVoom]

Recently, heav posted a rule in the Conwaylife discord based on an idea I had: Life, but if a cell (live or dead) has 5 neighbors 15 generations in the future from the current state, it becomes alive in the current state. Here’s the ruletable:

message 3.txt

(6.21 KiB) Downloaded 99 times

This is unbearably laggy in lifeviewer. I recommend running it in Golly.
Also, other than long^n boats being a FTL fuse and gliders having a dot ahead of them, there's not much interesting behavior. Neither does B3/S23 +B4-15g have much interesting behavior. Are there any time travel rules with interesting behavior?
This thread is for exploring rules with temporal dynamics (like rules with odd time travel, update order, or stuff like that) or spacial dynamics (for example, a rule where whenever 8 live cells surround a dead cell it toggles between being a life or seeds vacuum cell, or other stuff like that) or rules with both (for example, life with regions where things update twice as fast.)

[confocaloid]

[...] Life, but if a cell (live or dead) has 5 neighbors 15 generations in the future from the current state, it becomes alive in the current state. [...]

What is the actual definition of the evolution rules? The above fails to answer the question "how this works", in part due to the paradoxes when a cell becoming alive prevents the condition that would "cause" it to become alive.

edit: possibly relevant: viewtopic.php?p=198896#p198896

[...] (for example, life with regions where things update twice as fast.)

[LuveelVoom]

[...] Life, but if a cell (live or dead) has 5 neighbors 15 generations in the future from the current state, it becomes alive in the current state. [...]

What is the actual definition of the evolution rules? The above fails to answer the question "how this works", in part due to the paradoxes when a cell becoming alive prevents the condition that would "cause" it to become alive.

Each generation is run forward 15 steps and all cells with 5 live neighbors are brought to life in the next generation. There are no paradoxes, but the future is changeable. There may be race conditions.

[LuveelVoom]

edit: possibly relevant: viewtopic.php?p=198896#p198896

[...] (for example, life with regions where things update twice as fast.)

This would be great, except the slow region expands uncontrollably. Can you provide a rule table where it’s stable?

[breaker's glider gun]

life P2's acting as usual, and an interesting preloaf oscillator

Code: Select all

x = 15, y = 18, rule = LifeB5+7g
4$7.A$6.2A4.A$6.2A4.A$6.A5.A6$5.A$4.A.A$7.A$4.A.A!

[LuveelVoom]

I have just realized that time travel life emulator suffers from the fatal flaw of not simulating time travel for the future generations, making it inaccurate. If it was accurate, long^n boat would be a infinityc/(finite number for startup) fuse. . This problem seems insurmountable with ruletables, though maybe a script could do it.

Anyway, what about future travel life? For example, a cell with b8 could remain in the timeline (an intangible marker state) for 7 generations, then reappear. This doesn't have cool things like paradox oscillators or antigardens (patterns which to exist must have existed at t= infinity), but might still be interesting.

[confocaloid]

This is a different idea, but maybe related or interesting. Some time ago I wondered about "reversibility" of oscillators. Take any oscillator from Conway's Life, for example the caterer or the jam or the mold or the pulsar etc. Is there a cellular automaton supporting an oscillator with the same period and the exact same phases, except with the phases cycled in the reverse order?

[LuveelVoom]

This is a different idea, but maybe related or interesting. Some time ago I wondered about "reversibility" of oscillators. Take any oscillator from Conway's Life, for example the caterer or the jam or the mold or the pulsar etc. Is there a cellular automaton supporting an oscillator with the same period and the exact same phases, except with the phases cycled in the reverse order?

The blinker from life has its reverse supported in B3/S23.

Anyway, this is an interesting question. I would think it would be fairly easy to construct a ruletable for any given oscillator and very difficult to construct one for all oscillators or find a r1 2 state moore rule for any high period (> 30 or so) oscillator.

[LuveelVoom]

Dual Life (eight cell for transfer, majority loses):

dual_life_8_majority.rule

(3.38 KiB) Downloaded 72 times

This rule has two life universes, between which cointeraction only occurs when at least 8 cells are present total around a center cell. The minority universe gets the cell. Ties send a cell to both universes. This is… spatial dynamics?

[unname4798]

Dual Life (eight cell for transfer, majority loses): dual_life_8_majority.rule

This rule has two life universes, between which cointeraction only occurs when at least 8 cells are present total around a center cell. The minority universe gets the cell. Ties send a cell to both universes. This is… spatial dynamics?

Please provide the ruletable, so I wouldn't have to download.

[pifricted]

Dual Life

Please provide the ruletable, so I wouldn't have to download.

Code: Select all

@RULE dual_life_8_majority


      A   B
0 =>  0   0
1 =>  1   0
2 =>  0   1
3 =>  1   1

@COLORS
0 0 0 0
1 255 0 0
2 0 0 255
3 255 0 255

@TABLE
neighborhood: Moore
symmetries: permute
n_states: 4

# any
var x1 = {0,1,2,3}
var x2 = x1
var x3 = x1
var x4 = x1
var x5 = x1
var x6 = x1
var x7 = x1
var x8 = x1

var s1 = {1,2,3}
var s2 = s1
var s3 = s1
var s4 = s1
var s5 = s1
var s6 = s1
var s7 = s1
var s8 = s1


# alive in a
var a1 = {1,3}
var a2 = a1
var a3 = a1
var a4 = a1
var a5 = a1
var a6 = a1
var a7 = a1
var a8 = a1

# alive in b
var b1 = {2,3}
var b2 = b1
var b3 = b1
var b4 = b1
var b5 = b1
var b6 = b1
var b7 = b1
var b8 = b1

# dead in a
var c1 = {0,2}
var c2 = c1
var c3 = c1
var c4 = c1
var c5 = c1
var c6 = c1
var c7 = c1
var c8 = c1

# dead in b
var d1 = {0,1}
var d2 = d1
var d3 = d1
var d4 = d1
var d5 = d1
var d6 = d1
var d7 = d1
var d8 = d1

# survival/birth special case
x1 3  3  3  3  3  3  3  3  3
x1 3  3  3  3  3  3  1  2  3
x1 3  3  3  3  1  1  2  2  3
x1 3  3  1  1  1  2  2  2  3
x1 1  1  1  1  2  2  2  2  3

c1 2  2  2  2  b5 s6 s7 s8 1
d1 1  1  1  1  a5 s6 s7 s8 2
c1 2  2  2  b4 s5 s6 3  3  1
d1 1  1  1  a4 s5 s6 3  3  2
c1 2  2  b3 s4 3  3  3  3  1
d1 1  1  a3 s4 3  3  3  3  2
c1 2 b3  3  3  3  3  3  3  1
d1 1 a3  3  3  3  3  3  3  2



# 3rd state irrelevant to above

# state 3 cases

# 2 dies overpop and 1 dies overpop
3 a1 a2 a3 a4 b5 b6 b7 b8 0
3 3  a2 a3 a4 b5 b6 b7 x8 0
3 3  3  a3 a4 b5 b6 x7 x8 0
3 3  3  3  a4 b5 x6 x7 x8 0
3 3  3  3  3  x5 x6 x7 x8 0

# 2 dies overpop and 1 survives
3 a1 a2 b3 b4 b5 b6 x7 x8 1
3 3  a2 b3 b4 b5 x6 x7 x8 1
3 3  3  b3 b4 x5 x6 x7 x8 1

# 2 dies overpop and 1 dies underpop
3 b1 b2 b3 b4 x5 x6 x7 x8 0

# 2 survives and 1 dies overpop
3 b1 b2 a3 a4 a5 a6 x7 x8 2
3 3  b2 a3 a4 a5 x6 x7 x8 2
3 3  3  a3 a4 x5 x6 x7 x8 2

# 2 survives and 1 survives
3 a1 a2 b3 b4 x5 x6 x7 x8 3
3 3  a2 b3 x4 x5 x6 x7 x8 3
3 3  3  x3 x4 x5 x6 x7 x8 3

# 2 survives and 1 dies underpop
3 b1 b2 x3 x4 x5 x6 x7 x8 2

# 2 dies underpop and 1 dies overpop
3 a1 a2 a3 a4 x5 x6 x7 x8 0

# 2 dies underpop and 1 survives
3 a1 a2 x3 x4 x5 x6 x7 x8 1

# 2 dies underpop and 1 dies underpop
3 x1 x2 x3 x4 x5 x6 x7 x8 0

# overpopulation death:

# 1 dies and 2 is born
1 2  2  2  1  1  1  1  d8 2
1 2  2  3  1  1  1  d7 d8 2
1 2  3  3  1  1  d6 d7 d8 2
1 3  3  3  1  d5 d6 d7 d8 2

# 2 dies and 1 is born
2 1  1  1  2  2  2  2  c8 1
2 1  1  3  2  2  2  c7 c8 1
2 1  3  3  2  2  c6 c7 c8 1
2 3  3  3  2  c5 c6 c7 c8 1

# death without birth
1 a1 a2 a3 a4 x5 x6 x7 x8 0
2 b1 b2 b3 b4 x5 x6 x7 x8 0

# survival

# 1 survives and 2 is born
1 2  2  2  1  1  d6 d7 d8 3
1 2  2  3  1  d5 d6 d7 d8 3
1 2  3  3  d4 d5 d6 d7 d8 3
1 3  3  3  d4 d5 d6 d7 d8 3

# 2 survives and 1 is born
2 1  1  1  2  2  c6 c7 c8 3
2 1  1  3  2  c5 c6 c7 c8 3
2 1  3  3  c4 c5 c6 c7 c8 3
2 3  3  3  c4 c5 c6 c7 c8 3

# survival without birth
1 a1 a2 x3 x4 x5 x6 x7 x8 1
2 b1 b2 x3 x4 x5 x6 x7 x8 2

# underpopulation death

# 1 dies and 2 is born
1 2  2  2  d4 d5 d6 d7 d8 2
1 3  2  2  d4 d5 d6 d7 d8 2

# 2 dies and 1 is born
2 1  1  1  c4 c5 c6 c7 c8 1
2 3  1  1  c4 c5 c6 c7 c8 1

# death without birth
1 x1 x2 x3 x4 x5 x6 x7 x8 0
2 x1 x2 x3 x4 x5 x6 x7 x8 0
3 x1 x2 x3 x4 x5 x6 x7 x8 0

# birth in state 0

0 3  3  3  0  0  0  0  0  3
0 3  3  1  2  0  0  0  0  3
0 3  1  1  2  2  0  0  0  3
0 1  1  1  2  2  2  0  0  3

0 a1 a2 a3 c4 c5 c6 c7 c8 1
0 b1 b2 b3 d4 d5 d6 d7 d8 2

# Table by Moosey, idea and stable form by LuveelVoom

[confocaloid]

The two large oscillators in the top row have the same phases as cross and cross 2 respectively, except the phases are cycled in the reverse order.
The small object on the right is a period-102 mod-51 orthogonal c/51 spaceship. The three other spaceships are a p3 orthogonal c/3, a p4 orthogonal c/2, and a p4 diagonal c/4.

Code: Select all

#C [[ GRID THEME MCell ]]
x = 55, y = 54, rule = R3,C0,S26-40,42-51,143-168,172,249,260-273,275-285,290,377-379,381-393,395-402,405,494-497,499-510,512-519,522,611-614,616-636,706,729-753,823,835,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,B39-51,67,156-168,273-276,278-285,390,393-402,495,497-498,507-509,511-519,614-615,624-626,628-636,741-753,858-870,975-987,1092-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,NW757500000075757501017501017500010D0D0D010000750D000D750000010D0D0D01007501017501017575750000007575
4b4o16b4ob4o$4bo2bo16bo2bobo2bo$2b3o2b3o12b3o2b3o2b3o$2bo6bo12bo11bo$
2bo6bo12bo11bo$2b3o2b3o12b3o7b3o$4bo2bo16bo7bo$4b4o14b3o7b3o17b2o$22bo
11bo19bo$22bo11bo18bo$22b3o2b3o2b3o17b3o$24bo2bobo2bo19bobo$24b4ob4o
19b2o6$2b2o8b3o$2b2o13$3bobo18b2o2bo15bo$3bobo19b3o17bo$2b2ob2o19bo16b
3o$3b3o11$3b2o$4bo2$2o$2o$10b2o$9bobo$10bo!

[...] "reversibility" of oscillators. Take any oscillator from Conway's Life, for example the caterer or the jam or the mold or the pulsar etc. Is there a cellular automaton supporting an oscillator with the same period and the exact same phases, except with the phases cycled in the reverse order?

[...] I would think it would be fairly easy to construct a ruletable for any given oscillator and very difficult to construct one for all oscillators or find a r1 2 state moore rule for any high period (> 30 or so) oscillator.

In addition to the "reversed cross and reversed cross 2" example above, here are some more examples:

"reversed glider"

Code: Select all

x = 46, y = 33, rule = R3,C0,S10-19,30-39,50-60,75-79,135,137-144,155-164,175-184,200-204,256,260-269,281-289,300-309,325-329,385-394,405-414,425-434,450-454,510-519,530-539,550-559,575-579,635-644,655-664,675-684,700-704,760-769,780-789,800-809,825-829,885-894,905-914,925-934,950-954,1010-1019,1030-1039,1050-1059,1075-1079,1135-1144,1155-1164,1175-1184,1200-1204,1260-1269,1280-1289,1300-1309,1325-1329,1385-1394,1405-1414,1425-1434,1450-1454,1510-1519,1530-1539,1550-1559,1575-1579,1635-1644,1655-1664,1675-1684,1700-1704,1760-1769,1780-1789,1800-1809,1825-1829,1885-1894,1905-1914,1925-1934,1950-1954,2010-2019,2030-2039,2050-2059,2075-2079,B15-19,35,37-39,55-59,65,75-79,140-144,160-164,176,182-184,200-204,256,265-269,285-289,305-309,325-329,390-394,410-414,430-434,450-454,515-519,535-539,555-559,575-579,640-644,660-664,680-684,700-704,765-769,785-789,805-809,825-829,890-894,910-914,930-934,950-954,1015-1019,1035-1039,1055-1059,1075-1079,1140-1144,1160-1164,1180-1184,1200-1204,1265-1269,1285-1289,1305-1309,1325-1329,1390-1394,1410-1414,1430-1434,1450-1454,1515-1519,1535-1539,1555-1559,1575-1579,1640-1644,1660-1664,1680-1684,1700-1704,1765-1769,1785-1789,1805-1809,1825-1829,1890-1894,1910-1914,1930-1934,1950-1954,2015-2019,2035-2039,2055-2059,2075-2079,NW00007D007D000000007D017D00007D7D1905197D7D000105000501007D7D1905197D7D00007D017D000000007D007D0000
b2o8b2o10bo8b2o9b2o$o2bo7bobo8bobo7bobo7bo2bo$o2bo8bo10bo9b2o8b2o$b2o
7$11bo10b2o9b2o$11bo10b2o9b2o$11bo23b2o$35b2o13$8bo$9bo$7b3o$33b2o$32b
ob2o$33bo$34bo!

"reversed pulsar"

Code: Select all

x = 59, y = 22, rule = R3,C0,S129,134,250-254,256-280,283-384,386-428,430-499,506,533,682,B57,278,375,377-404,406-430,432-499,525,NW000100190001000101010101010100017D7D7D010019017D007D011900017D7D7D01000101010101010100010019000100
2b3o3b3o14b2o8bo7b2o$25b2o7bobo6bobo$o4bobo4bo22bo8bo$o4bobo4bo$o4bobo
4bo$2b3o3b3o2$2b3o3b3o$o4bobo4bo12b2o9b2o7b2o8b2obo$o4bobo4bo12bobo7bo
2bo6bo2bo6bob2o$o4bobo4bo13b2o8b2o9b2o2$2b3o3b3o6$35b2o$35b2o11bo$25b
3o9b2o10bo$37b2o8b3o!

"reversed pulsar quadrant"

Code: Select all

x = 58, y = 22, rule = R3,C0,S10-11,30-55,137,155-280,385-400,415-530,555-581,B35-36,55,160,281,311,381,535-536,NW7D7D0001007D7D7D00000000007D0000051905000001001900190001000005190500007D00000000007D7D7D0001007D7D
2b3o19b2o8bo7b2o$24b2o7bobo6bobo$o4bo28bo8bo$o3bobo$o2bo2bo$2bo3b2o$3b
3o$5bo$24b2o9b2o7b2o8b2obo$24bobo7bo2bo6bo2bo6bob2o$25b2o8b2o9b2o8$34b
2o$34b2o11bo$24b3o9b2o10bo$36b2o8b3o!

"reversed pulsar and reversed quasar"

Code: Select all

x = 177, y = 89, rule = R3,C0,S18-27,135-144,252-369,388,496-614,624-642,751-856,879,985-1557,B27,172,281-282,381-398,495,613,615,623-624,939,NW09750175017509750075757500750175090909750175750900097575017509090975017500757575007509750175017509
2o39b2o17b2o$2o18b3o17bo2bo16bobo$41b2o18b2o18$bo18b2o18b2o18b2obo$obo
17bobo17bo2bo16bob2o$bo19bo20b2o6$142b3o3b3o2$140bo4bobo4bo$140bo4bobo
4bo$140bo4bobo4bo$142b3o3b3o2$140b3o7b3o$79b3o3b3o46b3o2bo4bo3bo4bo2b
3o$139bo4bo3bo4bo$77bo4bobo4bo42bo4bobo4bo3bo4bobo4bo$77bo4bobo4bo42bo
4bo17bo4bo$77bo4bobo4bo42bo4bo2b3o7b3o2bo4bo$79b3o3b3o46b3o19b3o2$77b
3o7b3o42b3o23b3o$32b3o3b3o30b3o2bo4bo3bo4bo2b3o30b3o2bo4bo19bo4bo2b3o$
76bo4bo3bo4bo40bo4bo19bo4bo$30bo4bobo4bo26bo4bobo4bo3bo4bobo4bo26bo4bo
bo4bo19bo4bobo4bo$30bo4bobo4bo26bo4bo17bo4bo26bo4bo33bo4bo$30bo4bobo4b
o26bo4bo2b3o7b3o2bo4bo26bo4bo2b3o23b3o2bo4bo$32b3o3b3o30b3o19b3o30b3o
35b3o2$30b3o7b3o26b3o23b3o26b3o39b3o$2b3o3b3o13b3o2bo4bo3bo4bo2b3o14b
3o2bo4bo19bo4bo2b3o14b3o2bo4bo35bo4bo2b3o$29bo4bo3bo4bo24bo4bo19bo4bo
24bo4bo35bo4bo$o4bobo4bo9bo4bobo4bo3bo4bobo4bo10bo4bobo4bo19bo4bobo4bo
10bo4bobo4bo35bo4bobo4bo$o4bobo4bo9bo4bo17bo4bo10bo4bo33bo4bo10bo4bo
49bo4bo$o4bobo4bo9bo4bo2b3o7b3o2bo4bo10bo4bo2b3o23b3o2bo4bo10bo4bo2b3o
39b3o2bo4bo$2b3o3b3o13b3o19b3o14b3o35b3o14b3o51b3o2$2b3o3b3o13b3o19b3o
14b3o35b3o14b3o51b3o$o4bobo4bo9bo4bo2b3o7b3o2bo4bo10bo4bo2b3o23b3o2bo
4bo10bo4bo2b3o39b3o2bo4bo$o4bobo4bo9bo4bo17bo4bo10bo4bo33bo4bo10bo4bo
49bo4bo$o4bobo4bo9bo4bobo4bo3bo4bobo4bo10bo4bobo4bo19bo4bobo4bo10bo4bo
bo4bo35bo4bobo4bo$29bo4bo3bo4bo24bo4bo19bo4bo24bo4bo35bo4bo$2b3o3b3o
13b3o2bo4bo3bo4bo2b3o14b3o2bo4bo19bo4bo2b3o14b3o2bo4bo35bo4bo2b3o$30b
3o7b3o26b3o23b3o26b3o39b3o2$32b3o3b3o30b3o19b3o30b3o35b3o$30bo4bobo4bo
26bo4bo2b3o7b3o2bo4bo26bo4bo2b3o23b3o2bo4bo$30bo4bobo4bo26bo4bo17bo4bo
26bo4bo33bo4bo$30bo4bobo4bo26bo4bobo4bo3bo4bobo4bo26bo4bobo4bo19bo4bob
o4bo$76bo4bo3bo4bo40bo4bo19bo4bo$32b3o3b3o30b3o2bo4bo3bo4bo2b3o30b3o2b
o4bo19bo4bo2b3o$77b3o7b3o42b3o23b3o2$79b3o3b3o46b3o19b3o$77bo4bobo4bo
42bo4bo2b3o7b3o2bo4bo$77bo4bobo4bo42bo4bo17bo4bo$77bo4bobo4bo42bo4bobo
4bo3bo4bobo4bo$139bo4bo3bo4bo$79b3o3b3o46b3o2bo4bo3bo4bo2b3o$140b3o7b
3o2$142b3o3b3o$140bo4bobo4bo$140bo4bobo4bo$140bo4bobo4bo2$142b3o3b3o!

"reversed bracket pulsar and reversed bracket quasar"

Code: Select all

x = 125, y = 55, rule = R3,C0,S50-176,280-287,456-511,532-708,1081-1157,B27,77,132,181,280,407,513,575,657,700,786-801,902,926,1026,1042,1155,NW7D7D7D007D7D7D7D007D057D007D7D7D0119017D7D000519001905007D7D0119017D7D7D007D057D007D7D7D7D007D7D7D
95bo3bo$95bo3bo$95bo3bo$94b2o3b2o$93bobo3bobo$90b5o5b5o3$5b2o18b3o$5b
2o83b5o5b5o$40bo3bo20bo19bo3bobo11bobo3bo$40bo3bo21bo18bo3b2o13b2o3bo$
40bo3bo19b3o18bo3bo15bo3bo$39b2o3b2o38b2o3bo15bo3b2o$38bobo3bobo36bobo
3bo15bo3bobo$35b5o5b5o30b5o25b5o4$35b5o5b5o30b5o25b5o$5bo3bo20bo3bobo
11bobo3bo20bo3bobo31bobo3bo$5bo3bo20bo3b2o13b2o3bo20bo3b2o33b2o3bo$5bo
3bo20bo3bo15bo3bo20bo3bo35bo3bo$4b2o3b2o18b2o3bo15bo3b2o18b2o3bo35bo3b
2o$3bobo3bobo16bobo3bo15bo3bobo16bobo3bo35bo3bobo$5o5b5o10b5o25b5o10b
5o45b5o4$5o5b5o10b5o25b5o10b5o45b5o$3bobo3bobo16bobo3bo15bo3bobo16bobo
3bo35bo3bobo$4b2o3b2o18b2o3bo15bo3b2o18b2o3bo35bo3b2o$5bo3bo20bo3bo15b
o3bo20bo3bo35bo3bo$5bo3bo20bo3b2o13b2o3bo20bo3b2o33b2o3bo$5bo3bo20bo3b
obo11bobo3bo20bo3bobo31bobo3bo$35b5o5b5o30b5o25b5o4$35b5o5b5o30b5o25b
5o$38bobo3bobo36bobo3bo15bo3bobo$39b2o3b2o38b2o3bo15bo3b2o$40bo3bo40bo
3bo15bo3bo$40bo3bo40bo3b2o13b2o3bo$40bo3bo40bo3bobo11bobo3bo$90b5o5b5o
4$90b5o5b5o$93bobo3bobo$94b2o3b2o$95bo3bo$95bo3bo$95bo3bo!

"reversed jam"

Code: Select all

x = 28, y = 7, rule = R3,C0,S12-236,254,265-371,380-469,479,488,490,596-607,623,715-722,741-848,B120,129,246,256-272,373,381,505,597,730-748,NW75097500750975097575097575097575010101757500090100010900757501010175750975750975750975097500750975
25b2o$24bo2bo$22bo2bobo$22bo3bo$bo20bo$2bo22bo$3o20b2o!

Are these interesting?

[confocaloid]

The two large oscillators in the top row have the same phases as cross and cross 2 respectively, except the phases are cycled in the reverse order. [...]
[...]

In addition to the example below (which I found today), what are other known stable reflectors with the same property that the CA rules can be changed so that both the reflected spaceship and the reflector will evolve the other way round (i.e. the reflecting reaction can be reversed by changing the CA rules), restricting to two-state isotropic cellular automata supported in Golly?

A "snek" and a "snek" reflector:

Code: Select all

#C p48 snek loop, made from four stable snek reflectors,
#C with snek track length 240 and five circulating sneks,
#C in a two-state isotropic CA defined using the following weighted neighbourhood:
#C 01 01 -- 01 -- 01 01
#C 01 01 69 69 69 01 01
#C -- 69 69 15 69 69 --
#C 01 69 15 -- 15 69 01
#C -- 69 69 15 69 69 --
#C 01 01 69 69 69 01 01
#C 01 01 -- 01 -- 01 01
#C
#C [[ GRID THEME Caterer ]]
x = 67, y = 67, rule = R3,C0,S148-153,232-236,253-259,342-468,569-906,B22-26,132-152,236,258,362,448,574,NW01010001000101010169696901010069691569690001691500156901006969156969000101696969010101010001000101
4o59b4o$4o59b4o$2o63b2o$2o19bob23o19b2o6$3bo59bo$3bo$3bo59bo$3bo59bo$
3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59b
o$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo
59bo$3bo59bo$63bo$3bo59bo24$3bo59bo$3bo$3bo59bo$3bo59bo$3bo59bo$3bo59b
o$2ob17obo23b19ob2o$2o63b2o$4o59b4o$4o59b4o!

A "reverse snek" and a "reverse snek" reflector:

Code: Select all

#C p48 reverse snek loop, made from four stable reverse snek reflectors,
#C with reverse snek track length 240 and five circulating reverse sneks,
#C in a two-state isotropic CA defined using the following weighted neighbourhood:
#C 7D 7D -- 7D -- 7D 7D
#C 7D 7D -- 05 -- 7D 7D
#C -- -- 01 19 01 -- --
#C 7D 05 19 -- 19 05 7D
#C -- -- 01 19 01 -- --
#C 7D 7D -- 05 -- 7D 7D
#C 7D 7D -- 7D -- 7D 7D
#C
#C [[ GRID THEME Caterer ]]
x = 67, y = 67, rule = R3,C0,S113,155,180-363,405,430-582,651-655,676-686,780,801-811,915,930-1070,B155-180,405,430,651-655,676-680,780,805,915-940,NW7D7D007D007D7D7D7D0005007D7D000001190100007D05190019057D000001190100007D7D0005007D7D7D7D007D007D7D
4o59b4o$4o59b4o$2o63b2o$2o19bob23o19b2o6$3bo59bo$3bo$3bo59bo$3bo59bo$
3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59b
o$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo
59bo$3bo59bo$63bo$3bo59bo24$3bo59bo$3bo$3bo59bo$3bo59bo$3bo59bo$3bo59b
o$2ob17obo23b19ob2o$2o63b2o$4o59b4o$4o59b4o!

Here are

• an extensible snek,
• period-256 snek loop, with stable snek reflectors,

[...]

[unname4798]

...

Code: Select all

#C p48 reverse snek loop, made from four stable reverse snek reflectors,
#C with reverse snek track length 240 and five circulating reverse sneks,
#C in a two-state isotropic CA defined using the following weighted neighbourhood:
#C 7D 7D -- 7D -- 7D 7D
#C 7D 7D -- 05 -- 7D 7D
#C -- -- 01 19 01 -- --
#C 7D 05 19 -- 19 05 7D
#C -- -- 01 19 01 -- --
#C 7D 7D -- 05 -- 7D 7D
#C 7D 7D -- 7D -- 7D 7D
#C
#C [[ GRID THEME Caterer ]]
x = 67, y = 67, rule = R3,C0,S113,155,180-363,405,430-582,651-655,676-686,780,801-811,915,930-1070,B155-180,405,430,651-655,676-680,780,805,915-940,NW7D7D007D007D7D7D7D0005007D7D000001190100007D05190019057D000001190100007D7D0005007D7D7D7D007D007D7D
4o59b4o$4o59b4o$2o63b2o$2o19bob23o19b2o6$3bo59bo$3bo$3bo59bo$3bo59bo$
3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59b
o$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo59bo$3bo
59bo$3bo59bo$63bo$3bo59bo24$3bo59bo$3bo$3bo59bo$3bo59bo$3bo59bo$3bo59b
o$2ob17obo23b19ob2o$2o63b2o$4o59b4o$4o59b4o!

...

I think I should name this rule "Extensible Factorio".
It has a linestretcher:

Code: Select all

#R R3,C0,S113,155,180-363,405,430-582,651-655,676-686,780,801-811,915,930-1070,B155-180,405,430,651-655,676-680,780,805,915-940,NW7D7D007D007D7D7D7D0005007D7D000001190100007D05190019057D000001190100007D7D0005007D7D7D7D007D007D7D
6o!

And a growing spaceship (back end c/10):

Code: Select all

#R R3,C0,S113,155,180-363,405,430-582,651-655,676-686,780,801-811,915,930-1070,B155-180,405,430,651-655,676-680,780,805,915-940,NW7D7D007D007D7D7D7D0005007D7D000001190100007D05190019057D000001190100007D7D0005007D7D7D7D007D007D7D
4o2$4bo!

[confocaloid]

[...] I think I should name this rule "Extensible Factorio".

I think it's worth noting that the subspace is tremendously large. The evolutionary sequence is preserved in 2^5088 cellular automata that can be defined with the same weighted neighbourhood, I believe:

optional birth conditions (2526): 3-4, 6-24, 28-124, 128-129, 131-149, 153-154, 156-179, 181-187, 190-249, 253-254, 256-274, 278-280, 283-285, 287-374, 379, 381-384, 386-399, 404, 408-410, 413-415, 418-425, 429, 431-435, 438-441, 443-499, 503-504, 508-509, 511-524, 528-529, 533-535, 537-540, 543-560, 563-565, 568-624, 627-629, 631-634, 636-649, 652-654, 657-675, 677-679, 681-749, 751-754, 756-759, 761-764, 766-774, 776-779, 782-804, 806-874, 876-879, 881-884, 886-889, 891-909, 911-914, 916-939, 941-999, 1001-1124, 1126-2624
optional survival conditions (2562): 0-112, 114-129, 131-154, 156-159, 161-179, 181-184, 186-207, 209-211, 213-237, 239-304, 306-309, 312-331, 334-336, 338-362, 364-379, 381-404, 406-409, 411-429, 432-434, 437-456, 459-461, 463-487, 489-554, 557-559, 562-581, 583-625, 627-629, 631-650, 652-654, 657-659, 661-675, 677-679, 682-684, 687-754, 756-779, 782-784, 786-800, 802-804, 807-809, 812-889, 891-914, 916-919, 921-929, 932-934, 936-939, 941-944, 946-1055, 1057-1064, 1066-1069, 1071-2624

Once all of those are investigated, one could change the weighted neighbourhood.

That means you might not want to name this particular representative.

[unname4798]

But that's the minrule.

[confocaloid]

But that's the minrule.

Not really - if all optional living conditions are omitted, the definition becomes longer and the soups become more boring:

Code: Select all

#C [[ GRID THEME Caterer RANDOMIZE RANDWIDTH 80 RANDHEIGHT 60 RANDFILL 25 ]]
x = 51, y = 27, rule = R3,C0,S113,155,180,185,208,212,238,305,310-311,332-333,337,363,405,430-431,435-436,457-458,462,488,555-556,560-561,582,651,655,676,680-681,685-686,780,801,805-806,810-811,915,930-931,935,940,945,1056,1065,1070,B155,180,405,430,651,655,676,680,780,805,915,940,NW7D7D007D007D7D7D7D0005007D7D000001190100007D05190019057D000001190100007D7D0005007D7D7D7D007D007D7D
4o43b4o$4o43b4o$2o47b2o$2o11bob23o11b2o20$2o47b2o$2o47b2o$4o43b4o$4o
43b4o!