Forums for Conway's Game of Life
https://conwaylife.com/forums/
Ok, thanks. Apparently 3 cells can be infinitely high, and the highest for 2 cells is this:yujh wrote: September 11th, 2025, 11:12 am This thread provides way better examples for 2 cell and 3 cell oscillators
viewtopic.php?f=11&t=3248
Code: Select all
x = 3, y = 1, rule = B2aei3-aijy4-actyz5cjny6-en7c8/S01e3r4acejtw5einy6cn7e8
obo!
Code: Select all
x = 83, y = 37, rule = B38/S23Investigator
18.2A43.2A$16.3A.A41.A.3A$15.A4.A41.A4.A$16.3A.A.2A.2A29.2A.2A.A.3A$18.
A.2A.A.A31.A.A.2A.A$6.2A13.A.A2.A29.A2.A.A13.2A$5.A2.A6.2A4.2A.A.A29.
A.A.2A4.2A6.A2.A$5.2A.A6.A.A3.2A.A.2A27.2A.A.2A3.A.A6.A.2A$6.A.2A7.A4.
A.A3.AE2A19.2AEA3.A.A4.A7.2A.A$.A2.A.A10.2A3.A.2A.2AE.A19.A.E2A.2A.A3.
2A10.A.A2.A$.5A2.3A10.A2.A5.EA.A15.A.AE5.A2.A10.3A2.5A$6.2A2.A12.A2.2A
.AE.2A15.2A.EA.2A2.A12.A2.2A$3.3A2.A2.A8.2A.A2.A.2A23.2A.A2.A.2A8.A2.
A2.3A$3.A2.A4.A8.2A39.2A8.A4.A2.A$4.2A3.A2.A.3A4.A16.2A3.2A16.A4.3A.A
2.A3.2A$13.4A49.4A$4.2A5.2A22.A3.A3.A3.A22.2A5.2A$4.A.A26.2A4.A3.A4.2A
26.A.A$7.A24.2A.A2.2A3.2A2.A.2A24.A$.2A2.2A.A23.3A3.2A3.2A3.3A23.A.2A
2.2A$A5.A.A7.3A8.2A3.A3.A.3A.3A.A3.A3.2A8.3A7.A.A5.A$A4.A2.2A5.A3.A5.
A4.A2.2A13.2A2.A4.A5.A3.A5.2A2.A4.A$.2A.2A2.A6.2A.2A5.A4.A21.A4.A5.2A
.2A6.A2.2A.2A$8.2A.2A12.A4.A2.2A13.2A2.A4.A12.2A.2A$.2A.2A2.A18.2A3.A
3.A.3A.3A.A3.A3.2A18.A2.2A.2A$A4.A2.2A22.3A3.2A3.2A3.3A22.2A2.A4.A$A5.
A.A23.2A.A2.2A3.2A2.A.2A23.A.A5.A$.2A2.2A.A24.2A4.A3.A4.2A24.A.2A2.2A
$7.A27.A3.A3.A3.A27.A$4.A.A69.A.A$4.2A32.2A3.2A32.2A$19.2A41.2A$15.2A
2.2A41.2A2.2A$14.A.A15.2A15.2A15.A.A$14.A16.A.A15.A.A16.A$13.2A16.A19.
A16.2A$30.2A19.2A!
Code: Select all
x = 163, y = 77, rule = B38/S23
29.2A3.2A91.2A3.2A$29.2A3.2A9.2A69.2A9.2A3.2A$29.2A3.2A9.A71.A9.2A3.2A
$29.2A3.2A6.2A.A71.A.2A6.2A3.2A$25.2A3.2A.2A3.2A.A.A.2A69.2A.A.A.2A3.
2A.2A3.2A$25.A2.A.A3.A.A2.A.A.A.A2.2A63.2A2.A.A.A.A2.A.A3.A.A2.A$26.A
.2A5.2A.A3.A4.2A.A61.A.2A4.A3.A.2A5.2A.A$27.A9.A7.A4.A61.A4.A7.A9.A$28.
4A.4A6.A.A.3A63.3A.A.A6.4A.4A$30.A.A.A6.5A.A67.A.5A6.A.A.A$41.2A.A73.
A.2A$31.3A5.2A.A77.A.2A5.3A$39.A.A79.A.A$20.A19.A81.A19.A$20.3A117.3A
$23.A8.2A6.2A6.2A3.A55.A3.2A6.2A6.2A8.A$22.2A16.2A7.A2.A.A53.A.A2.A7.
2A16.2A$46.3A3.A.A53.A.A3.3A$46.A4.2A.2A51.2A.2A4.A$13.2A8.2A7.2A.2A6.
A11.A51.A11.A6.2A.2A7.2A8.2A$14.A8.2A7.A3.A5.A3.A4.4A53.4A4.A3.A5.A3.
A7.2A8.A$14.A.A16.3A6.A5.A2.A59.A2.A5.A6.3A16.A.A$15.2A2.2A12.3A6.A2.
5A2.A57.A2.5A2.A6.3A12.2A2.2A$19.2A29.3A3.2A47.2A3.3A29.2A$4.2A37.2A.
4A6.A.A45.A.A6.4A.2A37.2A$4.A.A39.A4.2A8.2A37.2A8.2A4.A39.A.A$7.A35.2A
3.3A.A6.2A.A37.A.2A6.A.3A3.2A35.A$5.2A.A35.A.A.A9.2A43.2A9.A.A.A35.A.
2A$4A2.A.A34.A2.2A67.2A2.A34.A.A2.4A$6A2.2A9.3A21.2A73.2A21.3A9.2A2.6A
$4.A3.A2.A6.A3.A33.2A47.2A33.A3.A6.A2.A3.A$9.A.A6.2A3.A9.A22.A2.3A39.
3A2.A22.A9.A3.2A6.A.A$4.A3.A2.A12.A6.A.A19.2A.A.A.A41.A.A.A.2A19.A.A6.
A12.A2.A3.A$6A2.2A11.A2.A7.2A20.A.A.A.A41.A.A.A.A20.2A7.A2.A11.2A2.6A
$4A2.A.A15.A27.A2.A.A47.A.A2.A27.A15.A.A2.4A$5.2A.A9.2A3.A28.2A.A.3A43.
3A.A.2A28.A3.2A9.A.2A$7.A10.A3.A30.A.A.A.A43.A.A.A.A30.A3.A10.A$4.A.A
12.3A31.A.2A.2A5.2A29.2A5.2A.2A.A31.3A12.A.A$4.2A5.2A41.A3.2A4.A2.A27.
A2.A4.2A3.A41.2A5.2A$11.A.A.2A33.2A3.2A2.A.2A2.A.A27.A.A2.2A.A2.2A3.2A
33.2A.A.A$4.2A3.2A.A2.2A32.A2.A3.A.A3.2A.2A29.2A.2A3.A.A3.A2.A32.2A2.
A.2A3.2A$3.A2.A2.3A8.3A27.2A2.A.A3.A3.A33.A3.A3.A.A2.2A27.3A8.3A2.A2.
A$3.3A2.2A9.A4.A.A.2A13.A8.4A.A3.2A.A33.A.2A3.A.4A8.A13.2A.A.A4.A9.2A
2.3A$9.2A13.A.2A.A14.2A4.2A3.A.A5.A35.A5.A.A3.2A4.2A14.A.2A.A13.2A$.5A
.3A12.A20.2A5.A2.2A3.2A2.A37.A2.2A3.2A2.A5.2A20.A12.3A.5A$.A2.A12.2A.
A.A.2A.2A22.2A2.2A2.3A39.3A2.2A2.2A22.2A.2A.A.A.2A12.A2.A$6.A.2A7.A4.
A.A3.A24.A4.2A43.2A4.A24.A3.A.A4.A7.2A.A$5.2A.A6.A.A3.2A.A.2A25.A.4A.
A41.A.4A.A25.2A.A.2A3.A.A6.A.2A$5.A2.A6.2A5.A.A.A27.A3.A.2A8.2A19.2A8.
2A.A3.A27.A.A.A5.2A6.A2.A$6.2A15.A2.A30.2A12.A19.A12.2A30.A2.A15.2A$18.
A.2A.A.A32.A.A.A8.A.A15.A.A8.A.A.A32.A.A.2A.A$16.3A.A.2A.2A31.A4.A8.2A
15.2A8.A4.A31.2A.2A.A.3A$15.A4.A42.A35.A42.A4.A$16.3A.A34.A3.4A37.4A3.
A34.A.3A$18.2A28.A7.A21.2A3.2A21.A7.A28.2A$48.3A3.3A49.3A3.3A$51.A23.
A3.A3.A3.A23.A$50.2A21.2A4.A3.A4.2A21.2A$72.2A.A2.2A3.2A2.A.2A$72.3A3.
2A3.2A3.3A$51.2A3.3A8.2A3.A3.A.3A.3A.A3.A3.2A8.3A3.2A$51.2A2.A3.A5.A4.
A2.2A13.2A2.A4.A5.A3.A2.2A$55.2A.2A5.A4.A21.A4.A5.2A.2A$65.A4.A2.2A13.
2A2.A4.A$67.2A3.A3.A.3A.3A.A3.A3.2A$72.3A3.2A3.2A3.3A$72.2A.A2.2A3.2A
2.A.2A$73.2A4.A3.A4.2A$75.A3.A3.A3.A2$78.2A3.2A$59.2A41.2A$55.2A2.2A41.
2A2.2A$54.A.A15.2A15.2A15.A.A$54.A16.A.A15.A.A16.A$53.2A16.A19.A16.2A
$70.2A19.2A!
First one I found:WhiteHawk wrote: September 12th, 2025, 3:56 pm Is there a way to weld these SL stabilizations together without eternally off cells? The result would be another p45 in Pedestrian Life, a rule which has a great dearth of them.
Code: Select all
x = 83, y = 37, rule = B38/S23Investigator 18.2A43.2A$16.3A.A41.A.3A$15.A4.A41.A4.A$16.3A.A.2A.2A29.2A.2A.A.3A$18. A.2A.A.A31.A.A.2A.A$6.2A13.A.A2.A29.A2.A.A13.2A$5.A2.A6.2A4.2A.A.A29. A.A.2A4.2A6.A2.A$5.2A.A6.A.A3.2A.A.2A27.2A.A.2A3.A.A6.A.2A$6.A.2A7.A4. A.A3.AE2A19.2AEA3.A.A4.A7.2A.A$.A2.A.A10.2A3.A.2A.2AE.A19.A.E2A.2A.A3. 2A10.A.A2.A$.5A2.3A10.A2.A5.EA.A15.A.AE5.A2.A10.3A2.5A$6.2A2.A12.A2.2A .AE.2A15.2A.EA.2A2.A12.A2.2A$3.3A2.A2.A8.2A.A2.A.2A23.2A.A2.A.2A8.A2. A2.3A$3.A2.A4.A8.2A39.2A8.A4.A2.A$4.2A3.A2.A.3A4.A16.2A3.2A16.A4.3A.A 2.A3.2A$13.4A49.4A$4.2A5.2A22.A3.A3.A3.A22.2A5.2A$4.A.A26.2A4.A3.A4.2A 26.A.A$7.A24.2A.A2.2A3.2A2.A.2A24.A$.2A2.2A.A23.3A3.2A3.2A3.3A23.A.2A 2.2A$A5.A.A7.3A8.2A3.A3.A.3A.3A.A3.A3.2A8.3A7.A.A5.A$A4.A2.2A5.A3.A5. A4.A2.2A13.2A2.A4.A5.A3.A5.2A2.A4.A$.2A.2A2.A6.2A.2A5.A4.A21.A4.A5.2A .2A6.A2.2A.2A$8.2A.2A12.A4.A2.2A13.2A2.A4.A12.2A.2A$.2A.2A2.A18.2A3.A 3.A.3A.3A.A3.A3.2A18.A2.2A.2A$A4.A2.2A22.3A3.2A3.2A3.3A22.2A2.A4.A$A5. A.A23.2A.A2.2A3.2A2.A.2A23.A.A5.A$.2A2.2A.A24.2A4.A3.A4.2A24.A.2A2.2A $7.A27.A3.A3.A3.A27.A$4.A.A69.A.A$4.2A32.2A3.2A32.2A$19.2A41.2A$15.2A 2.2A41.2A2.2A$14.A.A15.2A15.2A15.A.A$14.A16.A.A15.A.A16.A$13.2A16.A19. A16.2A$30.2A19.2A!
Code: Select all
x = 83, y = 37, rule = B38/S23
18b2o43b2o$16b3obo41bob3o$15bo4bo41bo4bo$16b3obob2ob2o29b2ob2obob3o$
18bob2obobo31bobob2obo$6b2o13bobo2bo4b2o17b2o4bo2bobo13b2o$5bo2bo6b2o
4b2obobo3bobo17bobo3bobob2o4b2o6bo2bo$5b2obo6bobo3b2obob2o2bo21bo2b2ob
ob2o3bobo6bob2o$6bob2o7bo4bobo3bob2o19b2obo3bobo4bo7b2obo$bo2bobo10b2o
3bob2ob2o2bo19bo2b2ob2obo3b2o10bobo2bo$b5o2b3o10bo2bo4bobobo15bobobo4b
o2bo10b3o2b5o$6b2o2bo12bo2b2obo2b2o15b2o2bob2o2bo12bo2b2o$3b3o2bo2bo8b
2obo2bob2o23b2obo2bob2o8bo2bo2b3o$3bo2bo4bo8b2o39b2o8bo4bo2bo$4b2o3bo
2bob3o4bo16b2o3b2o16bo4b3obo2bo3b2o$13b4o49b4o$4b2o5b2o22bo3bo3bo3bo
22b2o5b2o$4bobo26b2o4bo3bo4b2o26bobo$7bo24b2obo2b2o3b2o2bob2o24bo$b2o
2b2obo23b3o3b2o3b2o3b3o23bob2o2b2o$o5bobo7b3o8b2o3bo3bob3ob3obo3bo3b2o
8b3o7bobo5bo$o4bo2b2o5bo3bo5bo4bo2b2o13b2o2bo4bo5bo3bo5b2o2bo4bo$b2ob
2o2bo6b2ob2o5bo4bo21bo4bo5b2ob2o6bo2b2ob2o$8b2ob2o12bo4bo2b2o13b2o2bo
4bo12b2ob2o$b2ob2o2bo18b2o3bo3bob3ob3obo3bo3b2o18bo2b2ob2o$o4bo2b2o22b
3o3b2o3b2o3b3o22b2o2bo4bo$o5bobo23b2obo2b2o3b2o2bob2o23bobo5bo$b2o2b2o
bo24b2o4bo3bo4b2o24bob2o2b2o$7bo27bo3bo3bo3bo27bo$4bobo69bobo$4b2o32b
2o3b2o32b2o$19b2o41b2o$15b2o2b2o41b2o2b2o$14bobo15b2o15b2o15bobo$14bo
16bobo15bobo16bo$13b2o16bo19bo16b2o$30b2o19b2o!Code: Select all
x = 5, y = 5, rule = B3/S23
2$b2o$bo!Code: Select all
x = 22, y = 22, rule = B3-a/S23
3bo5bo2b5o$bo9b2o8bo$o3bo2bo8bo2bobo$o2bo2b2o2b4o$2obobo7bo3bob2o$9bo
7bo2bo$2bobo3bo5b2o$o2bob3o3bo5bo2bo$3bo5b2o3b2obob3o$7bo2bo4b3o$b2o
10bobobobo$bobobob2o6bobo2bo$bobo4bo2bo5b3obo$ob2o6b2o$b2o5bobobobo5bo
$b2obo7bo$3bo5bobo7bo$b2o4bobo5bobo2bo$2b2o8bo$2bo4bob3o5bo$2bo4b2o$2o
3b5o7bo!
There are so many it's not really interesting to keep a record. For example, this example one cell thick spaceship works in 2^75 INT rules:
Code: Select all
x = 4, y = 1, rule = B2cin3aiy6c/S02ac3i
2obo!It's impossible in an isotropic 2-state rule because spaceships can't have rotational symmetry. However, there are B1e rules where a dot turns into four spaceships or a four-directional gun.wildmyron wrote: September 20th, 2025, 8:08 am If you are specifically interested in rules with a one cell spaceship, then I don't know of any, and I suspect there are none.
I don't know what happened there, but what I was trying to say was:hotdogPi wrote: September 20th, 2025, 8:19 amIt's impossible in an isotropic 2-state rule because spaceships can't have rotational symmetry. However, there are B1e rules where a dot turns into four spaceships or a four-directional gun.wildmyron wrote: September 20th, 2025, 8:08 am If you are specifically interested in rules with a one cell spaceship, then I don't know of any, and I suspect there are none.
Is it possible for it to turn into a eight-directional gun?hotdogPi wrote: September 20th, 2025, 8:19 am It's impossible in an isotropic 2-state rule because spaceships can't have rotational symmetry. However, there are B1e rules where a dot turns into four spaceships or a four-directional gun.
What was special enough about my rule that I didn't get a reply like that?confocaloid wrote: May 2nd, 2025, 4:27 am In general, avoid creating a separate thread for one specific cellular automaton. Posting in an already-existing thread is almost always a better idea. (Related discussion)
What happens in practice is that most such threads are abandoned, cluttering the forums, with only a few replies. There are way too many CA of the same type to investigate each of them in depth. There are already forum threads created specifically to collect posts about any CA, avoiding the need to start lots of threads for non-notable topics. For specific CA, posting in one of those existing threads is almost always a better choice, compared to starting a new thread:
viewtopic.php?f=11&t=803 Thread For Your Unrecognised CA
viewtopic.php?f=11&t=1971 Miscellaneous Discoveries in Other Cellular Automata
(Also, you need already existing evidence of interest from other people, before starting a new thread.confocaloid wrote: May 1st, 2025, 2:23 pm
- Most cellular automata that were explored by at least one people are interesting enough to have a post in an existing forum thread, such as MDiOCA or TfYUCA or TfYAD. The forum rules ( viewtopic.php?f=3&t=2092 ) apply; in particular, describe what pattern(s) you're posting, link to any relevant sources for patterns made by other people (who discovered what and when).
- However, most of such CA aren't interesting enough to deserve a separate forum thread just for a specific cellular automaton. Usually there are only a few posts about a given CA, and discussion in an existing thread (such as those linked above) is better than making a new thread that will soon be abandoned.
- In some cases, when there is already substantial amount of discussion/exploration of some CA, with several people other than the initial discoverers involved, sometimes that can add up to evidence that the CA deserves a separate forum thread. (Then probably the first post of the new thread should clearly present the status of exploration; what's already known and what is unknown, who discovered what, what are reasons to choose and investigate further this particular cellular automaton (why it's interesting).)
pifricted wrote: May 1st, 2025, 9:49 am Is this rule enough interesting to have a post in OCA subfourm?Code: Select all
x = 311, y = 53, rule = B3-q6i/S2-i35i
Just because someone might reply now with a claim that it's "interesting", doesn't mean it was a good idea to start the thread.)
Confocaloid was banned around May 10th for being incredibly pedantic even when asked multiple times to stop. They were the main person posting these replies.ThePlayzr wrote: September 21st, 2025, 8:49 pm This might not belong here, but why is it that when I made the Travelling Ts thread (4 months ago now!) That I didn't get a reply like this:What was special enough about my rule that I didn't get a reply like that?
Wow. I guess I chose the perfect time to make the thread then.LuveelVoom wrote: September 21st, 2025, 9:44 pmConfocaloid was banned around May 10th for being incredibly pedantic even when asked multiple times to stop. They were the main person posting these replies.ThePlayzr wrote: September 21st, 2025, 8:49 pm What was special enough about my rule that I didn't get a reply like that?
Code: Select all
x = 16, y = 1, rule = MAPAAD//zAwPz8AAP//MDA/PwAA//8AAP//AAD//wAA//8AAD8/AAD//wAAPz8AAP//wMD//wAA///AwP//AAD//w
16o!Well, I suppose creating a 2-state rule table and using Copy as MAP works:muzik wrote: September 23rd, 2025, 1:04 pm How exactly do you make a hexagonal map rule? Which binary digit represents which cell arrangement?
Code: Select all
x = 48, y = 1, rule = hexleaf
48o!
@RULE hexleaf
@TABLE
n_states:2
neighborhood:hexagonal
symmetries:none
0,1,0,0,0,0,1,1
0,0,0,0,1,1,0,1
0,0,0,1,1,1,0,1
0,1,0,1,0,0,1,1
0,1,1,0,0,0,1,1
0,0,1,0,1,1,0,1
1,0,0,0,0,0,1,0
1,0,0,1,0,1,0,0
1,0,0,1,0,0,1,0
1,0,1,0,0,0,1,0
1,0,1,0,0,1,0,0
1,0,0,0,0,1,0,0Code: Select all
x = 48, y = 1, rule = MAPEd0AdxDfAH8A/4j/AP+A/w
48o!Code: Select all
x = 1, y = 48, rule = wiggletriangle
o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$
o$o$o$o$o$o$o$o$o$o$o$o$o!
@RULE wiggletriangle
@TABLE
n_states:2
neighborhood:hexagonal
symmetries:none
0,0,0,0,0,1,1,1
0,1,1,1,0,0,0,1
0,0,0,1,0,1,1,1
0,1,1,0,0,0,0,1
0,0,0,0,1,1,1,1
0,1,1,0,1,0,0,1
1,0,0,0,0,0,1,0
1,1,0,1,0,0,0,0
1,1,0,0,0,0,0,0
1,1,0,0,1,0,0,0
1,0,0,0,1,0,1,0
1,0,0,1,0,0,1,0Code: Select all
x = 1, y = 48, rule = MAPBJ8g/wSfIP8EnyD/AP8A/w
o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o$
o$o$o$o$o$o$o$o$o$o$o$o$o!Code: Select all
x = 5, y = 3, rule = B35cj6ce7/S34-cry5-jnr6ci78
2b2o$5o$2b2o!