Kumal et al. 2025 - Using AI to search for interesting Life-like rulesets

[Nosferattus]

Akarsh Kumar at MIT published an interesting paper last year where he used a vision-language foundation model to find the most open-ended artificial life simulations across all possible Life-like cellular automata (all 262,144 possible B/S rulesets). Pretty much everything that would be of interest to folks here is presented in Figure 5: https://direct.mit.edu/view-large/figur ... 8_f005.tif

The most open-ended, according to the model, were B013456/S123, B01356/S0123, B012345/S02356, and B0145/S01234. They are all explosive strobing rulesets, which aren't a genre that gets much attention. After doing some cursory exploration I would personally rank them as follows from most to least interesting:

B0145/S01234: I call this one "Trains" for obvious reasons. It is mainly defined by various wickstretchers and spacefillers. The wickstretchers have several variations, some of which are actually puffers or spaceships, and often spawn other wickstretchers. This ruleset forms remarkably complex and beautiful patterns from simple seeds. I know that is a common feature of cellular automata, but this one is S tier. Here's an example that dvgrn found:

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x = 21, y = 11, rule = B0145/S01234
5o11b5o2$2bo15bo$2bo15bo$2bo15bo$2bo15bo$2bo15bo$2bo15bo$2bo15bo2$5o11b
5o!

B01356/S0123: This automaton is dominated by a replicator and a spectacular 126-period oscillator that starts from a square 4-pixel block. There is a very simple double glider gun, which is pretty neat.

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x = 14, y = 10, rule = B01356/S0123
4$6b2o$6b2o!

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x = 13, y = 9, rule = B01356/S0123
8b2o$3b2o3bo$4bo3b2o$3b2o4b2obo$ob2o5b2obo$ob2o4b2o$3b2o3bo$4bo3b2o$3b
2o!

B013456/S123: This one I call "Vines" for obvious reasons. It's dominated by a wickstretcher that either slowly dies at the tail or stretches from both ends. There are two common gliders.

B012345/S02356: This one isn't super interesting, IMO. It's dominated by a very simple 2-cell replicator, which tends to consume everything else. It does at least have a couple gliders.

Do you think any of these rulesets are worth exploring and/or documenting?

I'm also curious what people think of Kumar's heatmap of all possible Life-like cellular automata. Has anyone else ever tried to map the space of possible automata? I know Wolfram basically did that for the 1-dimensional automata, but what about for 2-dimensional? Since the space is so vast and complex, do people think that using AI models to map it is a promising idea? I wonder if there are any unifying characteristics to the islands mapped by Kumar.

[I6_I6]

What I find interesting is that all the life-like rules that were shown other than CGoL have B0.
EDIT:
I think it'd be cool to also do this for INT and LtL rules, because their rulespaces are much larger.

[Nosferattus]

I think that might be due to the fact that B0 rulesets seem to be really good at creating replicators. Kumar's model seems to mainly be identifying automata that are extremely dynamic, and replicators definitely help with that. I also noticed there are few still lifes in the automata picked by the model, but often lots of oscillators.

[I6_I6]

I like this rule, but only in a torus at 2x step:

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#C [[ STEP 2 ]]
x = 1, y = 1, rule = B012378/S28:T512,512
o!

It came from here:
https://direct.mit.edu/view-large/figur ... 8_f015.tif
Edit: The strobing makes the population graph look diabolical

[Nosferattus]

B014/S02 from that extended list is also quite interesting. It looks so organic. And this glider totally looks like a butterfly:

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x = 11, y = 11, rule = B014/S02
3$4b2o$3b3o$4b4o$3b5o$4bobo!

[LuveelVoom]

Someone should contact the authors and tell them about isotropic non-totalistic cellular automata.