Pleased to say I've completely solved Conway's Game of Life for a finite, toroidally connected square field of side 1
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The problem is that when spacefillers encounter any noise at all, the noise propagates. Try putting the Max pattern file (http://www.conwaylife.com/wiki/Max ) into a simulator (https://copy.sh/life/ ) with a single 2x2 still life somewhere in space and watch the agar dissolve into chaos.
Dang, so is there no such thing as a stable structure in Life? As in, something which resists/suppresses perturbations?
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I can't prove it mathematically, but information in CGOL can't travel faster than c/2 in vacuum, and disorder CAN travel faster than c/2 in occupied space. To resist perturbations, I think you'd need a way for the environment to spread order faster than disorder when perturbed.
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If you want to look at a cellular-automaton-like environment in which the behavior of an infinite amount of sparsely-populated space over an infinite amount of time is unknown, I recommend primordial particle systems. https://youtu.be/makaJpLvbow?t=301 …https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5346932/ …
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