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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ME: Gosh it's way past two in the morning, I should be in bed ALSO ME: I wonder what we know about the long-term behaviour of an infinite, sparsely populated Conway's Game of Life universe
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So it seems logical to me to think that the Conway's Game of Life universe would eventually be dominated by quadratic-growth forms http://www.conwaylife.com/wiki/Quadratic_growth#Quadratic_growth …
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But this raises really thorny questions about what happens when two quadratically growing forms meet one another. Does one swamp the other? Does the interface between them settle with "borders" between two "territories"?
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I guess Life patterns are generally incredibly unstable, so typically the result when two patterns meet is just ruined chaos
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If there's a stable agar http://www.conwaylife.com/wiki/Agar and there's some kind of spacefiller http://www.conwaylife.com/wiki/Spacefiller … which quadratically fills space with that agar, then that pattern's likely to dominate the universe
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Specifically, whichever pattern satisfies these conditions and is also the least complex is going to be the one which occurs the most frequently in a sparse Life universe, and therefore dominate...?
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There'll be some confusion at the boundaries where these spacefillers meet and absorb other structures, or one another, but other than that, square light years of stable agar...?
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End of conversation
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Whole systems wiped out by momentary accidental glider gun construction kilo-squares away
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