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Conway's Game of Life is Omniperiodic (arxiv.org)

submitted 11 months ago by yogthos@lemmy.ml to c/mathematics@lemmy.ml

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[–] davel@lemmy.ml 1 points 11 months ago* (last edited 11 months ago) (2 children)

I must be missing something. If CGL has already been proven to be Turing complete, and if Turing completion implies omniperiodicity (which seems trivially true), then what was the point of this exercise?

[–] qwertyasdef@programming.dev 1 points 11 months ago

I don't think Turing-completeness implies omniperiodicity. I'm imagining a cellular automaton which follows Game of Life rules on even-numbered generations and does nothing on odd-numbered generations, which is trivially Turing-complete because it's just Conway's Game of Life if you ignore every other generation, but also trivially has no odd-period oscillators.

[–] davel@lemmy.ml 1 points 11 months ago

On an unrelated note, it looks as if someone's downvoting your every post on c/mathematics.