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