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.
It sounds like you’re conflating the state of the cellular automaton with state of the Game of Life. The GoL isn’t NOOPing every other generation, only the CA is.
All Turing complete languages are equivalent, so if one is capable of omniperiodicity then they all are. A routine that cycles i times for any integer i is omniperiodic, and beginning developers learn how to do that with a modulo function.
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?
On an unrelated note, it looks as if someone’s downvoting your every post on c/mathematics.
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.
It sounds like you’re conflating the state of the cellular automaton with state of the Game of Life. The GoL isn’t NOOPing every other generation, only the CA is.
All Turing complete languages are equivalent, so if one is capable of omniperiodicity then they all are. A routine that cycles
itimes for any integeriis omniperiodic, and beginning developers learn how to do that with a modulo function.