Note that each single "step" of the Turing Machine may take n steps of advancing the GoL cellular automaton itself. This means that only periods of n*i where i

Note that each single "step" of the Turing Machine may take n steps of advancing the GoL cellular automaton itself. This means that only periods of n*i where i is an integer corresponding to the number of steps made by the TM, are guaranteed to exist. Worse even, I don't think that a proof of Turing completeness requires there to be any time bounds on the machine, so n might not even be a constant... If that's the case, then Turing completeness only proves that there exists an infinite number of periods of various lengths, but nothing about how comprehensively they "cover" all possible periods.