Oh, I see where you're going Adam: because of the halting problem [1], we cannot know if a machine like the the Fermat Prime Calculator [2] ever terminates in a finite pattern. But I think Dan was asking something more like this: Is there a finite-sized pattern AE (for "Adam and Eve") whose evolution eventually includes all other finite-sized Life patterns, except those that have no ancestors ("orphans", "grandfatherless", etc. patterns). If so, then for every pattern P, there would be a number N such that the Nth generation of AE is (or contains) the pattern P. - Robert [1] http://en.wikipedia.org/wiki/Halting_problem [2] http://www.conwaylife.com/wiki/Fermat_prime_calculator On Tue, Dec 6, 2011 at 02:56, Adam P. Goucher <apgoucher@gmx.com> wrote:
Good point. Now let me make a feeble attempt to rescue the Adam & Eve
question.
Consider those patterns each having an infinite sequence of ancestors.
Is there a starting pattern for which every one of these eventually appears somewhere among its descendants?
That is a ludicrously difficult question to solve; it may even be undecidable.
For the special case where 'pattern having an infinite sequence of ancestors' is replaced with 'pattern with a finite well-spaced glider synthesis', the answer is yes.
Sincerely,
Adam P. Goucher
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