Re: [math-fun] "life" generalized CAs classified ala Wolfram?
IIRC these are called "totalistic" rules. The most interesting aspect of this project, it seems to me, is the isInteresting() predicate. However (as the OEIS shows) defining "interesting" can be a challenge. One possible choice in this context might be "can be used to build a Turing machine". But--considering the heroics entailed constructing a Turing-equivalent pattern just for the single Life rule--this seems kinda daunting. But if we had even a quick partial implementation at least we might winnow out the vast majority of the quarter million rules and just concentrate on the most promising candidates.
--indeed. S.Wolfram wrote a paper where he carried out the analogous project for 1-dimensional cellular automata with cardinality-8 neighborhoods, 256 machines considered in all. His "IsInteresting()" predicate consisted of him looking at graphical output and pushing one of several buttons. In fact, he undoubtably would have liked to use "Turing machines exist" as one of his predicates, but was unable and instead merely made conjectures... and indeed, eventually Matthew Cook managed to prove Wolfram's "rule 110" conjecture http://en.wikipedia.org/wiki/Rule_110 in an excellent piece of work which Wolfram responded to with a lawsuit (!). Anyhow, you'd have to make an "Automated Wolfram eyeball" as your IsInteresting() heuristic predicate.
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Warren D Smith