Cellular Automata with Symmetric Local Rules

Details Cellular Automata with Symmetric Local Rules Cellular Automata with Symmetric Local Rules

2006-05-11

arxiv.org/abs/math-ph/0605040v2

CASC 2006, LNCS 4194, pp. 240--250, 2006. Springer-Verlag Berlin Heidelberg 2006

Physics

Mathematical Physics

11 pages, corrected to match published version

Scientific paper

The cellular automata with local permutation invariance are considered. We show that in the two-state case the set of such automata coincides with the generalized Game of Life family. We count the number of equivalence classes of the rules under consideration with respect to permutations of states. This reduced number of rules can be efficiently generated in many practical cases by our C program. Since a cellular automaton is a combination of a local rule and a lattice, we consider also maximally symmetric two-dimensional lattices. In addition, we present the results of compatibility analysis of several rules from the Life family.

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