The cellular automata with local permutation invariance are considered. Weshow that in the two-state case the set of such automata coincides with thegeneralized Game of Life family. We count the number of equivalence classes ofthe rules under consideration with respect to permutations of states. Thisreduced number of rules can be efficiently generated in many practical cases byour C program. Since a cellular automaton is a combination of a local rule anda lattice, we consider also maximally symmetric two-dimensional lattices. Inaddition, we present the results of compatibility analysis of several rulesfrom the Life family.
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