Cellular automata with symmetric local rules

Authors:
Vladimir V. Kornyak
Affiliations:
Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia
Venue:
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Year:
2006

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Abstract

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.