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Towards the classification of all Boolean cellular automata

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  • Kohring, G.A.

Abstract

A classification scheme for all Boolean cellular automata models involving an arbitrary number of inputs is proposed. The scheme is based upon counting the number of stable points for a given rule, i.e., points whose time development is stable with respect to small perturbations. When applied to all cellular automata with 2, 3, 4, or 5 Boolean inputs (the latter involving more than 4000 million cases), it yields, in each case, a nontrivial classification (i.e., there is no single class in which nearly all the rules lie). In addition, it is shown how rules satisfying a given Boolean differential equation can easily be obtained.

Suggested Citation

  • Kohring, G.A., 1992. "Towards the classification of all Boolean cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(3), pages 320-324.
    • Handle: RePEc:eee:phsmap:v:182:y:1992:i:3:p:320-324
    DOI: 10.1016/0378-4371(92)90345-Q
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