Journal of Statistical Physics

, Volume 43, Issue 3–4, pp 463–478 | Cite as

Exact results for deterministic cellular automata with additive rules

  • Pu-hua Guan
  • Yu He
Articles

Abstract

Deterministic cellular automata (CA) with additive rules are studied by exploiting the properties of circulant matrices on finite fields. Complete state transition diagrams for higher-order and multidimensional CA on finite lattices are analyzed. Conditions on the rules which make them reversible are obtained. It is shown that all state transition diagrams of the CA have identical trees rooted on cycles. General formulae for cycle lengths and multiplicities are given.

Key words

Cellular automata discrete dynamical systems 

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References

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    S. Wolfram,Rev. Mod. Phys. 55:601 (1983);Physica 10D:247 (1984).Google Scholar
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    O. Martin, A. M. Odlyzko, and S. Wolfram,Commun. Math. Phys. 93:219 (1984).Google Scholar
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    Philip J. Davis,Circulant Matrices (John Wiley & Sons, New York, 1979).Google Scholar
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    F. J. MacWilliams and N. J. A. Sloane,The Theory of Error-Correcting Codes (North-Holland, New York, 1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Pu-hua Guan
    • 1
  • Yu He
    • 2
  1. 1.Department of MathematicsOhio State UniversityColumbus
  2. 2.Department of PhysicsOhio State UniversityColumbus

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