Scaling Properties of a Family of Transformations Defined on Cellular Automaton Rules

  • N. Boccara
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 46)


A one-parameter family of transformations defined on the set of one-dimensional two-state cellular automaton rules is studied. The class of a given cellular automaton is unchanged under these transformations. For class-3 cellular automata, the probability distribution of the asymptotic density of nonzero-value sites satisfies a simple scaling property.




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  1. [1]
    J. von Neumann, 1963, Collected Works, edited by A. H. Taub, 5, 288.Google Scholar
  2. [2]
    Cellular Automata, edited by D. Farmer, T. Toffoli and S. Wolfram, 1984, North-Holland.MATHGoogle Scholar
  3. [3]
    S. Wolfram, Theory and Applications of Cellular Automata (World Scientific, 1986).MATHGoogle Scholar
  4. [4]
    S. Wolfram, 1984, Physica, 10 D, 1.Google Scholar
  5. [5]
    S. Wolfram, 1983, Rev. Mod. Phys., 55, 601.MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • N. Boccara
    • 1
    • 2
  1. 1.CEN-SaclayDPh-G/PSRMGif-sur-Yvette CedexFrance
  2. 2.Department of PhysicsUniversity of IllinoisChicagoUSA

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