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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)

Abstract

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.

Keywords

Cellular Automaton Cellular Automaton Discrete Dynamical System Space Direction Asymptotic Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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