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Fractals and Disordered Systems pp 297–322Cite as

Cellular Automata

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Abstract

Cellular automata [9.1] offer a very wide field of choices, and within the space given to me by the editors it will not be possible to write, say, 4 294 967 296 different chapters, each dealing with one particular automaton separately. Instead, I will concentrate on two more systematic approaches. The first approach mixes all possible cellular automata together by letting each site select at the beginning which cellular automata rule it wants to obey. This is the Kauff-man model for genetics, and its fractal dimensions at the phase transition have been studied in detail by many people since 1986. The second approach tries to classify all possible cellular automata according to some unified simple criteria; such criteria could be the fractal dimensions, but since they are only beginning to be known we concentrate on the simpler Wolfram classification. Some readers may wish to look only at some restricted class of cellular automata, and not at all of them; for these readers I offer some appendices.

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Authors
  1. Dietrich Stauffer
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Editors and Affiliations

  1. I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstrasse 9, W-2000, Hamburg 36, Germany

    Armin Bunde

  2. Department of Physics, Bar-Ilan University, Ramat Gan, Israel

    Shlomo Havlin

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© 1991 Springer-Verlag Berlin Heidelberg

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Stauffer, D. (1991). Cellular Automata. In: Bunde, A., Havlin, S. (eds) Fractals and Disordered Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51435-7_9

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  • DOI: https://doi.org/10.1007/978-3-642-51435-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-51437-1

  • Online ISBN: 978-3-642-51435-7

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