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Selforganization by Nonlinear Irreversible Processes pp 213–219Cite as

Complexity of Patterns Generated by One-Dimensional Cellular Automata

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Part of the book series: Springer Series in Synergetics ((SSSYN,volume 33))

Abstract

Cellular automata are mathematical models for complex systems in which many simple components act together to produce complicated patterns of behaviour. These automata serve as key models to study the origins of chaos (randomness) in physical systems. There are examples in which a cellular automaton evolving from a single initial state produces a structure so complicated that some features of it seem random. WOLFRA’M, PACKARD and co-workers have been investigated one- dimensional and two-dimensional automata extensively in several ways /1/. In his “Twenty Problems in the Theory of Cellular Automata” /2/ WOLFRAM formulates in problem 15 a question concerning the randomness of sequences generated by cellular automata.

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Reference

  1. D. Farmer, T. Toffoli. S. Wolfram (Eds.): Cellular Automata; Proceeding of an Interdisciplinary Workshop, Physica 10D, (1984) no. 1/2

    Google Scholar 

  2. S. Wolfram: Nature 311, 419 (1984)

    Article  ADS  Google Scholar 

  3. N.H. Packard, S. Wolfram: J.Stat.Phys. 38, 901 (1985)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. S. Wolfram: Physica Scripta T9, 170 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  5. W. Ebeling, R. Feistel: Physik der Selbstorganisation und Evolution (Akademie-Verlag, Berlin 1982)

    Google Scholar 

  6. S. Wolfram: Rev.Mod.Phys. 55, 601 (1983)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. W. Ebeling, M.A. Jimenez-Montana: Math.Biosci. 52, 53 (1980)

    Article  MATH  Google Scholar 

  8. H. Thiele: Zur Definition von Kompliziertheitsmaßen für endliche Objekte, in: Organismische Informationsverarbeitung (Ed.: F. Klix) (Akademie-Verlag, Berlin 1974)

    Google Scholar 

  9. M. Heinz: Elektr.Inform.u.Kybern. (EIK) 13, 27 (1977)

    MathSciNet  MATH  Google Scholar 

  10. W. Ebeling, R. Mahnke: studia biophysica,17, 173 (1978)

    Google Scholar 

  11. R. Mahnke: Wiss.Zeitschr.WPU Rostock, MNR 27, 931 (1978)

    Google Scholar 

  12. R. Mahnke: Zur Komplexität und Evolution biologischer Makro moleküle, Thesis, Wilhelm-Pieck-Universität Rostock 1980

    Google Scholar 

  13. L. Hunyadvari, A. Ivanyi: On some complexity measures of words, in: Proc.of Conf. Automata, Languages and Mathematical Systems, Budapest, Karl-Marx-Universität, 1985, p. 67–82

    Google Scholar 

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Author information

Authors and Affiliations

  1. Sektion Physik, Wilhelm-Pieck-Universität Rostock, Universitätsplatz 3, DDR-2500, Rostock, Germany

    R. Mahnke & A. Budde

Authors
  1. R. Mahnke
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  2. A. Budde
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Editors and Affiliations

  1. Sektion Physik, Humboldt-Universität Berlin, Invalidenstraße 42, DDR-1040, Berlin, Germany

    Werner Ebeling

  2. Sektion Physik, Wilhelm-Pieck-Universität, Universitätsplatz 3, DDR-2500, Rostock, Germany

    Heinz Ulbricht

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© 1986 Springer-Verlag Berlin Heidelberg

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Mahnke, R., Budde, A. (1986). Complexity of Patterns Generated by One-Dimensional Cellular Automata. In: Ebeling, W., Ulbricht, H. (eds) Selforganization by Nonlinear Irreversible Processes. Springer Series in Synergetics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71004-9_29

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  • DOI: https://doi.org/10.1007/978-3-642-71004-9_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-71006-3

  • Online ISBN: 978-3-642-71004-9

  • eBook Packages: Springer Book Archive

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