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Cellular Automata Dynamical Systems

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Handbook of Natural Computing

Abstract

We present recent studies on cellular automata (CAs) viewed as discrete dynamical systems. In the first part, we illustrate the relations between two important notions: subshift attractors and signal subshifts, measure attractors and particle weight functions. The second part of the chapter considers some operations on the space of one-dimensional CA configurations, namely, shifting and lifting, showing that they conserve many dynamical properties while reducing complexity. The final part reports recent investigations on two-dimensional CA. In particular, we report a construction (slicing construction) that allows us to see a two-dimensional CA as a one-dimensional one and to lift some one-dimensional results to the two-dimensional case.

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Acknowledgments

The research was supported by the Research Program CTS MSM 0021620845, by the Interlink/MIUR project “Cellular Automata: Topological Properties, Chaos and Associated Formal Languages,” by the ANR Blanc “Projet Sycomore” and by the PRIN/MIUR project “Mathematical aspects and forthcoming applications of automata and formal languages.”

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Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Milan, Italy

    Alberto Dennunzio

  2. Département d'Informatique, Université de Nice-Sophia Antipolis, Nice, France

    Enrico Formenti

  3. Center for Theoretical Studies, Academy of Sciences and Charles University in Prague, Prague, Czechia

    Petr Kůrka

Authors
  1. Alberto Dennunzio
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  2. Enrico Formenti
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  3. Petr Kůrka
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Editor information

Editors and Affiliations

  1. LIACS, Leiden University, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Computer Science Department, University of Colorado, Boulder, USA

    Grzegorz Rozenberg

  3. LIACS, Leiden University, Leiden, The Netherlands

    Thomas Bäck

  4. LIACS, Leiden University, Leiden, The Netherlands

    Joost N. Kok

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Dennunzio, A., Formenti, E., Kůrka, P. (2012). Cellular Automata Dynamical Systems. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds) Handbook of Natural Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92910-9_2

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