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Chaotic Behavior of Cellular Automata

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Encyclopedia of Complexity and Systems Science

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Glossary

Equicontinuity:

All points are equicontinuity points (in compact settings).

Equicontinuity point:

A point for which the orbits of nearby points remain close.

Expansivity:

From two distinct points, orbits eventually separate.

Injectivity:

The next state function is injective.

Linear CA:

A CA with additive local rule.

Regularity:

The set of periodic points is dense.

Sensitivity to initial conditions:

For any point x there exist arbitrary close points whose orbits eventually separate from the orbit of x.

Strong transitivity:

There always exist points which eventually move from any arbitrary neighborhood to any point.

Surjectivity:

The next state function is surjective.

Topological mixing:

There always exist points which definitely move from any arbitrary neighborhood to any other.

Transitivity:

There always exist points which eventually move from any arbitrary neighborhood to any other.

Definition of the Subject

A discrete time dynamical system (DTDS) is a pair 〈X, F〉 where Xis...

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Acknowledgments

This work has been supported by the Interlink/MIUR project “Cellular Automata:

Topological Properties, Chaos and Associated Formal Languages”, by the ANR Blanc Project “Sycomore” and by the PRIN/MIUR project “Formal Languages and Automata: Mathematical and Applicative Aspects”.

Author information

Authors and Affiliations

  1. Laboratoire d’Informatique de l’Institut Gaspard–Monge, Université Paris-Est, Marne- la-Vallée, France

    Julien Cervelle

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

    Alberto Dennunzio

  3. Laboratoire I3S, Université de Nice-Sophia Antipolis, Sophia Antipolis, France

    Enrico Formenti

Authors
  1. Julien Cervelle
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  2. Alberto Dennunzio
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  3. Enrico Formenti
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Corresponding author

Correspondence to Julien Cervelle .

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Editors and Affiliations

  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

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Cervelle, J., Dennunzio, A., Formenti, E. (2017). Chaotic Behavior of Cellular Automata. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_65-4

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_65-4

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