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Topological Dynamics of Cellular Automata

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Abbreviations

Almost equicontinuous CA:

has an equicontinuous configuration.

Attractor:

omega-limit of a clopen invariant set.

Blocking word:

interrupts information flow.

Closing CA:

distinct asymptotic configurations have distinct images.

Column subshift:

columns in space-time diagrams.

Cross section:

one-sided inverse map.

Directional dynamics:

dynamics along a direction in the space-time diagram.

Equicontinuous configuration:

nearby configurations remain close.

Equicontinuous CA:

all configurations are equicontinuous.

Expansive CA:

distinct configurations get away.

Finite time attractor:

is attained in finite time from its neighborhood.

Jointly periodic configuration:

is periodic both for the shift and the CA.

Lyapunov exponents:

asymptotic speed of information propagation.

Maximal attractor:

omega-limit of the full space.

Nilpotent CA:

maximal attractor is a singleton.

Open CA:

image of an open set is open.

Permutive CA:

local rule permutes an extremal coordinate.

Quasi‐attractor:

a countable intersection of attractors.

Signal subshift:

weakly periodic configurations of a given period.

Spreading set:

clopen invariant set which propagates in both directions.

Subshift attractor:

limit set of a spreading set.

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Acknowledgments

I thank Marcus Pivato and Mathieu Sablik for careful reading of the paper and manyvaluable suggestions. The research was partially supported by the Research Program CTS MSM 0021620845.

Author information

Authors and Affiliations

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

    Petr Kůrka

  2. Center for Theoretical Study, Academy of Sciences and Charles University, Prague, Czechia

    Petr Kůrka

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  1. Petr Kůrka
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Kůrka, P. (2009). Topological Dynamics of Cellular Automata. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_556

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