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Classification of Cellular Automata

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Cellular Automata

Part of the book series: Encyclopedia of Complexity and Systems Science Series ((ECSSS))

  • Originally published in
  • R. A. Meyers (ed.), Encyclopedia of Complexity and Systems Science, © Springer-Verlag 2009

Glossary

Cellular automaton:

For our purposes, a (one-dimensional) cellular automaton (CA) is given by a local map ρ : Σw → Σ where Σ is the underlying alphabet of the automaton and w is its width. As a data structure, suitable as input to a decision algorithm, a CA can thus be specified by a simple lookup table. We abuse notation and write ρ(x) for the result of applying the global map of the CA to configuration x ∈ Σℤ.

Finite configurations:

One often considers CA with a special quiescent state: the homogeneous configuration where all cells are in the quiescent state is required to be fixed point under the global map. Infinite configurations where all but finitely many cells are in the quiescent state are often called finite configurations. This is somewhat of a misnomer; we prefer to speak about configurations with finite support.

Reversibility:

A discrete dynamical system is reversible if the evolution of the system incurs no loss of information: the state at time tcan be...

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    Klaus Sutner

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  1. Klaus Sutner
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Correspondence to Klaus Sutner .

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Editors and Affiliations

  1. Unconventional Computing Centre, University of the West of England, Bristol, UK

    Andrew Adamatzky

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Sutner, K. (2009). Classification of Cellular Automata. In: Adamatzky, A. (eds) Cellular Automata. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8700-9_50

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