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Growth Phenomena in Cellular Automata

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Cellular Automata

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

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  • Originally published in
  • R. A. Meyers (ed.), Encyclopedia of Complexity and Systems Science, © Springer Science+Business Media New York 2013

Glossary

Asymptotic density:

The proportion of sites in a lattice occupied by a specified subset is called asymptotic density or, in short, density.

Asymptotic shape:

The shape of a growing set, viewed from a sufficient distance so that the boundary fluctuations, holes, and other lower order details disappear, is called the asymptotic shape.

Cellular automaton:

A cellular automaton is a sequence of configurations on a lattice which proceeds by iterative applications of a homogeneous local update rule. A configuration attaches a state to every member (also termed a site or a cell) of the lattice. Only configurations with two states, coded 0 and 1, are considered here. Any such configuration is identified with its set of 1’s.

Final set:

A site whose state changes only finitely many times is said to fixate or attain a final state. If this happens for every site, then the sites whose final states are 1 comprise the final set.

Initial set:

A starting set for a cellular automaton evolution...

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Author information

Authors and Affiliations

  1. Mathematics Department, University of California, Davis, CA, USA

    Janko Gravner

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  1. Janko Gravner
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Correspondence to Janko Gravner .

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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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Gravner, J. (2018). Growth Phenomena in 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_266

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