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Encyclopedia of Complexity and Systems Science pp 1–16Cite as

Basins of Attraction of Cellular Automata and Discrete Dynamical Networks

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Glossary

Attractor, basin of attraction, subtree:

The terms “attractor” and “basin of attraction” are borrowed from continuous dynamical systems. In this context the attractor signifies the repetitive cycle of states into which the system will settle. The basin of attraction in convergent (injective) dynamics includes the transient states that flow to an attractor as well as the attractor itself, where each state has one successor but possibly zero or more predecessors (pre-images). Convergent dynamics implies a topology of trees rooted on the attractor cycle, though the cycle can have a period of just one, a point attractor. Part of a tree is a subtree defined by its root and number of levels. These mathematical objects may be referred to in general as “attractor basins.”

Basin of attraction field:

One or more basins of attraction comprising all of state-space.

Cellular automata, CA:

Although CA are often treated as having infinite size, we are dealing here with finite CA, which...

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References

  • Note: Most references by A. Wuensche are available online at http://www.uncomp.ac.uk/wuensche/publications.html

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Author information

Authors and Affiliations

  1. Discrete Dynamics Lab, Flat 6, 3 Grape Street, WC2 H8DX, London, UK

    Andrew Wuensche

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  1. Andrew Wuensche
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Correspondence to Andrew Wuensche .

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Editors and Affiliations

  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

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Wuensche, A. (2017). Basins of Attraction of Cellular Automata and Discrete Dynamical Networks. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_674-1

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_674-1

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  • Print ISBN: 978-3-642-27737-5

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