Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Basins of Attraction of Cellular Automata and Discrete Dynamical Networks

  • Andrew WuenscheEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_674-1


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 usually...

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Authors and Affiliations

  1. 1.Discrete Dynamics LabLondonUK