# Cobweb Diagrams of Elementary Cellular Automata

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Each possible state in the evolution of an elementary cellular automaton (ECA) can be uniquely labeled by an integer. For a finite-width ECA, this set is mapped to itself during the ECA evolution. Thus an ECA defines a recurrence relation on a finite set of integers. In fact, this can be applied to map the Cantor set to itself (see Related Links and Details sections).

[more]Contributed by: Vitaliy Kaurov (April 2013)

## Snapshots

## Details

References

[1] J. D. Farmer, "Dimension, Fractal Measures, and Chaotic Dynamics," in *Evolution of Order and Chaos in Physics, Chemistry, and Biology: Proceedings of the International Symposium on Synergetics*, Bavaria, Germany (H. Haken, ed.), Berlin: Springer-Verlag, 1982 pp. 228-246. doi:http://dx.doi.org/10.1007/978-3-642-68808-9_20.

[2] J. D. Farmer, "Information Dimension and the Probabilistic Structure of Chaos," *Zeitschrift für Naturforschung A*, *37*, 1982 pp. 1304-1325.

## Permanent Citation

"Cobweb Diagrams of Elementary Cellular Automata"

http://demonstrations.wolfram.com/CobwebDiagramsOfElementaryCellularAutomata/

Wolfram Demonstrations Project

Published: April 18, 2013