Topology Proceedings 30 No. 1 (2006), pp. 197-222

Equicontinuity Properties of D-Dimensional Cellular Automata

Emily Gamber Burkhead

We introduce a topological classification of cellular automata in dimensions two and higher based on a one-dimensional classification given by Petr Krka [Topological dynamics of cellular automata in Codes, Systems, and Graphical Models, Ed. Brian Marcus and Joachim Rosenthal. 2001]. We give results, examples, and a diagram showing the dichotomy of sensitive dependence on initial conditions versus the existence of equicontinuity points.

Keywords: cellular automata, equicontinuity, sensitive dependence on initial conditions, topological dynamics

Mathematics Subject Classification: 37B15 37B10 54H20

Document formats: PDF file 309.8 Kb

Topology Proceedings, Volume 30, No. 1 (2006)
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