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Classification of Elementary Cellular Automata Up to Topological Conjugacy

Jeremias Epperlein

21st IFIP WG 1.5 International Workshop, AUTOMATA 2015
Conference location

Turku, Finland,

Topological conjugacy is the natural notion of isomorphism in topological dynamics. It can be used as a very fine grained classification scheme for cellular automata. In this article, we investigate different invariants for topological conjugacy in order to distinguish between non-conjugate systems. In particular we show how to compute the cardinality of the set of points with minimal period n for one-dimensional CA. Applying these methods to the 256 elementary one-dimensional CA, we show that up to topological conjugacy there are exactly 83 of them.

*Applied Mathematics > Complex Systems