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Classification of Elementary Cellular Automata Up to Topological Conjugacy

Abstract : 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.
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Submitted on : Friday, January 20, 2017 - 4:09:47 PM
Last modification on : Thursday, January 7, 2021 - 2:30:03 PM
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Jeremias Epperlein. Classification of Elementary Cellular Automata Up to Topological Conjugacy. 21st Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2015, Turku, Finland. pp.99-112, ⟨10.1007/978-3-662-47221-7_8⟩. ⟨hal-01442485⟩