Classification of elementary cellular automata up to topological conjugacy

Jeremias Epperlein

doi:10.1007/978-3-662-47221-7_8

Classification of elementary cellular automata up to topological conjugacy

Jeremias Epperlein

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

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 nonconjugate 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.

Original language	English
Title of host publication	Cellular Automata and Discrete Complex Systems - 21st IFIPWG 1.5 International Workshop, AUTOMATA 2015, Proceedings
Editors	Jarkko Kari
Publisher	Springer Verlag
Pages	99-112
Number of pages	14
ISBN (Electronic)	9783662472200
DOIs	https://doi.org/10.1007/978-3-662-47221-7_8
State	Published - 1 Jan 2015
Externally published	Yes
Event	21st IFIPWG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2015 - Turku, Finland Duration: 8 Jun 2015 → 10 Jun 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9099
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	21st IFIPWG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2015
Country/Territory	Finland
City	Turku
Period	8/06/15 → 10/06/15

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-662-47221-7_8

Cite this

Epperlein, J. (2015). Classification of elementary cellular automata up to topological conjugacy. In J. Kari (Ed.), Cellular Automata and Discrete Complex Systems - 21st IFIPWG 1.5 International Workshop, AUTOMATA 2015, Proceedings (pp. 99-112). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9099). Springer Verlag. https://doi.org/10.1007/978-3-662-47221-7_8

Epperlein, Jeremias. / Classification of elementary cellular automata up to topological conjugacy. Cellular Automata and Discrete Complex Systems - 21st IFIPWG 1.5 International Workshop, AUTOMATA 2015, Proceedings. editor / Jarkko Kari. Springer Verlag, 2015. pp. 99-112 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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 nonconjugate 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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Epperlein, J 2015, Classification of elementary cellular automata up to topological conjugacy. in J Kari (ed.), Cellular Automata and Discrete Complex Systems - 21st IFIPWG 1.5 International Workshop, AUTOMATA 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9099, Springer Verlag, pp. 99-112, 21st IFIPWG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2015, Turku, Finland, 8/06/15. https://doi.org/10.1007/978-3-662-47221-7_8

Classification of elementary cellular automata up to topological conjugacy. / Epperlein, Jeremias.
Cellular Automata and Discrete Complex Systems - 21st IFIPWG 1.5 International Workshop, AUTOMATA 2015, Proceedings. ed. / Jarkko Kari. Springer Verlag, 2015. p. 99-112 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9099).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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 nonconjugate 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.

AB - 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 nonconjugate 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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Epperlein J. Classification of elementary cellular automata up to topological conjugacy. In Kari J, editor, Cellular Automata and Discrete Complex Systems - 21st IFIPWG 1.5 International Workshop, AUTOMATA 2015, Proceedings. Springer Verlag. 2015. p. 99-112. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-47221-7_8

Classification of elementary cellular automata up to topological conjugacy

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