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A full computation-relevant topological dynamics classification of elementary cellular automata


Schüle, M; Stoop, R (2012). A full computation-relevant topological dynamics classification of elementary cellular automata. Chaos (Woodbury, N.Y.), 22(4):043143.

Abstract

Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and chaoticity. The “complex” ECA emerge to be sensitive, but not chaotic and not eventually weakly periodic. Based on this classification, we conjecture that elementary cellular automata capable of carrying out complex computations, such as needed for Turing-universality, are at the “edge of chaos.”

Abstract

Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and chaoticity. The “complex” ECA emerge to be sensitive, but not chaotic and not eventually weakly periodic. Based on this classification, we conjecture that elementary cellular automata capable of carrying out complex computations, such as needed for Turing-universality, are at the “edge of chaos.”

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8 citations in Web of Science®
8 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Date:2012
Deposited On:07 Mar 2013 08:32
Last Modified:13 May 2016 09:16
Publisher:American Institute of Physics
Number of Pages:11
ISSN:1054-1500
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1063/1.4771662

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