Classifying 1D elementary cellular automata with the 0-1 test for chaos

Mohammed Terry-Jack; Simon O'Keefe

doi:10.1016/j.physd.2023.133786

Classifying 1D elementary cellular automata with the 0-1 test for chaos

Mohammed Terry-Jack^*, Simon O'Keefe

^*Corresponding author for this work

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We utilise the 0-1 test to automatically classify elementary cellular automata. The quantitative results of the 0-1 test reveal a number of advantages over Wolfram’s qualitative classification. For instance, while almost all rules classified as chaotic by Wolfram were confirmed as such by the 0-1 test, there were two rules which were revealed to be non-chaotic. However, their periodic nature is hidden by the high complexity of their spacetime patterns and not easy to see without looking very carefully. Comparing each rule’s chaoticity (as quantified by the 0-1 test) against its intrinsic complexity (as quantified by its Chua complexity index) also reveals a number of counter-intuitive discoveries; i.e. non-chaotic dynamics are not only found in simpler rules, but also in rules as complex as chaos.

Original language	English
Article number	133786
Number of pages	17
Journal	Physica D: Nonlinear Phenomena
Volume	453
Early online date	16 Jun 2023
DOIs	https://doi.org/10.1016/j.physd.2023.133786
Publication status	Published - Nov 2023

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Cite this

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title = "Classifying 1D elementary cellular automata with the 0-1 test for chaos",

abstract = "We utilise the 0-1 test to automatically classify elementary cellular automata. The quantitative results of the 0-1 test reveal a number of advantages over Wolfram{\textquoteright}s qualitative classification. For instance, while almost all rules classified as chaotic by Wolfram were confirmed as such by the 0-1 test, there were two rules which were revealed to be non-chaotic. However, their periodic nature is hidden by the high complexity of their spacetime patterns and not easy to see without looking very carefully. Comparing each rule{\textquoteright}s chaoticity (as quantified by the 0-1 test) against its intrinsic complexity (as quantified by its Chua complexity index) also reveals a number of counter-intuitive discoveries; i.e. non-chaotic dynamics are not only found in simpler rules, but also in rules as complex as chaos.",

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