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Article Dans Une Revue Complex Systems Année : 2022

Operator Representation and Class Transitions in Elementary Cellular Automata

Résumé

We exploit the mirror and complementary symmetries of elementary cellular automata (ECAs) to rewrite their rules in terms of logical operators. The operator representation based on these fundamental symmetries enables us to construct a periodic table of ECAs that maps all unique rules in clusters of similar asymptotic behavior. We also expand the elementary cellular automaton (ECA) dynamics by introducing a parameter that scales the pace with which operators iterate the system. While tuning this parameter continuously, further emergent behavior in ECAs is unveiled as several rules undergo multiple phase transitions between periodic, chaotic and complex (class 4) behavior. This extension provides an environment for studying class transitions and complex behavior in ECAs. Moreover, the emergence of class 4 structures can potentially enlarge the capacity of many ECA rules for universal computation.
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Dates et versions

hal-04092449 , version 1 (09-05-2023)

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Muhamet Ibrahimi, Arda Güçlü, Naide Jahangirov, Mecit Yaman, Oguz Gülseren, et al.. Operator Representation and Class Transitions in Elementary Cellular Automata. Complex Systems , 2022, 31 (4), pp.415-432. ⟨10.25088/ComplexSystems.31.4.415⟩. ⟨hal-04092449⟩
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