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Synchronization and predictability under rule 52, a cellular automaton reputedly of class 4

Freire JG, Gallas JAC
olume 366, Issues 12, 18 June 2007, Pages 25-29, https://doi.org/10.1016/j.physleta.2007.01.071

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Abstract

We study the complexity exhibited by the gliders of rule 52, a totalistic cellular automaton reputedly capable of highly intricate behaviors. Such gliders are responsible for information flow and long-range spatial correlations frequently used to classify complexity. We discover an unexpected simplicity in all computable gliders, shown to arise from simple juxtaposition between active and inactive synchronization patches linked by a remarkably small set of communication interfaces. We classify such interfaces and argue rule 52 to be interesting but of limited asymptotic complexity.