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

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. © 2007 Elsevier B.V. All rights reserved. One of the most challenging and interesting phenomena of dynamical systems is that connected with the spontaneous generation of complex structures and patterns in space and time [1–3]. While the emergence of periodic and chaotic temporal behaviors has been studied in detail during the last two decades, the genesis of spatio-temporal regularities in extended chaotic systems with several degrees of freedom remains a much less understood topic. A very popular way of investigating complicated spatiotemporal behaviors is by assuming their complexity to be due to cooperative effects between a number of smaller subsystems evolving under simple rules and operating on relatively few local degrees of freedom. This “reductionistic approach”, which in essence asserts that complex things may be reduced or explained by simpler “more fundamental” parts, is a point of view that may be traced back to the ancient pre-Socratic Greek atomistic view of nature or, much more recently, to Descartes, who argued that, e.g., animals could be reductively explained as automata [4]. Descartes envisioned the world like a huge machine, * Corresponding author. E-mail addresses: [email protected] (J.G. Freire), [email protected]