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A Symbolic Dynamics Perspective of Elementary Cellular Automaton Rule 12 with Minority Memory
Bo Chen, Fangyue Chen, Weifeng Jin and Junbiao Guan

This paper provides a symbolic dynamics perspective to the empirical observations concerning the elementary cellular automata with a minority memory (ECAM). By introducing the symbol vector space and exploiting the mathematical definition of ECAM, we present an analytical characterization of complex asymptotic dynamics of ECAM rule 12. Elementary cellular automaton rule 12, a member of Wolfram’s class II which was said to be simple as fixed points before, actually exists a chaotic subsystem in the historic model. More specifically, ECAM rule 12 is topologically mixing and possesses the positive topological entropy on its subsystem. Finally, it is worth mentioning that the method presented in this paper is also applicable to other ECAM.

Keywords: Elementary cellular automata; minority memory; symbolic dynamics; chaos; topologically mixing; topological entropy.

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