Computing in Spiral Rule Reaction-Diffusion Hexagonal Cellular Automaton

A hexagonal ternary-state two-dimensional cellular automaton is de-signed which imitates an activator-inhibitor reaction-diffusion system,where the activator is self-inhibited in particular concentrations and theinhibitor dissociates in the absence of the activator. The automaton ex-hibits both stationary and mobile localizations (eaters and gliders), andgenerators of mobile localizations (glider-guns). A remarkable feature ofthe automaton is the existence of spiral glider-guns, a discrete analog of aspiral wave that splits intolocalizedwave-fragments (gliders) at some dis-tance from the spiral tip. It is demonstrated that the rich spatio-temporaldynamics of interacting traveling localizations and their generators canbe used to implement computation, namely manipulation with signals,binary logical operations, multiple-value operations, and finite-state ma-chines.

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