Computing in Spiral Rule Reaction-Diffusion Hexagonal Cellular Automaton

A hexagonal ternary-state two-dimensional cellular automaton is designed which imitates an activator-inhibitor reaction-diffusion system, where the activator is self-inhibited in particular concentrations and the inhibitor dissociates in the absence of the activator. The automaton exhibits both stationary and mobile localizations (eaters and gliders), and generators of mobile localizations (glider-guns). A remarkable feature of the automaton is the existence of spiral glider-guns, a discrete analog of a spiral wave that splits into localized wave-fragments (gliders) at some distance from the spiral tip. It is demonstrated that the rich spatio-temporal dynamics of interacting traveling localizations and their generators can be used to implement computation, namely manipulation with signals, binary logical operations, multiple-value operations, and finite-state machines.