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Logic Gates and Complex Dynamics in a Hexagonal Cellular Automaton:
The Spiral Rule
Rogelio Basurto, Paulina A. Leon, Genaro J. Martinez and Juan C. Seck-Tuoh-Mora

In previous works, hexagonal cellular automata (CA) have been studied as a variation of the famous Game of Life CA, mainly for spiral phenomena simulations; where the most interesting constructions are related to the Belousov-Zhabotinsky reaction. In this paper, we analyse a special kind of hexagonal CA, Spiral rule. Such automaton shows a non-trivial complex behaviour related to discrete models of reaction-diffusion chemical media, dominated by spiral guns which easily emerge from random initial conditions. The computing capabilities of this automaton are shown by means of logic gates. These are defined by collisions between mobile localizations. Also, an extended classification of complex self-localization patterns is presented, including some self-organised patterns.

Keywords: Hexagonal cellular automata, Spiral rule, logic gates, localizations, collisions

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