Complex Dynamics in a Hexagonal Cellular Automaton

Abstract

Hexagonal cellular automata (CA) were studied with interest 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 study a special kind of hexagonal CA known as the Spiral rule. Such automaton displays a non-trivial complex behaviour related to discrete models of reaction-diffusion chemical media, dominated by spiral guns that easily emerge from random initial conditions. Computing abilities of Spiral rule automata are shown by means of logic gates, defined by collisions between mobile self-localizations. Also, a more extended classification of complex self-localization patterns is presented, including some self-organized patterns.