Logic gates and complex dynamics in a hexagonal cellular automaton: the Spiral rule

TL;DR

This paper analyzes the Spiral rule hexagonal cellular automaton, revealing its complex dynamics, logic gate capabilities, and diverse self-localization patterns, demonstrating its potential for modeling reaction-diffusion systems and computation.

Contribution

It introduces the Spiral rule automaton, demonstrating its complex behavior, logic gate implementation, and classification of self-localization patterns, advancing understanding of reaction-diffusion inspired cellular automata.

Findings

Spiral rule exhibits complex spiral and self-localization patterns.

Logic gates are implemented through collisions of mobile localizations.

Automaton models reaction-diffusion chemical media effectively.

Abstract

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, {\it 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-localisation patterns is presented, including some self-organised patterns.