Evolving localizations in reaction-diffusion cellular automata

TL;DR

This paper explores how mobile and stationary localizations emerge in hexagonal reaction-diffusion cellular automata through evolutionary algorithms, revealing conditions favoring their formation and potential applications in spatial computing.

Contribution

It introduces an evolutionary approach to breed local transition functions supporting mobile localizations in reaction-diffusion cellular automata and analyzes their relation to quasi-chemical systems.

Findings

Mobile localizations likely emerge with limited diffusion of one reagent.

Few molecules are needed to amplify traveling localizations.

Stationary localizations involve balanced quasi-chemical species.

Abstract

We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in each one state. We employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. Analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules is required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. Techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems.