Operating binary strings using gliders and eaters in reaction-diffusion cellular automaton

TL;DR

This paper explores how binary strings can be manipulated using gliders and eaters in a reaction-diffusion cellular automaton, demonstrating potential for chemical computing applications.

Contribution

It introduces a method to encode and transform binary strings within a reaction-diffusion cellular automaton using glider-eater interactions, advancing chemical computing models.

Findings

Binary strings can be encoded in eater states.

Sequences of gliders can implement binary operations.

Potential for chemical computer design using reaction-diffusion automata.

Abstract

We study transformations of 2-, 4- and 6-bit numbers in interactions between traveling and stationary localizations in the Spiral Rule reaction-diffusion cellular automaton. The Spiral Rule automaton is a hexagonal ternary-state two-dimensional cellular automaton -- a finite-state machine imitation of an activator-inhibitor reaction-diffusion system. The activator is self-inhibited in certain concentrations. The inhibitor dissociates in the absence of the activator. The Spiral Rule cellular automaton has rich spatio-temporal dynamics of traveling (glider) and stationary (eater) patterns. When a glider brushes an eater the eater may slightly change its configuration, which is updated once more every next hit. We encode binary strings in the states of eaters and sequences of gliders. We study what types of binary compositions of binary strings are implementable by sequences of gliders brushing an eater. The models developed will be used in future laboratory designs of reaction-diffusion chemical computers.