How to make dull cellular automata complex by adding memory: Rule 126 case study

TL;DR

This paper shows that adding memory to the chaotic Rule 126 cellular automaton induces complex dynamics, including periodic patterns and glider interactions, expanding its computational capabilities.

Contribution

It introduces a method to enhance cellular automata complexity by incorporating memory, demonstrated through a detailed case study of Rule 126.

Findings

Memory addition leads to complex, periodic patterns in Rule 126.

Glider interactions enable simple computations within the automaton.

Analysis includes mean field theory, basins, and de Bruijn diagrams.

Abstract

Using Rule 126 elementary cellular automaton (ECA) we demonstrate that a chaotic discrete system --- when enriched with memory -- hence exhibits complex dynamics where such space exploits on an ample universe of periodic patterns induced from original information of the ahistorical system. First we analyse classic ECA Rule 126 to identify basic characteristics with mean field theory, basins, and de Bruijn diagrams. In order to derive this complex dynamics, we use a kind of memory on Rule 126; from here interactions between gliders are studied for detecting stationary patterns, glider guns and simulating specific simple computable functions produced by glider collisions.