Simple networks on complex cellular automata: From de Bruijn diagrams to jump-graphs

TL;DR

This paper reviews network-based methods derived from cellular automata rules, such as de Bruijn diagrams and jump-graphs, to analyze complex dynamics like pattern emergence, self-organization, and chaos.

Contribution

It provides a comprehensive overview of how various network representations can elucidate the properties of cellular automata dynamics, focusing on traveling self-localizations.

Findings

Networks reveal pattern formation and self-organization.

Jump-graphs help understand reversibility and chaos.

Self-localizations are key to network structure.

Abstract

We overview networks which characterise dynamics in cellular automata. These networks are derived from one-dimensional cellular automaton rules and global states of the automaton evolution: de Bruijn diagrams, subsystem diagrams, basins of attraction, and jump-graphs. These networks are used to understand properties of spatially-extended dynamical systems: emergence of non-trivial patterns, self-organisation, reversibility and chaos. Particular attention is paid to networks determined by travelling self-localisations, or gliders.