Spontaneous Emergence of Spatio-Temporal Order in Class 4 Automata

TL;DR

This paper demonstrates that a class 4 cellular automaton can spontaneously develop regular, periodic patterns in both space and time from disordered initial states, revealing new insights into emergent order in discrete systems.

Contribution

It provides the first evidence of spontaneous emergence of spatio-temporal order in a specific cellular automaton rule, expanding understanding of pattern formation from disorder.

Findings

Patterns become periodic in space and time from disordered states

First evidence of spontaneous spatio-temporal order in class 4 automata

Demonstrates emergence of order in a discrete rule-based system

Abstract

We report surprisingly regular behaviors observed for a class 4 cellular automaton, the totalistic rule 20: starting from disordered initial configurations the automaton produces patterns which are periodic not only in time but also in space. This is the first evidence that different types of spatio-temporal order can emerge under specific conditions out of disorder in the same discrete rule based algorithm.