Asynchronism Induces Second Order Phase Transitions in Elementary Cellular Automata

TL;DR

This paper demonstrates that introducing asynchronism in elementary cellular automata induces second-order phase transitions, which can be classified within known universality classes like directed percolation.

Contribution

It provides a detailed analysis of how asynchronous updating leads to phase transitions in cellular automata, linking computational models to statistical physics universality classes.

Findings

Asynchronism causes second-order phase transitions in cellular automata.

Transitions belong to directed percolation or parity conservation universality classes.

Monte-Carlo simulations reveal qualitative behavioral changes with varying synchrony rates.

Abstract

Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. For some particular rules, varying the synchrony rate continuously produces a qualitative change in the behaviour of the cellular automaton. We investigate the nature of this change of behaviour using Monte-Carlo simulations. We show that this phenomenon is a second-order phase transition, which we characterise more specifically as belonging to the directed percolation or to the parity conservation universality classes studied in statistical physics.