Block approximations for probabilistic mixtures of elementary cellular automata

TL;DR

This paper explores the use of block approximation methods to analyze the phase diagrams of probabilistic cellular automata with multiple stationary states, providing insights into their complex behaviors and interactions.

Contribution

It introduces an algorithmic implementation of block approximation for systems with multiple stationary states, enhancing the analysis of phase diagrams in probabilistic cellular automata.

Findings

Block approximation effectively captures phase diagram structures.

The method handles multiple absorbing states.

Improves understanding of interactions in complex automata.

Abstract

Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied, making the study of their phase diagrams particularly interesting. The block approximation method, also known in this context as the local structure approach, is a powerful tool for studying the main features of these diagrams, improving upon Mean Field results. This work considers systems with multiple stationary states, aiming to understand how their interactions give rise to the structure of the phase diagram. Additionally, it shows how a simple algorithmic implementation of the block approximation allows for the effective study of the phase diagram even in the presence of several absorbing states.