Self-Organized States in Cellular Automata: Exact Solution

TL;DR

This paper presents an exact method to determine the structure, fluctuations, and state probabilities of self-organized steady states in cellular automata using Markovian dynamics, demonstrated on a sand pile model.

Contribution

It introduces a novel explicit approach to analyze self-organized states in cellular automata based on their Markovian properties.

Findings

Exact solutions for state probabilities and fluctuations

Application to a natural sand pile model

Demonstration of the method's effectiveness

Abstract

The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {\em explicitly} from their Markovian dynamics. The method is shown on an example of a natural sand pile model with a gradient threshold.