Analytic approach to stochastic cellular automata: exponential and inverse power distributions out of Random Domino Automaton

TL;DR

This paper introduces a stochastic cellular automaton model inspired by earthquakes, deriving nonlinear equations and showing it can produce both exponential and inverse power distribution patterns of clusters.

Contribution

The paper presents an exact analytical framework for a stochastic domino automaton that captures different statistical distributions of avalanches.

Findings

Model reproduces exponential and inverse power cluster distributions.

Derivation of nonlinear equations describing the automaton.

Provides exact relations between average parameters.

Abstract

Inspired by extremely simplified view of the earthquakes we propose the stochastic domino cellular automaton model exhibiting avalanches. From elementary combinatorial arguments we derive a set of nonlinear equations describing the automaton. Exact relations between the average parameters of the model are presented. Depending on imposed triggering, the model reproduces both exponential and inverse power statistics of clusters.