Formation of Space-Time Structure in a Forest-Fire Model

TL;DR

This paper introduces a stochastic forest-fire model with three states and three parameters, revealing diverse space-time structures including spiral fire fronts, phase transitions, and self-organized criticality, with potential applications to excitable systems.

Contribution

The paper develops a comprehensive forest-fire model that captures various complex structures and transitions, combining analytical and simulation approaches.

Findings

Identification of spiral-shaped fire fronts

Observation of percolation-like phase transition

Evidence of self-organized criticality

Abstract

We present a general stochastic forest-fire model which shows a variety of different structures depending on the parameter values. The model contains three possible states per site (tree, burning tree, empty site) and three parameters (tree growth probability $p$, lightning probability $f$, and immunity $g$). We review analytic and computer simulation results for a quasideterministic state with spiral-shaped fire fronts, for a percolation-like phase transition and a self-organized critical state. Possible applications to excitable systems are discussed.