Forest Fire SOC

Self-Organized Criticality & Power Laws

Rules (Drossel-Schwabl 1992):
1. Empty → Tree: prob p
2. Tree → Fire: prob f (lightning)
3. Fire neighbor → burn all

SOC: p/f → ∞ slow limit
P(s) ∼ s^{−τ}, τ≈1.2

Growth prob p×10⁻³ 3

Lightning f×10⁻⁵ 1

Grid size N 100

fires: 0 mean size: —

Drossel-Schwabl forest fire is a paradigm SOC model. Growth (p) slowly adds trees, rare lightning (f≪p) ignites them, and fire propagates like percolation. When p/f→∞, the system self-tunes to criticality: fire sizes follow a power law — no characteristic scale. The exponent τ≈1.2 is a universal property of 2D forest fires.