Self-organized criticality — power-law avalanche distribution P(s) ~ s⁻¹ without tuning
The BTW sandpile (Bak, Tang, Wiesenfeld 1987) evolves under a simple rule: when a cell reaches height ≥4, it topples, passing one grain to each neighbor. The system self-organizes to a critical state with no parameter tuning. Avalanche sizes follow P(s) ~ s^(−1), spanning all scales — a signature of criticality. SOC has been proposed as a mechanism for 1/f noise, earthquakes (Gutenberg-Richter), and neural avalanches.