BTW Sandpile — Self-Organized Criticality

BTW Sandpile (Bak, Tang, Wiesenfeld 1987):

Each cell has height z ≥ 0. When z ≥ 4: topple → z−=4, neighbors += 1. Boundary cells lose grains.

Self-organized criticality: the system drives itself to a critical state without parameter tuning. Avalanche sizes follow P(s) ~ s^{−τ} with τ ≈ 1.2.

Colors:
0 = black, 1 = dark, 2 = medium, 3 = bright.
Flash = active toppling during avalanche.