Sand Pile Model

Bak–Tang–Wiesenfeld (1987). Grains accumulate until a cell reaches the critical height K — then it topples, distributing one grain to each of its four neighbours. Cascading avalanches of all sizes emerge spontaneously.

Drop Mode

Parameters

Critical height K 4

Drop rate 5/frame

Grid 80×80

Height colours

Statistics

Grains dropped

Last avalanche

Max avalanche

Avalanches

Topple rule: if cell height ≥ K → lose K grains → each of 4 neighbours gains 1 grain. Boundary cells: grains leaving the grid are lost (open boundary).

SOC: the system self-organises to a critical state. Avalanche size P(s) ~ s^−τ (power law, τ ≈ 1.2).