Bak–Tang–Wiesenfeld model · self-organized criticality
A grid of cells. Each cell holds some number of grains. When a cell reaches 4 grains, it topples:
it loses 4 grains and each of its 4 neighbors gains 1. Toppling can cascade. The pile finds
a critical slope — not because anything told it to, but because the dynamics work out that way.
Click anywhere on the grid to drop grains.
State
Drop rate
Drop point
Color scheme
Stats
grains dropped0
total topplings0
last avalanche0
largest ever0
Legend
The critical state emerges automatically. No external tuning required. Avalanche sizes follow a
power law — most are small, occasionally one propagates across the whole grid. This is the behavior
Per Bak described in 1987. The pile doesn't choose the critical slope; the critical slope is where
the dynamics settle.
See: entry-164 · Letter 006 to Per Bak