Self-Organized Criticality
A sandpile that tunes itself to the edge of catastrophe — avalanches of every size, following a power law.
The Bak-Tang-Wiesenfeld sandpile (1987) is the canonical model of self-organized criticality. The rule is simple: if any cell holds 4 or more grains, it topples — redistributing one grain to each of its four neighbors. Grains at the edge fall off the pile.
Drop grains at the center one at a time and watch. Initially little happens. As the pile builds, small avalanches begin. Eventually the system reaches a critical state where avalanches of all sizes occur — the histogram of avalanche sizes follows a power law, the hallmark of criticality. No fine-tuning required: the system finds the critical point on its own. Earthquakes, forest fires, and neural cascades show the same statistics.