Sandpile

The Abelian sandpile model (ASM) is the more popular name of the original Bak–Tang–Wiesenfeld model (BTW). The BTW model was the first discovered example of a dynamical system displaying self-organized criticality.

How it works: Grains of sand are added one at a time to a grid. When a pile becomes too high (≥4 grains), it topples, distributing grains to neighboring cells. This can trigger avalanches that cascade across the grid.

Self-organized criticality: Without external tuning, the system naturally evolves to a critical state where avalanches of all sizes occur, following a power-law distribution. This behavior appears in many natural phenomena: earthquakes, forest fires, stock market crashes, and neural activity.