Abelian Sandpile Model - A cellular automaton

This model is made up of a grid of square tiles in which each tile can hold 0-3 "grains" of sand.

When a tile reaches 4 grains, it topples, distributing itself out to its four neighbors (up, down, left, right).

Eventually the model will settle, reaching a point where no more tiles will topple, this is the finally produced image.

Animated pile where a grain of sand is dropped onto the center tile repeatedly

A pile containing 2 million grains