Drop a heap of sand on a grid. Any cell holding four or more grains topples: it passes one grain to each of its four neighbors. That can make neighbors topple in turn, until every cell holds three grains or fewer. Press Play to watch a pile of 10,000 grains settle into a symmetric pattern. Click anywhere to add more grains where you click.

Colors show how many grains a cell holds: pale blue for one, darker for two and three, and red while it still has four or more. Cells with no grains are blank. Grains pushed past the edge fall off the table. The order in which cells topple never changes the final picture, which is why the model is called Abelian, and the shapes it settles into (squares and diamonds of nested lines and curves) have been studied as fractals. If you drop two piles on top of each other the result is not the sum of the two pictures, which is where much of the interest lies.

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