Imagine a tall pile of sand balanced precariously in a narrow column over a flat surface. The pile will be unstable, sending a wave of grains of sand propagating outward. The base of the pile will enlarge, reducing the slope of its upper surface until the pile stabilizes and sand stops moving. This is not to say the sand is far from instability. A single extra grain placed in an arbitrary location might be enough to cause another chain reaction through part or all of the pile.
Although physical grains of sand move continuously into an infinity of possible states, in certain circumstances it may be warranted to consider a discrete model with a finite number of positions. A 1987 paper, "Self-Organized Criticality: An explanation of the 1/f noise", by Bak, Tang and Weisenfeld proposed such a model, which has since developed into the abelian sandpile. The authors use the model as an explanatory framework for the widespread phenomenon of "pink noise," where power spectral density and noise frequency are more or less inversely related. Later contributions by Dhar and many others have expanded and generalized the theory.
The scripts here allow the modeling and display of abelian sandpiles on various tessellating grids. Further, certain optimizations can be made when both the grid and the initial configuration share one or more symmetries. These optimizations have been made in wedge_hex_grid.sage and wedge_square_grid.sage.