The Sand Pile Avalanche Model simulates the occurences of avalanches in sand piles and plots the frequencies of the size of these avalanches.  The general shape, size, and growth of a sand pile is easy to model as new sand grains are added.  Although the pile assumes a conical shape, a new grain of sand can trigger an avalanche which causes some number of grains to slide down the side of the cone into new positions.  These avalanches are chaotic and it is nearly impossible to predict if the next grain of sand will cause an avalanche, where that avalanche will occur on the pile, how many grains of sand will be involved in the event, and so on.

The avalanche models have been related to other more chaotic phenomena, such as the frequency and intensity of earthquakes, historical fluctuations in cotton prices, extinction of species, sizes of cities, and solar eruptions.