Avalanche!

Avalanche! is a customization of the CA Framework. It models the phenomenon of cascades in the microstate of a system that may cause changes in the macro-state. For example, adding one grain of sand to a pile may cause an avalanche. This could create a cascade of avalanches. The sizes of avalanches follows the power law.

In this model each patch has a population of sand grains (rice works better). The maximum number of sand grains a patch can contain is num-states. The shade of brown indicates the number of grains of sand contained by a patch. Darker patches have more than lighter patches.

Each time the model is updated, ten patches are chosen at random and a single grain of sand is added to each. If a patch contains more than num-states grains of sand, it transfers one grain to each neighboring patch that has fewer grains of sand. Of course this may cause these patches to overflow onto their neighbors. (Is an infinite recursion possible here?)

The avalanche-plotter histogram shows the numbers of patches containing 0, 1, 2, 3, 4, 5, 6, 7, and 8 patches.

The "avalanche sizes plotter" histogram shows the sizes of the avalanches in terms of the number of subsequent avalanches caused. Note that this follows the Power Law. There are many small avalanches, but the number of large avalanches drops off exponentially.