An inverse-cascade model for self-organized critical behavior

We introduce an inverse-cascade model to explain self-organized critical behavior. This model is motivated by the forest-fire model. In the forest-fire model trees are randomly planted on a grid, sparks are also dropped on the grid resulting in fires in which trees are lost. In the inverse-cascade model single trees are introduced and these combine to form larger and larger clusters. This is the inverse cascade and gives a power-law (fractal) frequency-size distribution of clusters. Model fires eliminate trees from all cluster sizes but significant numbers of trees are lost only from the largest clusters and this loss terminates the power-law scaling. Finally, our model illustrates important differences between critical and self-organized critical behavior.