Deterministic Avalanches on a Branching Koch Curve

Abstract

A sandpile model on a branching Koch curve is presented to study the self-organized criticality. The model is defined as a variant of the Bak, Tang and Wiesenfeld model on a branching Koch curve with a preferred direction. The avalanch process is exactly solved on the lattice. The temporal evolution of avalanches is shown to occur self-similarly. It is found that the distribution function of event magnitudes I shows exactly the scaling behavior of “1⁄I”. It is also shown that the distribution function N_s of size s of avalanches scales as N_s≈s^{−log6⁄log2}.