Self Organized Criticality in Digging Myopic Ant Model

Abstract

We demonstrate the phenomenon of self organized criticality (SOC) in a simple random walk model described by a random walk of a myopic ant. The ant acts on the underlying lattice aiming at uniform digging of the surface but is unaffected by the underlying lattice. In 1-d, 2-d and 3-d we have explored this model and have obtained power laws in the time intervals between consecutive events of `digging'. Being a simple random walk, the power laws in space translate to power laws in time. We also study the finite size scaling of asymptotic scale invariant process as well as dynamic scaling in this system. This model differs qualitatively from the cascade models of SOC.