Advances in symmetric sandpiles
A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed-point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover, we provide a simple closed formula for counting the number of fixed points originated by initial conditions made of a single column of grains. Bounds for the transient length are also given.
sandpiles transient length discrete dynamical systems soc systems fixed point dynamics