DIVISIBLE SANDPILE ON SIERPINSKI GASKET GRAPHS

Sandpile model on the Sierpinski gasket fractal.

We investigate the sandpile model on the two-dimensional Sierpinski gasket fractal. We find that the model displays interesting critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes, and topplings and calculate the associated critical exponents t51.5160.04, a51.6360.04, and m51.3660.04. The avalanche size distribution shows power-law behavior modulated by lo...

Sampling on the Sierpinski Gasket

Distribution of consecutive waves in the sandpile model on the Sierpinski gasket

The scaling properties of waves of topplings of the sandpile model on a Sierpinski gasket are investigated. The exponent describing the asymptotics of the distribution of last waves in an avalanche is found. Predictions for scaling exponents in the forward and backward conditional probabilities for two consecutive waves are given. All predictions were examined by numerical simulations and were ...

A 2-parametric generalization of Sierpinski gasket graphs

Graphs S[n, k] are introduced as the graphs obtained from the Sierpiński graphs S(n, k) by contracting edges that lie in no triangle. The family S[n, k] is a previously studied class of Sierpiński gasket graphs Sn. Several properties of graphs S[n, k] are studied in particular, hamiltonicity and chromatic number.

Random walks on the Sierpinski Gasket

The generating functions for random walks on the Sierpinski gasket are computed. For closed walks, we investigate the dependence of these functions on location and the bare hopping parameter. They are continuous on the infinite gasket but not differentiable. J. Physique 47 (1986) 1663-1669 OCTOBRE 1986, Classification Physics Abstracts 05.40 05.50 1. Preliminaries and review of known results. C...