Sandpiles on a Sierpinski gasket

Abstract

We perform extensive simulations of the sandpile model on a Sierpinski gasket. Critical exponents for waves and avalanches are determined. We extend the existing theory of waves to the present case. This leads to an exact value for the exponent tau(w) which describes the distribution of wave sizes: tau(w) = ln(9/5)/ln 3. Numerically, it is found that the number of waves in an avalanche is proportional to the number of distinct sites toppled in the avalanche. This leads to a conjecture for the exponent tau that determines the distribution of avalanche sizes: tau = 1 + tau(w) = ln (27/5)/ln 3. Our predictions are in good agreement with the numerical results. (C) 1998 Elsevier Science B.V. All rights reserved.