SANDPILES ON A SIERPINSKI GASKET

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