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. We extend the existing theory of waves to the present case. This leads to an exact value for the exponent τw which describes the distribution of wave sizes: τw=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 τ that determines the distribution of avalanche sizes: τ=1+τw=ln(27/5)/ln 3. Our predictions are in good agreement with the numerical results.