Sandpile model on the Sierpinski gasket fractal

We investigate tile 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 tile associated critical exponents tau=1.51+/-0.04, alpha=1.63+/-0.04, and mu=1.36+/-0.04. The avalanche size distribution shows power-lau behavior modulated by logarithmic oscillations which can be related ro the discrete scale invariance of the underlying lattice. Such a distribution can be formally described by introducing a complex scaling exponent tau*=tau+i delta, where the real parr tau corresponds to the power lau and the imaginary part delta is related to the period of the logarithmic oscillations.