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 logarithmic oscillations which can be related to the discrete scale invariance of the underlying lattice. Such a distribution can be formally described by introducing a complex scaling exponent t*[t1id , where the real part t corresponds to the power law and the imaginary part d is related to the period of the logarithmic oscillations. @S1063-651X~96!03907-4#