Some Properties of the Derivatives on Sierpinski Gasket Type Fractals

Sampling on the Sierpinski Gasket

Random walks on the Sierpinski Gasket

The generating functions for random walks on the Sierpinski gasket are computed. For closed walks, we investigate the dependence of these functions on location and the bare hopping parameter. They are continuous on the infinite gasket but not differentiable. J. Physique 47 (1986) 1663-1669 OCTOBRE 1986, Classification Physics Abstracts 05.40 05.50 1. Preliminaries and review of known results. C...

Spanning Forests on the Sierpinski Gasket

We present the numbers of spanning forests on the Sierpinski gasket SGd(n) at stage n with dimension d equal to two, three and four, and determine the asymptotic behaviors. The corresponding results on the generalized Sierpinski gasket SGd,b(n) with d = 2 and b = 3, 4 are obtained. We also derive the upper bounds of the asymptotic growth constants for both SGd and SG2,b.

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 lo...

Orthogonal Polynomials on the Sierpinski Gasket

Abstract. The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket (SG) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of polynomials and power series on SG has been developed by one of us and his coauthors. We build on this body of work to construct certain analogs of classical orthogonal polynomials (OP) on S...