Laplacian and Effective Resistance Metric in Sierpinski Gasket Fractal

Laplacian operator for functions on fractal field plays a vital role in the study of partial differential equations of nonlinear in fractals. In this paper self-similar fractal Sierpinski gasket is considered with regular harmonic structures, and energy renormalization factor and scaling constant are obtained. Effective resistance presents a metric with which the properties of the fractal and the transmission can be discussed. Hausdorff dimension of Sierpinski gasket fractal is obtained by scaling constant. Spectral dimension of Sierpinski gasket fractal is calculated by using Laplacian and effective resistance metric. Finally the dimensions of the Sierpinski gasket are interpreted.