Resistance scaling and random walk dimensions for finitely ramified Sierpinski carpets

Abstract

We present a new algorithm to calculate the random walk dimensionof finitely ramified Sierpinski carpets. The fractal structure isinterpreted as a resistor network for which the resistance scalingexponent is calculated using Mathematica. A fractal form of theEinstein relation, which connects diffusion with conductivity, isused to give a numerical value for the random walk dimension.