Physical Properties of a New Fractal Model of Percolation Clusters

Abstract

We investigate nonrandom, half-random, and random variants of clusters generated by the "squig" process, using renormalization or Monte Carlo methods. Each variant is compared to two-dimensional percolation clusters at criticality from the viewpoints of the fractal dimensionalities of the whole, the backbone, the multiconnected parts, the ring hulls, the backbone links, the shortest paths, and the recurrences of diffusion, hence the fracton dimensionality. The random variant fits very well when its only parameter $s$ is a bit above 0.4.