Fractal eigendimensionalities for percolation clusters

Abstract

A recently proposed transfer matrix of fractals (TMF) method is demonstrated on a simple fractal model for clusters at the percolation threshold and used to analyze computer simulation clusters. The eigenvalues of the TMF yield fractal dimensionalities of internal structures (e.g., the backbone), representing corrections to the leading power-law behavior. The eigenvectors contain information on these corrections, as well as on the asymptotic distribution of basic shapes.