Computer simulation of the interplay between fractal structures and surrounding heterogeneous multifractal distributions. Applications

For a geometric set A⊂R2 and a mass distribution (measure) μ supported in S⊂R2, being A⊂S, the mass μ(A(ε)) gives account of the interplay between the geometric structure and the surrounding distribution. A computation method is developed for the estimation and corresponding scaling analysis of μ(A(ε)), being A a fractal plane set of Minkowski dimension D and μ a multifractal measure produced by random multiplicative cascades. The method is applied to natural and mathematical fractal structures in order to study the influence of both, the irregularity of the geometric structure and the heterogeneity of the distribution, in the scaling of μ(A(ε)). Applications to the analysis and modeling of interplay of phases in environmental scenarios are given.