A Theory of Fractal Dimensionality for Generalized Diffusion-Limited Aggregation

Abstract

A dimensional consideration is presented to obtain the fractal dimension D of the diffusion-limited aggregates which grow in a space with general dimensionality d s (any number ≧1) through deposition of diffusing particles following trajectories with a fractal dimension d w (Levy flight). We find rigorously D =( d s 2 + d w -1)/( d s + d w -1), which is in excellent agreement with many computer simulation results.