Iterative conformal mapping approach to diffusion-limited aggregation with surface tension effect

Abstract

We present a simple method for incorporating the surface tension effect into an iterative conformal mapping model of two-dimensional diffusion-limited aggregation. A curvature-dependent growth probability is introduced and the curvature is given by utilizing the branch points of a conformal map. The resulting cluster exhibits a crossover from compact to fractal growth. In the fractal growth regime, it is confirmed, by the conformal map technique, that the fractal dimension of its area and perimeter length coincide.