Directed recursion models for fractal growth

Abstract

Fractals constructed by recursive processes are introduced to model growth phenomena. These fractals are simultaneously directed and self-similar in analogy with patterns growing under diffusion-limited conditions. The multifractal nature of the harmonic measure associated with Laplacian interfaces is qualitatively interpreted using the models. Calculation of the largest singularity exponent allows one to make conclusions about the behaviour of diffusion-limited aggregates.