2000•arXiv (Cornell University)Open access

Analytic Theory of Fractal Growth Patterns in 2 Dimensions

Benny Davidovich, Itamar Procaccia

Abstract

Diffusion Limited Aggregation (DLA) is a model of fractal growth that was introduced in 1981 and had since attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. Despite tremendous efforts there is no theory to compute the fractal dimension of DLA from first principles. In this Letter we offer such a theory for fractal growth patterns in two dimensions, including DLA as a particular case. In this theory the fractal dimension of the asymptotic cluster manifests iteself as a renormalization exponent observable already at very early growth stages. Using early stage dynamics we compute 1.6896

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Key concepts: Fractal, Fractal dimension, Statistical physics, Fractal dimension on networks, Mathematics, Econometrics, Mathematical economics, Fractal analysis