Analytic Theory of Fractal Growth Patterns in 2 Dimensions

Details Analytic Theory of Fractal Growth Patterns in 2 Dimensions Analytic Theory of Fractal Growth Patterns in 2 Dimensions

2000-03-03

arxiv.org/abs/cond-mat/0003044v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 figures

Scientific paper

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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