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Convergent calculation of the asymptotic dimension of diffusion limited aggregates: Scaling and renormalization of small clusters

2000/08/03 by Benny Davidovitch, Anders Levermann, Itamar Procaccia · 3 citations
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.62.r5919

arxiv created 2000/08/03 · openalex publication_date 2000/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Diffusion limited aggregation (DLA) is a model of fractal growth that had attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. We present a convergent calculation of the fractal dimension D of DLA based on a renormalization scheme for the first Laurent coefficient of the conformal map from the unit circle to the expanding boundary of the fractal cluster. The theory is applicable from very small (2-3 particles) to asymptotically large (n-->infinity) clusters. The computed dimension is D=1.713+/-0.003.

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