Dimension of fractal growth patterns as a dynamical exponent

  • Davidovitch B
  • Procaccia I
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Abstract

We consider a conformal theory of fractal growth patterns in two dimensions, including diffusion limited aggregation (DLA) as a particular case. In this theory the fractal dimension of the asymptotic cluster manifests itself as a dynamical exponent observable already at very early growth stages. Using a renormalization relation we show from early stage dynamics that the dimension D of DLA can be estimated, 1.69

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Authors

  • Benny Davidovitch

  • Itamar Procaccia

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