title: Dimension of fractal growth patterns as a dynamical exponent
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<D<1.72. We explain why traditional numerical estimates converged so slowly. We discuss similar computations for other fractal growth processes in two dimensions.
authors.affiliation: Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
authors.initials: B
authors.lastname: Davidovitch
authors.initials: I
authors.lastname: Procaccia