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

Diffusion limited aggregation (DLA) is a model of fractal growth that had a ttained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. We present a convergent calcul ation of the fractal dimension D of DLA based on a renormalization scheme f or 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) clus ters. The computed dimension is D = 1.713 +/- 0.003.