Dimension of fractal growth patterns as a dynamical exponent

We consider a conformal theory of fractal growth patterns in two dimensions , including diffusion limited aggregation (DLA) as a particular case. In th is theory the fractal dimension of the asymptotic cluster manifests itself as a dynamical exponent observable already at very early growth stages. Usi ng a renormalization relation we show from early stage dynamics that the di mension D of DLA can be estimated, 1.69 < D < 1.72. We explain why traditio nal numerical estimates converged so slowly. We discuss similar computation s for other fractal growth processes in two dimensions.