  Diffusion Limited Aggregation (DLA) is a model of fractal growth that was
introduced in 1981 and had since attained a paradigmatic status due to its
simplicity and its underlying role for a variety of pattern forming processes.
Despite tremendous efforts there is no theory to compute the fractal dimension
of DLA from first principles. In this Letter we offer such a theory for fractal
growth patterns in two dimensions, including DLA as a particular case. In this
theory the fractal dimension of the asymptotic cluster manifests iteself as a
renormalization exponent observable already at very early growth stages. Using
early stage dynamics we compute 1.6896<D<1.7135, and explain why traditional
numerical estimates converged so slowly. We discuss similar computations for
other fractal growth processes in 2-dimensions.
