Multifractals in diffusion and aggregation

The origin of the multifractal features which appear in several random systems is discussed. It is shown that for random fractals the multifractal features in the probability density of the diffusion can be derived rigorously, and therefore its origin can be fully understood. For the growth probabilities in DLA it is shown that a novel self-similar model for the structure of the branches of DLA leads to a multifractal behavior for the positive moments and a logarithmic singularity for the minimum growth probability. This behavior is strongly supported by recent numerical simulations.