Multifractal structure of clusters and growing aggregates

Various phenomena on a given fractal object have different critical behavior. This is related to the underlying multifractal structure of the aggregate. Here we discuss the problem with particular emphasis on a scaling approach which leads to a simple real space renormalization group. A mechanism which generates multifractality, based on a multiplicative process, is also illustrated. The multifractal structure of the incipient infinite cluster in percolation and diffusion limited aggregation is discussed in detail.