Multifractal Decompositions of Digraph Recursive Fractals

We prove that the multifractal decomposition behaves as expected for a family of sets K known as digraph recursive fractals, using measures ^ of Markov type. For each value of a parameter a between a minimum amin and maximum amax, we define 'multifractal components' K^ a) of K, and show that they are fractals in the sense of Taylor. The dimension /(or) of K^ is computed from the data of the problem. The typical concave 'multifractal /(<*)' dimension spectrum curve results. Under appropriate disjointness conditions, the multifractal components K are given by l i M , y I e|o logdiam Be(x) ) that is, K consists of those points where /i has pointwise dimension a.