A new exact method for obtaining the multifractal spectrum of multiscaled multinomial measures and IFS invariant measures

In this paper we present a new exact method for obtaining the multifractal spectrum of multiscaled multinomial measures and invariant measures associa ted with iterated function systems (IFS). A multinomial measure is shown to be generated as the invariant measure of an associated IFS. Then, the mult ifractal spectrum of the measure is determined by a couple of parametric im plicit equations. This analysis generalizes some results previously obtaine d for the case of single-scaled multinomial measures (e.g., the binomial me asure). A geometric interpretation of this new framework working in the spa ce of codes of the IFS gives new insight into the nature of the multifracta l formalism. This paper extends the results presented in Gutierrez et. al. Fractals 4, (1996) 17-27. (C) 2000 Elsevier Science Ltd. All rights reserve d.