EFFECTIVE MULTIFRACTAL SPECTRUM OF A RANDOM-WALK

An infinite uniform random walk on a lattice is a monofractal, but any finite-length random walk contains both bulk and surface, which canno t be easily distinguished, but which have intrinsically different frac tal dimensions. When we examine both the bulk and the surface using th e sandbox method, we obtain a reproducible effective multifractal spec trum that is independent of the length of the random walk. This techni que allows us to calculate the multifractal spectrum for short (approx imately 10 000 base pairs) DNA-sequence data sets. We show that human beta globin DNA is significantly different from its length-, base-freq uency-, and dimer-frequency-matched controls.