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 cannot be easily distinguished, but which have intrinsically different fractal dimensions. When we examine both the bulk and the surface using the sandbox method, we obtain a reproducible effective multifractal spectrum that is independent of the length of the random walk. This technique allows us to calculate the multifractal spectrum for short (approximately 10 000 base pairs) DNA-sequence data sets. We show that human beta globin DNA is significantly different from its length-, base-frequency-, and dimer-frequency-matched controls.