IMPROVED MULTIFRACTAL BOX-COUNTING ALGORITHM, VIRTUAL PHASE-TRANSITIONS, AND NEGATIVE DIMENSIONS

Most algorithms for numerical multifractal analysis rely on some evalu ation of related scaling laws. We present a self-consistent way to obt ain from a partition sum S-q(l) the spectrum of singularities f(alpha) and its confidence intervals. With this tool we gain insights into th e intricacies of fixed-size algorithms and propose consequent improvem ents. We give a numerical analysis of the Henon attractor which displa ys theoretical predictions of a phase transition.