THE INTERPRETATION AND MEASUREMENT OF THE F(ALPHA) SPECTRUM OF A MULTIFRACTAL MEASURE

The authors analyse the growth probability distribution for differential limited aggregates (DLA) in terms of its f(α) curve, and f and α computed independently as generalized entropies, using data from 10 clusters of 10000 to 100000 particles. The growth probability is obtained by solving the Laplace equations numerically with a hierarchical method which improves accuracy and speed. Two additional methods are used to compare results for DLA clusters and for a few objects with simple geometry and known f(α) spectrum. These comparisons reinforce their results for the part of the DLA spectrum corresponding to q0. They also bring to light some unexpected features for q-0.1, which suggest a non-universality of the scaling exponents in this region in two dimensions.