UNIVERSALITY AND SCALE-INVARIANT DYNAMICS IN LAPLACIAN FRACTAL GROWTH

The individuation of the scale invariant dynamics in Laplacian fractal growth processes, like diffusion-limited aggregation (DLA), is an imp ortant problem whose solution would clarify some crucial issues concer ning the origin of fractal properties and the identification of univer sality classes for such models. Here, we develop a real space renormal ization group scheme to study the dynamic evolution of DLA in a restri cted space of relevant parameters. In particular, we investigate the e ffect of a sticking probability P-s and an effective noise reduction p arameter S. The renormalization equations flow towards an attractive f ixed point corresponding to the scale invariant DLA dynamics (P-s = 1 , S similar or equal to 2.0). The existence of a non-trivial fixed po int value for S, shows that noise is spontaneously generated by the DL A growth process, and that screening, which is at the origin of fracta l properties, persists at all scales.