UNCOVERING FIBONACCI SEQUENCES IN THE FRACTAL MORPHOLOGY OF DIFFUSION-LIMITED AGGREGATES

We use the wavelet transform microscope to explore the internal frozen geometry of large mass off-lattice diffusion limited aggregates (DLA). We show that the statistical self-similarity of these aggregates is intimately related to the existence of a predominant structural five-fold symmetry. We report on the discovery of Fibonacci sequences in the DLA morphology, with a branching ratio which converges asymptotically to the golden mean. We comment on a tentative interpretation of the geometrical complexity of DLA clusters as a "quasifractal" architecture, intermediate between the well-ordered hierarchy of snowflakes and the disordered structures of random aggregates.