Crosscut analysis of large radial dla: Departures from self-similarity and lacunarity effects.

Abstract

In order to understand better the morphology and the asymptotic behavior in Diffusion-Limited Aggregation (DLA), we studied a large number of very large off-lattice circular clusters. We inspected both dynamical and geometric asymptotic properties via the scaling behavior of the transverse growth crosscuts, ie. the one-dimensional cuts by circles. The emerging picture corresponds qualitatively and quantitatively to the scenario of infinite drift that starts from the familiar five-armed shape for small sizes and proceeds through increasingly tight multi-armed shapes. The transverse crosscuts show quantitatively how the lacunarity of circular clusters becomes increasingly «compact» with size. Finally, we find the transverse-cut dimensions to be in agreement for clusters grown in circular and cylindrical geometry, suggesting that the question of universality is best addressed on the crosscut. © 1995 IOP Publishing Ltd.