Computer simulations of diffusion-limited aggregation processes

Abstract

The diffusion-limited aggregation (DLA) model of Witten and Sander has been used to model a wide variety of physical processes. Here the way in which our picture for the structures generated by DLA models in two dimensions has evolved during the past few years is described. Results from very large scale square-lattice simulations are presented and it is shown how simulations with noise reduction are helping us to understand the effects of anisotropy on the DLA process. It now appears that in the asymptotic (large-mass) limit clusters generated on regular two-dimensional lattices are self-similar fractals with a non-universal fractal dimensionality which is close to but not equal to 1.5. Results are also presented for DLA on two- and three-dimensional percolation clusters.