Structure of large two-dimensional square-lattice diffusion-limited aggregates : approach to asymptotic behavior

Efficient algorithms have been used to grow large (4×106 site) diffusion-limited aggregation (DLA) clusters on two-dimensional (2D) square lattices. As the clusters grow larger, their envelope grows, from a more or less round shape characteristic of small clusters, through a diamond shape characteristic of clusters containing about 105 sites, into a cross shape. Results from about 25 clusters indicate that the exponents describing the length l and width w of the four major arms vary continuously with M (the cluster mass) over the range 103<M