Comparative study of large-scale Laplacian growth patterns

We investigate the scaling of cluster size with mass for our simulations of diffusion-limited aggregation (DLA) clusters and dielectric-breakdown (DB) clusters of 106 particles grown on a square lattice, and DLA clusters of 106 particles grown off lattice. We find that the mass distribution and scaling behavior for the on-lattice DB model are intermediate between those for the on-lattice DLA model and the off-lattice DLA model. We take this as evidence that signatures of lattice anisotropy and the microscopic kinetics of attachment are both manifest at large length scales.