The Diffusion-Limited Aggregation Model and Geological Pattern Formation

In the original diffusion-limited aggregated (DLA) model of Witten and Sander (1981) ‘particles’, represented by lattice sites, are added, one at a time, to a growing cluster or aggregate of particles via random walk paths starting from outside of the region occupied by the cluster. In the most simple version of the model (Witten and Sander, 1981), a simulation is started by occupying a site in the center of a square or triangular lattice to represent the ‘seed’, ‘growth site’ or ‘nucleation site’. A site far from the cluster is then selected and a random walk is started from the selected site. If the random walker moves too far from the growing cluster, it is terminated and a new random walk is started. If the random walker eventually reaches a site that is the nearest neighbor to a previously occupied site, the random walk is stopped and the unoccupied perimeter site (the last site occupied by the random walker) is filled to represent the growth process. The process of launching random walkers from outside of the region occupied by the growing cluster and terminating them when they wander too far from the cluster or ‘sticking’ them to the growing cluster when they reach an occupied perimeter site is repeated many times to simulate the cluster growth process.