Diffusion-Limited Aggregation

A simple model of kinetic growth process is Diffusion-Limited Aggregation (DLA), which consists of particles in Brownian motion in a square lattice that "stick" together. In the 1D case, particles are added in random positions with the same height value, which increases at each step. For the 2D case, some subtleties are involved; a particle is released from a randomly selected initial location within a circle of radius . If a particle moves to a location contiguous to an occupied site, then the particle is added to the cluster. Then the cycle repeats, until the particle moves a distance away from the original position in the circle. The cluster has an associated fractal dimension depending on the density of particles.