Effect of Starting Location on Clusters Formed by Diffusion-Limited Aggregation

Louise Coltharp

Abstract


This study examines the effect of the starting location on particles that undergo diffusion-limited aggregation. Proposed in 1981 by T.A. Witten Jr. and L.M. Sander, diffusion-limited aggregation (DLA) is one of the primary models of diffusion. DLA is a growth process in which particles form a cluster by undergoing a random walk and attaching themselves one-by-one to the cluster, which is initialized by a central seed particle. This model of diffusion explains many patterns occurring in nature, such as coral growth, dielectric breakdown, electro-deposition and others. Frequently when DLA is modeled computationally, the particle’s starting location prior its random walk is on the perimeter of a circle, with a radius that is larger than the size of the cluster. However, what has been studied less is selecting a random unoccupied point for the starting location of the particle, including points within the perimeter of the cluster. To examine the effects of the different starting locations, we have created a two- dimensional off-lattice computational simulation of DLA. By using measurements such as radius of gyration, fractal dimension and lacunarity, we can characterize and compare the clusters formed. Since research on DLA is heavily reliant on computational models and simulations, our results could shed light on whether the starting locations of the particles need to be more explicitly considered for certain physical examples of DLA.


Keywords


Diffusion-limited Aggregation; Starting Location; Cluster Growth

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