Visualization of a 3D DLA cluster

A three-dimensional DLA cluster

A popular undergraduate course at MIT is Introduction to Modeling and Simulation. The majority of the grade depends a simulation term project, that is done in collaboration with an MIT research group. Our group has supervised several students, and in Spring 2004, and Jacqueline Yen was supervised by Kevin Chu on simulating a three-dimensional diffusion-limited aggregration problem. The simulation starts with a single particle seed. Other particles then do random walks in the vicinity of the seed, and when they collide with the seed, they stick to it, to create a growing cluster of particles. The process continues in this fashion, and since particles which protrude more are more likely to get hit by a random walker, they grow preferentially, resulting in a beautiful fractal shape. Shapes such as this can often naturally occur in mineral deposition processes.

In Spring 2005, I gave at talk on fractals and chaos at the Simple Person's Applied Math Seminar. I wanted to give an example of a physical process resulting in a fractal shape, so I got Jacqueline's code from Kevin, and rendered a three-dimensional movie of it using the excellent freeware raytracer POV-Ray. Due to the enormous complexity of the clusters, I made use my department's Beowulf cluster to carry out the rendering process. During the movie, the cluster is rotated, to give a better perception of depth. The image above shows the cluster after 126,993 particles have aggregated.

See the resulting movie (QuickTime format, 97 MB). The nine images below are snapshots during cluster growth.

Snapshot 1 Snapshot 2 Snapshot 3
Snapshot 4 Snapshot 5 Snapshot 6
Snapshot 7 Snapshot 8 Snapshot 9