Diffusion Limited Aggregation Clusters
|The clusters grown by Diffusion Limited Aggregation appear to be Fractal
and their statistical properties have generated much scientific interest, even controversy.
The colour coding here relates to time of addition of the growth. You can see that new growth deep inside the cluster is rare - so there is a very wide range in growth probability between sites deep inside and exposed outer tips. The growth probability distribution is believed to be multifractal.
This simulation, as in the original work of Witten and Sander, is based on a square lattice. We now know that leads to cluster arms preferentially growing along the lattice directions, but only when clusters reach about 100,000 particles!
The lattice and its bias can be eliminated, but that is still not the end fo the story ...