Diffusion-Limited Aggregation (DLA) is what results when you start with a seed particle and then release another particle from far away that moves according to Brownian motion. When it hits the seed, it attaches. You release another particle moving according to Brownian motion, and wait for it to hit the structure and attach somewhere. You keep doing this. The resulting structure is DLA. As mentioned in the Wikipedia entry, this appears naturally in certain mineral deposits and in dielectric breakdown. Here is a fun java simulation. Apparently, this phenomenon is still not well understood. At the colloquium about this I went to yesterday, the speaker said he had been working on this stuff for 20 years and had made little progress. The hope is that they can exploit the connection between DLA and Schramm-Loewner Evolution (SLE)  to better understand the phenomenon, e.g., are such structures self-similar.

Vincent Andres writes:

Here is an interesting book on the topic (by an ex-colleague).





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