Diffusion Part 3: Diffusion-Limited Aggregation

This is certainly my most aesthetically-pleasing simulation so far. Give it a click!

This is a momentous occasion in your life, you’ve just seeded your very first Brownian tree! The simulation above contains random walkers and one simple rule: wherever you click, a seed is planted that causes any particle that collides with it to stick in place. Any subsequent particle that collides with one that is already stuck becomes part of the tree, and is itself stuck in place. The result is a fractal tree that is named after the random motion from which it emerges. This process is called Diffusion-limited aggregation, and occurs naturally in a variety of contexts including electroplating, mineral deposits, and dielectric breakdown. The latter is particularly interesting; it occurs when an electrically-insulating material is subjected to a high enough Voltage that it suddenly and violently becomes conductive. This is precisely what happens when a lightning strike occurs, which is why bolts of lightning form Brownian trees through the air, and why victims of lightning strikes often have scarring in the shape of Brownian trees.

Code adapted from the work of Daniel Shiffman.