Diffusion-Limited Aggregation

Snow

Every child living in climates with winters is fascinated by snowflakes.
Why do they occur in such a vast multitude of forms?
For every snowflake, why does each of the six branches look so like the other five?
Using DLA, we can begin to provide at least qualitative answers to these questions.
First, here are a few of the thousands of snowflake pictures taken by Wilson Bentley, from his wonderful book Snow Crystals.
Here is some basic mechanics of snowflake growth.
To emphasize the relation between DLA and the aggregation of ice crystals, consider Bentley's pictures of frost on a windowpane.
Here is a sketch of how DLA accounts for basic snowflake structure.
Yet nature still has some surprises.
Finally, here are some simulations.

Return to DLA.