Diffusion-Limited Aggregation

Snow - An Explanation of the Shape

From a small seed, tiny bulges form in the six directions preferred by the crystal.
These grow into needle-shaped arms, the arms in turn develop bulges from which side branches grow, the side branches themselves sprout tiny side branches, and so on.
The specific branch thickness and spacing are very sensitive to small changes in temperature, humidity, and pressure.
Since these conditions are almost constant over the size of a snowflake, its six branches grow in a nearly identical fashion.
The atmosphere in a snow cloud is turbulent over the scale of meters, so each flake takes a different route through the cloud and encounters different sequences of conditions for its growth.
If we knew how to read it, each snowflake contains a record of the sequence of conditions through which it grew.

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