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The Mullins-Sekerka instability effect explains how complex, flowerlike crystal structures that we see in snowflakes can arise spontaneously from nothing more than freezing water vapor. As snow crystals grow, they use up the water vapor in their immediate surroundings, and it takes a certain amount of time for additional molecules to diffuse through the air to reach the crystal. Snow-crystal growth is therefore said to be diffusion limited, and different regions on a crystal effectively compete for available resources. If a spot on a crystal—for example, one of the points on a hexagonal plate—sticks out farther into the air, then water molecules will preferentially collect on that point, simply because the diffusion distance is slightly shorter. With a slightly greater source of material, the point will grow a bit more rapidly, which in turn causes the point to become more pronounced. The result is a positive feedback that reinforces the effect, so large branches eventually sprout from the six points of a hexagonal snow crystal. With time, numerous side branches may in turn sprout from random bumps or faceted tips on the main arms.
This accounts for the regular patterns we see in snowflakes, but the variation comes from each snowflake’s individual path through the atmosphere during its growth. Random changes in temperature, dust collision, and air pressure determine their unique structure.
(Source: , via hexagonalawarenessproject)