Okay, so the crystals tend to follow a 6-sided geometry. Why are snowflakes symmetrical ? Why does one arm have to fall into the exact same configuration as the opposite one? Why not have 6 different arms, all following the same 6-sided geometry? What mechanism communicates between the arms to achieve 6-sided symmetry?
Well, it turns out if you look closely that usually the arms aren't exactly the same. Which is rather a clue: the coordinating mechanism isn't some kind of quantum magic that enables the structure in the centre to determine exactly what the arms are like. Rather, (1) the arms all start out roughly the same because the crystal structure of ice has 6-fold symmetry, and then (2) the way growth happens at any place and any given moment is largely determined by (a) the structure there and (b) the external conditions, which vary as the snowflake is forming because it's being blown around. But because the snowflake is quite small, those external conditions are generally much the same for all six arms; so similar arms + similar conditions for each arm --> similar incremental growth for all arms --> still-similar arms, so the symmetry is preserved as the crystal grows. See, e.g., http://www.ams.org/notices/200504/fea-adam-3.pdf .
