More Snowflake Stuff

This is more a philosophical question than a puzzle, so apologies in advance for wasting bandwidth - but with the recent talk about snowflakes, it got me to thinking about something I've wondered for awhile: Most snowflakes show a six-way symmetry (or a lot of them, at least), and most of these have six 'arms' which are remarkably similar to each other. But Snowflake 1 has one style of arms, and snowflake 2 has another style, yet all 6 of a given snowflake's arms are remarkably similar.

The question is, when water vapor molecules are condensing out of the air to build the snowflake, how do they know where to condense? IOW, howcome arm 2 of snowflake 1 is almost an exact copy of arm 1 of snowflake 1, and not like, say, an arm of snowflake 2? They're just crystals, after all.

Cheers!

Different conditions of pressure, humidity and temperature cause ice crystals to grow into different shapes. Some conditions cause thin needle-like shapes and other conditions cause short fat ones. As the flake gets blown around the cloud the conditions vary with time, so each new ice layer is different from the one below it. Across the width of a single snowflake, however, the conditions will be pretty close to being identical at any instant, so the same types of crystal shapes grow

I believe it's a statistical thing. Salt crystals grow in cubes, not because new sodium and clorine atoms know to adhere to the six surfaces at an equal rate, but because it's statistically 'impossible' for more to adhere to one face than another. The cube doesn't become round because new ions don't adhere at the corners.

Now we apply the standard approximation, 'everything else is just like cubes'.

Hexagonal symmetry is maintained because the number of water molecules is so large that it would be statistically impossible for one arm to grow visibly fater than the others. The complex shape is maintained because the probability of new water molecules sticking is highly nonuniform over the flake (for example, the probability of new molecules sticking at the edges must be vastly higher than the probability of them sticking on the faces or snowflakes wouldn't be so thin).

It's got to be something like that.

George