Image from SnowCrystals.com

You may or may not know that I work for a Major Outdoor Retailer. Regardless, in the retail world, winter begins in, oh, August. But being a snowboarder, when they start busting out the boards and skis in my store, I start thinking dreamily of days on the slopes, or gliding through quiet forests. I probably won’t be doing much of it for some time, but hey, a girl can dream!

That being said, let’s talk about the thing that makes winter worthwhile: snow. And let’s all take a moment to pray to the snow gods that we get dumped on this season (sorry, Southern Hemisphere friends!).

Done? Good. Oh wait, I’m supposed to be an atheist. Oh well!

Fight Club says it best: “You are not a beautiful and unique snowflake.” But this begs the question: what is so unique and beautiful about snowflakes, anyway? Is it true that each one is unique? And if so, why?

Snowflakes are crystals made of ice. Crystals are solid structures where all the molecules, atoms, or ions within are arranged in an orderly, repeating pattern in all three dimensions. Usually the structure depends upon the structure of the molecule or atom or ion, and snowflakes are no different. Think about your average molecule of water, and its chemical formula: H₂O. This means that there are two hydrogen atoms attached to one oxygen atom, like so:

Image from Wikipedia

Now if you arrange this atom repeatedly in a crystalline structure, the structure is going to be very hexagonal: all snowflakes are, in fact, six-sided (but it’s easier to cut the 8-sided ones out of paper…). Now snowflakes aren’t just frozen raindrops—that’s our favorite weather phenomenon, sleet. Snowflakes are crystals formed when water vapor freezes. The patterns on snowflakes form because corners stick out farther than everything else, making the distance water vapor molecules have to travel less. Then you keep building on those corners, and it becomes, well, all a bit fractal.

Different sizes and shapes of snowflakes form at different temperatures: if you live anywhere where it snows, you’re well aware of this. When it’s very cold out, you get very small snowflakes. The warmer it gets, the larger they get, until it’s right at freezing and you’re getting smacked in the face by wet snowballs falling from the sky (or maybe that was just in Ithaca). This is dependent on the amount of water vapor that can actually exist in the air at a given temperature: the colder it gets, the less water vapor there is.

So we’ve covered the basics of snowflakes now, so what about the ultimate question? How unique is each snowflake? Well, let’s look at it this way: water is a molecule, not an elementary particle. Not every water molecule is alike: some water molecules have a different isotope of oxygen in them, or an atom of deuterium (hydrogen with a neutron). A typical small, basic snowflake contains 10¹⁸ water molecules, which is one quintillion molecules. How much is a quintillion? Well, if you had a quintillion pennies and you laid them out flat, they’d cover the surface of the earth twice. If you put them in a cube, Mt. Everest would only be 1700 feet taller than the cube. A quintillion is a lot.

We’ve already got plenty of potential for difference in that number alone. With that many molecules, the probability that two snowflakes will have the exact same arrangement of the exact same molecules is really, really small. However, there are definitely snowflakes that look alike. The most basic snowflake is just a hexagon, and if you set two of those next to each other, you probably wouldn’t be able to tell the difference without an electron microscope.

For the complex snowflakes, it’s another story entirely. Let’s talk math for a second, and return to a really cool concept you may have learned in high school: combinations and permutations. Say that you have one suit of a deck of cards, the clubs. How many ways can you line up those 13 cards? Well, you have 13 choices for the first slot, and then 12 choices for the next slot, and 11 for the next, and so on down the line. It ends up being 13x12x11x…., or in mathematical notation, 13!, or 13 factorial. 13! comes out to 6,227,020,800. That’s 6 billion. With only 13 cards. So if you have anything like the quintillion molecules described above, and you take that factorial, well, that’s a number that is so far beyond the number of atoms in the universe that it’s incomprehensible. The number of zeros following this number is 249,999,999,999,999,995. That’s a quintillion of zeros. The number of atoms in the observable universe is 10⁸⁰. That’s 80 zeros.

There are nowhere near enough atoms in the universe to create all of the permutations of the snowflake and have a repeat. The odds of two exact snowflakes are so astronomically small that they are effectively zero. Of course, there are only certain patterns that water molecules can combine in, but the order of magnitude is not going to be reduced significantly by taking out the ones that don’t work.

The odds are that we will never see a snowflake that is exactly like another, not in the history of the universe. And if that doesn’t melt your brain, I’m not sure what will.

Sources:

http://www.its.caltech.edu/~atomic/snowcrystals/–SnowCrystals.com is run by CalTech. Amused? Because I am.

http://en.wikipedia.org/wiki/Crystal

http://kokogiak.com/megapenny/eighteen.asp

http://www.mathsisfun.com/combinatorics/combinations-permutations.html

http://en.wikipedia.org/wiki/Observable_universe

http://www.wolframalpha.com/–I did all my calculations for this post using this wonderful computational engine.