Winter Wonderings: Are No Two Snowflakes Alike?

With hot weather currently making me sweat down here in Australia, it’s nice to fantasise about winter. Everyone’s heard the old adage “No two snowflakes are alike”, but how true is it? Clearly, checking every single snowflake on Earth would be impossible, so how can we be sure? Well, by using mathematics, of course. Complex snowflakes are made up of six symmetrical spokes, each extraordinarily detailed. Each tiny change in these details counts as new design of snowflake, and these small variations result in a staggeringly huge amount of possible combinations. To understand the math, let’s think about a smaller number for a moment. Let’s say you have 15 books—how many possible ways can you arrange them on your bookshelf? You can decide on 15 different spots for the first book, then 14 for the second, 13 for the third, 12 for the fourth…and all the way down to just 1 for the fifteenth book. These numbers are multiplied out to get the number of possible combinations, and although there are only fifteen numbers, multiplying them out gives you 1,307,674,368,000—i.e., over a trillion ways to organise just fifteen books. If you had 100 books, the combinations rocket up to a number a thousand times larger than the total number of atoms in the universe. A complex snowflake easily has one hundred separate features, so the math behind it is similar—the number of possible combinations is enormous, so the probability that there have ever been two identical snowflakes is so small that it’s indistinguishable from zero.

(Image Credit: 1, 2)