Are no two snowflakes alike?

Everyone’s heard the phrase “No two snowflakes are alike”,but is it true? and if so, how could we possibly know?

Complex snowflakes are made up of six symmetrical spokes, each extraordinarily detailed. If each tiny change in these details counts as new design of snowflake, these small variations result in a staggeringly huge amount of possible combinations.Clearly, checking every single snowflake that has ever fallen on Earth would be impossible. So we turn to mathematics...

To understand the maths  behind this (for those of you who haven't learnt about factorials), let’s think about a smaller number for a moment. Let’s say you have 10 books—how many possible ways can you arrange them on your bookshelf? You can decide on 10 different spots for the first book, then 9 for the second, 8 for the third, 7 for the fourth…and all the way down to just 1 for the tenth book. These numbers are then multiplied out to get the number of possible combinations, and although there are only ten numbers, multiplying them out gives you 3 628 800-i.e., over 3 million ways to organise just ten 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, and because the maths behind the number of different designs of a snowflake is analogous to that othe bookcase example, the number of possible combinations for a snowflake is enormous, so the probability that there have ever been two identical snowflakes is so small that it is indistinguishable from zero.

So, now you know.

Dayla