Questioning Received Wisdom.

I was looking at the pieces of coal in the coal scuttle tonight, wondering whether there were two pieces anywhere in the world that were exactly the same. I remembered being told at school that while snowflakes were all of the same general pattern, no two were identical.

I wanted to ask a mathematician whether it was possible that variations on a fixed pattern template could be infinite and allow no repetition. It seemed unlikely to me, and if the mathematician had said that the number of variations was calculable and finite, and that repetition was a random possibility, then the teachers would have been either misguided or lying. Unfortunately, I never knew any mathematicians so I never got to find out.