Maybe try reading the whole post before commenting? I know this one was really long (six whole paragraphs! It’s OK to take a break in the middle if you get tired.), but the end of the post may be especially relevant to you.

Let me try this counter argument that there have been two snowflakes that are exactly the same on a atomic level.

Suppose there is a mole of atom(10^23) in a millimeter of water and say that this is the size of an average snowflake. We make the simplifying assumption that the this represents on the order or the number of different atomic configurations.

The size of antartica is is 14million kilometers. So if we suppose that it snows once a year covering the area of antartica then you get something on the order 1.4 × 10^19. Also suppose that the average age of the earth is measured on the order of billions of years. Add another 9 to the 10^19 and you get 10^28. Of course the number of combinations of 10^23 is much much bigger. But we do get close to it. If you consider the possibility of snow bearing planets you get even closer.

The fact that you get similar configurations on a macroscopic level tends to imply a much smaller search space than is usually assumed.

-opengre

But then, you could say no 2 leaves would ever be identical on the atomic level. Or rocks. Or ice cubes.

Something I’ve always wondered – when snowflakes with apparent symmetry are studied, is the symmetry perfect all or much of the time? The picture above shows perfectly symmetrical dendrites and sectored plates. I can understand that the physical conditions (temperature, pressure etc) are identical across the snowflake when it is being formed, which might result in uniform growth, but if perfect symmetry of shape is often seen, how does the snowflake ‘know’ what is happening to it as a whole so that it can ‘make’ the growth symmetric? If, as I guess, it doesn’t, are such ‘perfect’ snowflakes the exception rather than the rule? Are snowflakes with fractured symmetry seen?