How is it that every snow flake is different from the last?

For this question, we can use the information that we have read in the comment above. It basically just goes down to the very making of the snowflake. The snow builds up differently on the particle it attaches to. The only thing that's the same in each and every snowflake is that it's a six sided ice crystal. The size, shape and other characteristics are determined by the build upon the particle.

Information from http://www.faqkids.com/idx/4/082/article/How_is_snow_made.html