We asked this question among friends and received a variety of answers.
One answer was that there was no further information. Another was that the two snowflakes might differ by one bit. Another was that finding two identical snowflakes would be more meaningful because it would create conversations.
Here’s a longer answer:
Remember the critical distinction between mere “complexity” and “information-bearing sequences.”
Snowflakes carry no information, no matter how many. They perform no function, because their shapes do not conform to an externally specified pattern or set of rules that would enable them to perform any function (like conveying information).
Many StrawMan attacks against ID theory will tend to focus solely on complexity alone and then use examples like snowflakes to debunk the claim that natural processes cannot produce mere complexity. But that is not ID theory, but a Straw Man.
Now, It might TAKE information to CAUSE two snowflakes to have identical shapes, because the undirected physical processes that form them have so many variables that the odds of producing two identical ones naturally are remote. ID theory may infer that intelligent/intentional causation would be required to produce two literally identical snowflakes, if one could calculate the probability of natural forces to produce that pattern twice.
Even then, the odds may be low but not impossibly low, and so the inference they were designed would not be strong. Ten identical snowflakes would produce a stronger inference.
But if the two “snowflakes” were plastic snowflake replicas like those sold in stores around Christmas, then knowing nothing in the physical processes associated with melted plastic congealing requires them to have that shape, coupled with the fact that both conform to the EXTERNALLY SPECIFIED pattern of what we imagine a stylized snowflake looks like, and the odds against a pool of melted plastic just happening to cool in those specific shapes not just once, but twice, would be astronomically remote. Design is obvious in those cases.
Even then, though, those plastic snowflakes contain no information, as they perform no function, not even communication. They simply exist.
Thoughts?