Is there a mathematical theory that explains the shape of a snowflake? Why is it not round?


 **Update** Tree-like metric spaces appear often as limits of sequences of metric spaces (say, [asymptotic cones](https://arxiv.org/abs/math/0405030) or  [boundaries](https://homepages.warwick.ac.uk/~masgak/abstracts/qid.html) of metric spaces). I wonder if similar objects can be obtained as shapes minimizing some kind of energy functional. This may lead to new constructions in geometric group theory.


I just saw Igor Rivin's answer which may be what is needed. Perhaps somebody can give a more detailed answer?



Shape of snowflakes
Yes, there is a quite active theory of crystal formation, in which the late Fred Almgren and the very much with us Jean Taylor did groundbreaking work. If you google "ALmgren Taylor dendrites" you will be enlightened. You can read the papers (and papers referring to the papers) -- I think the theory is not so simple.


