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 or boundaries 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?