Tell me more ×  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?  share|improve this question Water
crystallizes in a hexagonal lattice, so small snowflakes are
just hexagons. For reasons of surface chemistry that I don't
really understand, water molecules are more likely to attach at
a vertex than in the middle of an edge, so as the hexagons get
large the vertices grow faster than the edges, creating a non-
convex figure with 12 edges. Iterating this procedure (growing
faster at vertices than at edges) gives a snowflake--for a
picture of this, see pg. 884 here: (t