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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?

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?

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

Update Tree-like structures appear often as limits of sequences of metric spaces (say, asymptotic cones or boundaries of metric spaces). I wonder if similar structures 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?

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?