How to Build a Snowflake

Jan. 18, 2008 -- Two mathematicians have for the first time created a computer simulation that generates realistic three-dimensional snowflakes -- although even they aren't sure how it works.

"We know surprisingly little about how ice crystals grow," said Caltech physicist Ken Libbrecht, who is considered a leading expert in snow crystal physics.

Figuring out some of the details could perhaps teach physicists a lot about how nature "self-assembles" complex structures -- a trick that nano-engineers have been trying to learn in recent years, he said.

Mathematicians Janko Gravner of the University of California at Davis and David Griffeath of the University of Wisconsin-Madison avoided the old approach of virtually building the snow crystals molecule-by-molecule.

Instead, they used virtual 3-D cells much larger than water molecules, which behave according to the same physics thought to control crystal growth.

"This is kind of an intermediate approach," said Gravner. He and Griffeath created their virtual cells -- called cellular automata -- to be one cubic micron in size.

At that scale the cells, about the size of a speck of dust, mimic the physics of water vapor and crystalline growth.

They then ran the model many times to see what happened when they tweaked with temperatures and vapor pressures. The result was a wide variety of snow crystals -- including the complicated and stunning six-sided star crystals. Each crystal took about 24 hours to build using a powerful desktop computer, Gravner said.