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Jonathan Erickson

Dr. Dobb's Bloggers

Snowflakes, Snowfakes, and Boy Am I In Trouble Again

January 18, 2008

Sitting here watching my wife shovel snow, I'm wondering why Janko Gravner, a mathematics professor at the University of California-Davis, and David Griffeath, of the University of Wisconsin-Madison, went to all of the trouble of simulating 3-dimensional snowflakes (they call them "snowfakes") when there's plenty of the real stuff being shoveled outside.

 

I'm also wondering what Professor Gravner knows about snowflakes in the first place. To the best of my knowledge it hasn't snowed in Davis, California for a long, long time. Griffeath is another story. Madison, Wisconsin doesn't lack for snow. And finally I'm wondering what it is going to cost me -- I mean really cost me -- for watching my wife shovel snow instead of grabbing another shovel and pitching in.

According to Gravner, no two snowflakes are totally alike, but they can be very similar. But the mystery isn't so much why they're similiar, as much as why they're different. This is a question that's baffled mathematicians for hundreds of years. To come up with an answer, Gravner and Griffeath are modeling 3-D snowflakes by taking into account how flakes form around a nucleus, the temperature, atmospheric pressure, and water vapor density. Rather than trying to model every water molecule, their software divides the space into 3-D pieces 1 micrometer across. The program then takes about 24 hours to produce one "snowfake" on a PC. The algorithms that describe how they go about all this are presented in their paper Modeling Snow Crystal Growth III: Three-Dimensional Snowfakes. At their Snowfakes page, Gravner and Griffeath reference source code to their "Gravner-Griffeath 2d Snowfake Simulator" program (although it wasn't currently posted), provide videos (avi files) of snowflakes growing, and present some stunning photos of simulated snowflakes. Interestingly, Gravner and Griffeath also generated novel snowflakes, such as a "butterflake" that looks like three butterflies stuck together along the body. Gravner says there's no reason these shapes could not appear in nature, but would be fragile and unstable.

Gravner and Griffeath aren't the only people interested in snowflakes. Kenneth Libbrecht of the California Institute of Technology is another scientist who's been unraveling snowflakes. (Hmm, Cal Tech is in Pasadena, California. And how much snow has been shoveled there this winter?). In his recently published paper The Formation of Snow Crystals Libbrecht briefly describes some of the subtle molecular processes that lead to differences in snowflakes.

But while Gravner, Griffeath, and Libbrecht are worried about fake snow, I'm still worried about the real stuff -- and how much it's going to cost me that my wife shoveled the driveway. Let me think -- dinner or a snowblower? Any suggestions are welcome.

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