Math in the News
Mathematicians Model Actual Snowflakes
February 4, 2008
Snowflakes have puzzled mathematicians from the time Johannes Kepler predicted that the six-pointed structure reflects an underlying crystal structure. Now--four hundred years later--mathematicians claim to be able to model three-dimensional snowflakes via a computer program. More important, being able to model the process of creation might explain why no snowflakes are alike, according to Janko Gravner (UC Davis).
The surface of a growing snowflake crystal is a complex, semi-liquid layer upon which water molecules from surrounding vapor attach or detach. The model by Gravner and David Griffeath (University of Wisconsin-Madison) takes into account the fact that water molecules more often attach themselves at concavities in the crystal shape. Other factors involve temperature changes, atmospheric pressure, and water vapor density.
By running their model under varying conditions, the mathematicians recreated a wide range of natural snowflake shapes. Needles were the most common computer-generated pattern while the classic six-pointed "dendritic" or feathery snowflake was rare in their simulation--and just as rare in nature.
Gravner and Griffeath also managed to come up with some novel snowflakes, including a "butterflake" that looked like three butterflies stuck along the body. Gravner indicated that while there seemed to be no reason their novel shapes could not appear in nature, they would have to be fragile and unstable.
Source: Science Daily