For 400 years, since Kepler, Descartes, and Hooke, scientists have tried to learn how snowflakes grow. Recent advances in photomicroscopy, lab synthesis, and computer modeling provide new insights into this paragon of natural complexity, promising deeper understanding in the near future.

Snowflakes exhibit an intricate mix of geometric, chaotic, and stochastic form: vestiges of growth from nanoscale water molecules to micron scale branching to their final size a few mm across. Several dynamic instabilities produce more than 80 types according to one classification.

We will discuss the current version of a 3-d simulator for snow crystal growth, based on physical principles. This is the first computer algorithm that successfully emulates all the major snowflake morphology observed in nature. Our virtual snowflakes, or "snowfakes," have recently attracted considerable attention in the popular science media, e.g., on the Discovery Channel and the front page of the Chicago Tribune.

This is joint work with Janko Gravner of UC Davis Mathematics and Ken Libbrecht of Caltech Physics.

For background, see

http://www.its.caltech.edu/~atomic/snowcrystals/

and

http://psoup.math.wisc.edu/Snowfakes.htm