Janko Gravner's Homepage.

Useful links

MAT 16A (Fall 2007) class pages

RFG in Probability

MAT189: Advanced Problem Solving will be offered in the Winter Quarter of this year.


  • Paper Random growth models with polygonal shapes (with David Griffeath): in Postscript and in PDF.
  • Paper Modeling snow crystal growth I: Rigorous results for Packard's snowflakes (with David Griffeath): in Postscript and in PDF.
  • Paper Modeling snow crystal growth II: A mesoscopic lattice map with plausible dynamics (with David Griffeath) is available at the Snowfakes page.
  • Paper Modeling snow crystal growth III: three-dimensional snowfakes (with David Griffeath) is also available at the Snowfakes page.
  • Pictures of the 0->1->2 model: cont. time with lambda=2 and discr. time with p2=1, p1=0.55.