In January of 2005 I participated in the Snowflake-A-Thon hosted by the Simplicity group at the MIT Media Lab. The challenge was to write the simplest program that produced the most beautiful snowflake. You can see the gallery of all the snowflakes and a video of mine here. Update: The gallery is no longer available on the Media Lab site, but you can see my video below.
My program created a hexagonal grid, and assigned a number to each hexagon. The center started as "1" and the rest started as "0". After every time step, the value of each hexagon was added to each of its neighbors, modulo 32. I ran the code for a few time steps and then mapped the numbers to a gradient from dark blue to white. I got the idea from playing around with 2d cellular automata on a hexagonal grid when I was in high school.
I thought the resulting snowflake was really nice. Apparently the Simplicity people thought I was a total weirdo for coding a snowflake in MATLAB, but I remain pleased with the results.