Koch snowflakes are created by successively extending the sides of a triangle. I found a very nice description of the Koch method and a fortran program that was used to calculate all the examples given below at:

http://hmf.enseeiht.fr/travaux/CD9900/travaux/optmfn/hi/00pa/mfn16/part2.html

Enseeiht is a French engineering school in Tolouse and the author of the article is Alain Schuler.

Koch Snowflake by gadgetguydk, (thing:1039), is a composite of three stages of Koch iteration of a triangle and Koch curve/snowflake by Cross, (thing:3166), is an embroidered version. Koch_composite_color_1.stl and Koch_composite_color_2.stl, available below, is a two color version of the same composite for the Replicator.

Koch_three_snowflake.stl and Koch_four_snowflake.stl are monochrome examples of the Koch curve after 3 and 4 iterations of a triangle. The curves have been pierced with holes so that they can be hung as ornaments. The openSCAD programs that created the snowflakes are provided and they can be easily modified to create numerous variations.

Koch_three_snowflake.stl and Koch_four_snowflake.stl can be printed on a raft or directly on the build platform.