Koch Curve

This curve another curve named for the mathematician who dreamed it up. What we have is a curve that is continuous, but is made up entirely of angles. So the first derivative is undefined at every point. Even without getting bogged down in the calculus of why that is interesting, it makes a cool snowflake. The Fractal Dimension of this curve is approximately the same as the Fractal Dimension of a coastline. Of course this is carefully defined and repeating, where a coastline is more random, but hopefully it looks something like as bumpy as a natural coastline.