The Gosper curve,
a variation on the Koch curve, is generated
by this simple iterative process: replace every line segment (blue) with a three-part
broken line segment, sharing the endpoints of the original, and scaled by 1/sqrt(7).
Starting with a regular hexagon on the left, one application of the Gosper
process (to each segment of the hexagon) gives the red curve. On the right
is the fifth iterate. Click on it to see an animation of the iterates.