Gosper Curve

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, one application of the Gosper process (to each segment of the hexagon) gives the red curve:

Here is the fifth iterate. Click on it to see an animation of the iterates.

Return to Fractal Fiberoptics