Smooth Self-Similar Curves

Craig S. Kaplan
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 209–216 Regular Papers


I present a technique for constructing self-similar curves from smooth base curves. The technique is similar to that used in Iterated Function Systems like the Koch curve, except that it does not require a piecewise linear path in order to induce a set of similarities. I explain the mathematical machinery behind the technique, describe a practical numerical approximation that can be implemented in software, and show some results.