Smooth self-similar curves


Craig S. Kaplan. Smooth Self-Similar Curves. Bridges 2011: Mathematics, Music, Art, Architecture, Culture, pages 209–216. Tessellations Publishing, 2011.


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.


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