Smooth self-similar curves
Craig S. Kaplan
Smooth Self-Similar Curves.
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.