Smooth Self-Similar Curves

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Craig S. Kaplan: Smooth Self-Similar Curves. In: Bridges 2011. Pages 209–216



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.

Extended Abstract


Used References

[1] Michael F. Barnsley. Fractals Everywhere. Morgan Kauffman, second edition, 2000.

[2] Adam Finkelstein and David H. Salesin. Multiresolution curves. In Proceedings of the 21st annual confer- ence on Computer graphics and interactive techniques, SIGGRAPH ’94, pages 261–268. ACM, 1994.

[3] Aaron Hertzmann, Nuria Oliver, Brian Curless, and Steven M. Seitz. Curve analogies. In Proceedings of the 13th Eurographics workshop on Rendering, EGRW ’02, pages 233–246. Eurographics Association, 2002.

[4] Benoît B. Mandelbrot. The Fractal Geometry of Nature. Times Books, 1983.

[5] Peter Shirley. Fundamentals of Computer Graphics. A K Peters, second edition, 2005.


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