Removing Tremas with a Rational Function

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Anne Burns: Removing Tremas with a Rational Function. In: Bridges 2013. Pages 95–102



In his charming inimitable style, Benoit Mandelbrot, in his book The Fractal Geometry of Nature, describes the removal of “tremas”. Two examples of figures constructed by removing tremas are familiar fractals: carpets and gaskets. This paper will briefly describe the difference between a carpet and a gasket and then illustrate how the Julia set of a rational function can be a carpet, a gasket or another structure generated by “removing tremas”. An added bonus is beautiful images resulting from an imaginative assignment of color.

Extended Abstract


Used References

[1] Paul Blanchard, Robert L. Devaney,Daniel M. Look, Pradipta Seal, Stefan Siegmund, David Uminsky. Sierpinski Carpets and Gaskets as Julia Sets of Rational Maps, pp 97-119, Dynamics on the Riemann Sphere, A Bodil Branner Festschrift, Paul G. Horth and Carsten Lunde Petersen, Editors, European Mathematical Society, 2006, 3-03719-011-6

[2]Robert Devaney, 404

[3] Joel Louwsma. Homeomorphism Groups of the Sierpinski Carpet and Sierpinski Gasket, REU project at University of Michigan, July 1, 2004, 404

[4] Benoit B. Mandelbrot. The Fractal Geometry of Nature, W.H. Freeman and Company, New York, 1983


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