Removing Tremas with a Rational Function

Anne Burns
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (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.