A Mandelpinski maze for rational maps of the form [formula omitted

Abstract

In this paper we identify a new type of structure that lies in the parameter plane of the family of maps zn+λ/zd where n≥2 is even but d≥3 is odd. We call this structure a Mandelbrot–Sierpinski maze. Basically, the maze consists at the first level of an infinite string of alternating Mandelbrot sets and Sierpinski holes that lie along an arc in the parameter plane for this family. At the next level, there are infinitely many smaller Mandelbrot sets and Sierpinski holes that alternate on the arc between each Mandelbrot set and Sierpinski hole on the previous level, and then finitely many other Mandelbrot sets and Sierpinski holes that extend away from the given Mandelbrot set in a pair of different directions. And then this structure repeats inductively to produce the “Mandelpinski” maze.