Rings Rolling Alongside a Mandelbrot Set

This video illustrates the Mandelbrot set of the 3rd degree rational functions f(z) = z^2(z+a)/(1+conj(a)z) +m where the complex number a follows the circle of radius 3.1 about the origin. The video follows a curve of Herman rings that emerges from the cusp of the classic Mandelbrot set and follows alongside the main body of the Mandelbrot set as the winding numbers of the Herman rings increase to 2 pi. The planar images show the intersection of the Mandelbrot set with the m-plane. Points are colored according the result of iterating critical points. If a critical point lands in a cycle of length 1, the point is colored yellow. Other colors are used to indicate different periodic cycle lengths. Points iterating to infinity are colored green. Points that end up in a Herman ring or a Siegel disc are colored black. For more information, see docs.google.com/document/d/1qhtyoq9t6qXxnnkxHMmFpq…