Someone out there has to want to do this in POV-Ray...   :D

"... So epicycloids are related to Multibrot sets!


Mandelbrot set. This sounds tough, because light reflects off a curve in a way

but there still might be some trick to get around this, some sort of limiting
process. And people have definitely studied eigenfunctions of the Laplacian on
fractals, and these are related to the propagation of light waves, which reduce
to light rays in a certain limit: the geometrical optics limit. So one could at
least study what happens when light waves are emitted from a point source in the
Mandelbrot set, and then what happens in the limit where the frequency of this
light gets higher and higher."

https://johncarlosbaez.wordpress.com/2012/09/03/rolling-balls-and-circles-part-2/#comment-19646

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