Inversion seems to play a role.
Im not familiar with the concept of "inversion". But Google finds some pages that show images of inverted grids. And they have some similarity to the CDF.
Sam at Fractal Forums suggested to create a version that uses multiplication instead of division to "un-invert" the CDF. On the left is the resulting image from (-1/-1) to (1/1). Indeed, the circles turn into straigth lines.
Adam P. Goucher send me this link about Escher and inversion.