The software I use is Fractal Domains for Mac OSx. This is a raw newton fractal with formula (z-1)/(z^6 +1). I think the program uses fixed point convergence to iterate the interior portions of the function (the yellow region is the portions of the function iterated by fixed-point convergence, the grayscale region is the exterior of the function.) I'm glad it piques your interest!
OK, I remember you use Fractal Domains now The reason for my question is the structure of 2 fractal sets, a phenomena which is common to parameter plane pictures of 2D slices of higher polynomials (cubics and higher). See especially the illustrations in [link]
I am not certain the origins of this behavior in the program I am using. It is a higher order polynomial (in the denominator), but it seems to me to arise from the newton iteration method and the program iterating interior points using an approximation method with convergence limits set by the user. It is an uncanny comparison, though, I just am not sure if they arise from the same phenomenon.