A new kind of fractal?

Probably a part of what we see is due to rounding in your program: note that the value at $c$ is the same as that at $ic$ so that the image should be symmetric under rotation by 90 degrees. This roughly is the case, apart from the deformed squares all over the place. In fact, they all occupy one quadrant like region with one vertex at a point with a high value, probably due to rounding. Without the squares you would have a better approximation to the real picture.

The intensity as defined is $0$ for almost all values of $z$, so it is unclear how the visualization relates to the definition. If you post the code that generated the images you will have a better chance of getting a satisfactory answer, and that would also address @doetoe's observation of what are apparently artifacts.