A new kind of fractal?

http://www.gibney.de/does_anybody_know_this_fractal

Is this some known kind of fractal?

Update: This one got a lot of great feedback from around the net. I summarized it in the section labeled “Update 24.10.2012”.

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.