It reminded me of a picture I saw somewhere of a piece of the Mandelbrot set. I doubt that I can find the picture I remember. Can anyone reading this help, either by pointing me to an image, or by exploring the Mandelbrot set to find a place that looks like this? I'll post promising matches - send them to me at ebolker at gmail.
Here is some of the correspondence so far.
An image I found with a Google search: