September 19, 1998

Here’s another fractal that was in the final cut to submit to the fractal contest at the Fractalus site. Now that all of the entries are on display, I can see that the ones I submitted probably don’t have a chance. (If you haven’t already, check it out! The contest site is now the best fractal display on the Web!) However, I would have have had a little better chance if I had submitted this one and/or the previous “Fractal of the Week.”

When I originally generated this fractal, it had a much simpler color map (see the alternate colorings below). I thought it was pretty good already, but exploring different colorings using the random color map feature of Fractal Domains, I saw that there were some structures in the fractal not clearly revealed by the original smooth mapping. I then set out to color in the structures I had observed with hand-chosen colors with the explicit goal of creating a very colorful and “dazzling” fractal for the fractal contest.

I liked the result but ultimately I didn’t like it enough to make this one of the three that I submitted. My family didn’t particularly like my hand-colored fractal but did like one of the original, simpler colorings and encouraged me to enter that one in the contest. Ultimately I didn’t enter any of them…

This is a Julia set based on the “inverse Mandelbrot set” formula 1/(z^2 + c), c = 0.67

Following are some alternate colorings (click on the image to see full size):