Wholly Holey

September 12, 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.”

This is another fractal that I thought would be one of the ones I would submit up unti the last minute. Other members of my family were underwhelmed by this one, and that partially influenced me, but now I’ve reverted to my original opinion: I think it is a superb fractal (you should look at the large format version, though, to get the full effect).

Just to be contrary, I think I would have submitted this to the “Best Use of Color” category even though it is purely grayscale. Sometimes shades of gray can be more effective than a full color rendering. However, see the alternative color version below. This is a fractal that responds well to different color maps.

It’s a Julia set based on the formula z^2/(z^2 + 1) + c, c= -0.1 + 0.16 i. It uses angular decomposition and fixed point convergence with what I call “Pickover convergence.” This is an alternate convergence test suggested in a paper by Clifford Pickover in which, rather than testing consecutive points to see if they are close (the conventional fixed point test) you test the difference in their absolute values.

A tip of the hat to the Firesign Theater for inspiring the title (reference: “Everything You Know Is Wrong”)