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”)