Fractal of the Week for February 21, 1999

Gathering

Here is a fractal image closely related to the "Venus Flytrap" image of a couple of weeks ago. You can see the similarity immediately but I think this image is much more interesting (I have to get away from using the default color gradient maps, though. Next week I'll have one with some custom color maps, I promise!)

Although I usually give these fractal images a name suggested by the fractal, I usually don't look for any representational content in a fractal image and any such name is mainly for reference. In this case, the image didn't really suggest much to me and I picked "Gathering" because the converging rows of circles somehow suggested the name to me.

Then I noticed that the shapes in the center consisting of pairs of loops joined by a central curve look a little like some sort of entities holding hands...and the inverted crescents under each such loop look like smiles! The entire congregation seems to be gathered under the overarching roof of some sort of amphitheater. The whole effect is really kind of creepy, like a mass meeting of cultists.

On another subject, it recently came to my attention that there is a bug in Fractal Domains that puts up orbit traps at spurious "critical points" in some cases, and the "Venus Flytrap" fractal looks much less interesting when these spurious roots are suppressed! I think this image probably is a product of the same bug. I will correct this in the next version of Fractal Domains, but I'll be sure to provide a way to reproduce these fractals (perhaps through the capability to manually add trap origin points, a feature I was thinking of adding anyway) as these fractal images are too good to throw out even for the sake of mathematical accuracy.

This fractal is based on Newton's method applied to z^4 + 2z + 1. The resulting expression has the constant c = 0.1i added to it The "Venus Flytrap" image was the same except the original expression was z^4 - 2z + 1. This essentially moved the fixed points from +/-1 to +/-i.

Below is a version of "Gathering" in 1024 X 768 format.