Deeper into the Buddhabrot
My previous Buddhabrot images were built up from many thousands of ‘z‘ orbits. Over time the trails left by these orbits average out into nice soft symmetrical clouds. Most of what you can see are the trails left by the orbits that survive for relatively few iterations before escaping to infinity (there are so many more of this kind of orbit).
If you filter out these “shallow” iteration orbits and instead render only orbits with deep iterations something very interesting happens. The paths of the individual orbits become discernable. They almost look like temporary strange attractors, spinning and swirling before finally blowing away on the winds of chaos.
Take a look at these fantastic patterns (click to enlarge):
This image consists only of orbits with between 20,000 and 30,000 iterations.
As with my strange attractor images, due to a few very bright pixels, it was necessary to render in 16-bit greyscale and then equalize the images to bring out the details which would otherwise be too dark to see. Normalize or auto-levels won’t do the trick. I used ImageJ for the equalize function.
If more orbits were calculated, over time a regular and symmetrical pattern should arise.
Here is the same image as above allowed to accumulate roughly 3x the orbits:
Some interesting discussion of deeply iterated Buddhabrots can be found here.