Friday Fractal XXX*

Many things in nature seem to catch our eye, simply by hovering between a turbulent, chaotic mess, and a vacant, serene sense of order. Art tends to reflect these dichotomies in nature, even when it is fairly abstract in nature. Some say it stems from a fascination from good and evil, or light and dark, or lightness and weight. But I suspect we just enjoy exploring the point in between. This is the draw of fractal art... the edge of the fractal itself, the border between the "inside" and the "outside" of the shape, can be followed endlessly. To our eye, the wonders and variation never seem to cease.

This is a layered fractal, based on a torus-shaped "Juliabrot" (what happens when you leave the Julia set alone with the Mandelbrot set and a bottle of wine, perhaps?) But this is only the first shape with a complex edge; another set of variables controls the coloring used to fill in the complex edge of the first. This coloring algorithm chooses exactly how to fill in the pixel, based on a relationship between a trap placed on the complex plane and an orbit around that trap. This is further amplified by the coloring algorithm recalculating new directions every time a new pixel is placed. Just in case there wasn't enough tug between balance and chaos, both the coloring algorithm and the separate plasma background are based on fractal Brownian motion... essentially, yet another layer seeking the boundary between order and chaos. Remarkably, somehow all of these rather chaotic variables manage to converge in harmonic waves:

...an effect similar to, but not quite as complex as, the harmonic waves seen in a plunging waterfall:

Waterfall in La Fortuna, Costa Rica, taken by Scott Robinson.

Watching a living waterfall, it is easy to see that nature beats my computer-generated fractals in the complexity department. But not by much. The image on the left shows a "zoomed-in" shot of both the fractal and the photo. Which is the waterfall? I'll reveal the answer next Friday.

For more about metaphors found in falling water, along with a video, click here.

Waterfall image by Scott Robinson via Flickr. All fractals made by the author using ChaosPro

(*) Note for anyone who was hoping that Friday Fractal XXX might be a different sort of fractal, i.e., not one suitable for younger viewers: I will admit, I run across all sorts of natural forms while creating fractals. Some of them might even raise... an eyebrow. But this week, I wanted to post a waterfall... so, if you were hoping for a naughtier fractal than usual, you're out of luck. Unless you click here.