My programming talents are limited, at best. My Mandelbrot rendering program takes an arcanely formatted text file and a bitmap image (for color) as input, and proceeds to output a bitmap image in what is perhaps the most naive possible manner. The single advantage of my implementation is that, because I wrote it, I know how it behaves, and I know how to coddle it into outputting interesting or aesthetically pleasing images.
However, the process of finding regions of the Mandelbrot set that are worth looking at can often be a bit tedious. The text file must be manually edited, the colors have to be tweaked by hand, and every alteration requires that the program be run anew. To relieve some of that tedium, I sometimes use a program called Fractal Domains to look around. Fractal Domains has decent interface for zooming and panning, and is very fast to boot. I don’t use it to render the large images that I post here, but it can be a useful tool for finding features to render and fiddling around with different settings.
This brings us to today’s image. Centered near \(-1.766+0.042i\), it is near the western edge of the Mandelbrot set. The general structure of the Mandelbrot set in this region is something that we have seen before: a set of radially symmetrical “spokes,” “fan blades,” or “arms” surround a minibrot, and the arms are increasingly plentiful as we approach the minibrot. Specifically, they increase in number by powers of 2. In this case, the arms are relatively linear (though jagged) in form, while in the previous example they were more fern- or feather-like. That said, the basic structure is the same.
For whatever reason, I rather like these structures—they appeal to my aesthetic sense. I had selected this region (in greyscale) as being worthy of a large render, but was having difficulty in finding a color palette that brought out the structure in an attractive manner. Then, while following another train of thought while playing around with Fractal Domains, I came across a randomly generated color palette that seemed perfect. The palette started with dark purple with swiftly blended into a startling and unexpected orange. The randomly generated palette didn’t look great, but it provided some inspiration.
After a little bit of tweaking by hand, I eventually settled upon the colors in the image above. I never would have thought to combine purple and orange (two of the few English words without rhymes, by the way), but I think that the result is rather arresting, and worth some consideration.
As always, I hope you enjoy.