Click the image above to obtain a larger, uncropped version (approx. 10.8 MB).
Sometimes I like to simply explore the Mandelbrot set. Earlier this week, I started diving down into seahorse valley, just to see what was there. Eventually, I came across the little Mandelbrot-in-miniature shown above. In most of my explorations, I use a greyscale color scheme, as this allows me to see some interesting details, but doesn’t require a lot of thought with regard to picking colors. This region was interesting, but nothing special.
Then I started experimenting with colors, and found that a particular cycle of colors looked really interesting. After a bit more fiddling, I found a set of fall colors that struck me as quite nice. The end result is posted above.
For those that are interested, the above image is centered at the complex number \(0.74952535+0.09447165i\), which is relatively near the bottom of seahorse valley. The colors follow a smooth gradient from yellow to red, cycling between the two colors over a period of 64 iterations. As points approach the boundary of the Mandelbrot set, they grow darker, slowly fading into the set itself.