## Image Details

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.

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