Monday Mandelbrot Madness X

Forest - click to enlarge.

Image Details

The above image is a cropped and scaled portion of a larger image. Click the image above to obtain the full version (approx. 10.1 MB).

This week’s Mandelbrot image is centered near \(-1.375+0.015i\). The structure in the right half of the above image vaguely resembles a scepter—it is a linear, rod-like structure with ornate decoration. Even in the detail above, there are dozens of these scepter structures. Hence this region of the Mandelbrot set is known as “Scepter Valley.”

In addition to the repetition of the scepter structures, the full image contains hundreds of little miniature Mandelbrot clones. While I may be beating a dead horse by repeating this for the umpteenth time, fractals are defined by the repetition of structure at all scales. In the large image, there are big mini-Mandelbrots, there are small mini-Mandelbrots, and there are mini-Mandelbrots that are so small that they cannot be resolved in the image. Similarly, there are scepters of all sizes, many too small to be seen, even when the image is zoomed to its native resolution. Over and over again, we see the same structures repeated into infinity.

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