Celestial Elephants - click to enlarge.

Image Details

The Mandelbrot set is infinitely detailed, which means that every time someone creates a new images of the Mandelbrot set, it is likely to be a region of the set that has never been seen before. It may share characteristics with regions that have been pictured previously, but the exact piece of the set shown is likely to be unique. In a very real sense, artists looking for interesting features in the Mandelbrot set are exploring an unknown space.

When I create images, I tend to use a greyscale color scheme. The stark black and white can highlight interesting features which might disappear with a more varied palette. When exploring the set, I use greyscale images to find bits and bobbles that I think will make aesthetically pleasing final products, then allow the structure of the set or my mood to dictate an appropriate color scheme.

Today, the original greyscale was very satisfying.

The image itself is centered near \(0.339-0.051i\), in the southern half of elephant valley. The elephant at the center of the picture is both obvious and arresting, but there are some other interesting features in this region.

First, the self-similar nature of the Mandelbrot set is on display. Near the heart of the central elephant, we can see a miniature copy of the overall set, though it is slightly skewed. The copy is imperfect, though the general shape is readily apparent.

Perhaps more intriguingly, there are some swoops and swirls on the right side of the image which are tantalizingly similar to Julia sets. It turns out that these little Julia lookalikes are quite common in the Mandelbrot set. These “Julia islands” highlight the close relationship between the Mandelbrot set and Julia sets. One such Julia island is shown below (left), with a Julia set for comparison (right).

A Julia island from the Mandelbrot set (left), and a related Julia set for comparison (right).

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