Burning Seas - click to enlarge.

Image Details

As previously discussed, there is a region of the Mandelbrot set centered near \(0.75+0.10i\) called Seahorse Valley. This region, characterized by loops and spirals which resemble the tails of seahorses, is highlighted below.

The Mandelbrot set with the Seahorse Valley outlined.

Because the Mandelbrot set displays a degree of self-similarity, there are little miniature Mandelbrot sets that can be found in Seahorse Valley. That is, there are regions of the Mandelbrot set that can be found by zooming in which closely resemble the overall set. Suppose that we were to zoom in on one of those regions, and continue to zoom in on the area that is analogous to Seahorse Valley.

The image at the top of this post is something that we might find. There is a minibrot centered near \(-0.733+0.288i\). If we zoom in on the Seahorse Valley of that minibrot, we may eventually find the region pictured above (as always, click for a larger version). It looks similar to the familiar Seahorse Valley, but the seahorses themselves are a little mutated—rather than having a single tail, they have two tails. In the Mandelbrot set, it is often the case that if we see a feature at a large scale, we will see similar features at a smaller scale, but repeated.

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