FRACTAL LANDSCAPE
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Tannhauser Gate
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Tannhauser Gate

Exotic functions

This image includes many familiar Mandelbrot/Buddhabrot features such as the main cardioid cusp at the top as well as the arcing bulb-clouds. Both are fairly obvious hints as to the function behind the image although the details are of course impossible to guess from a picture alone. Unlike with the usual Mandelbrot here the sign of the c-term in zₙ=z²+c is flipped on every iteration. I refer to the function as the Beetlebrot simply because of its shape in its CrCi orientation. In this slightly diagonal four-dimensional orientation the beetle is nowhere to be found. Just like a lowly sponge can be transformed into something quite different when projected into higher dimensions.

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