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Imagine the most beautiful galaxy you can conceive, and you start to get the sense of a Buddhabrot fractal.

It took Benedikt Bitterli ten days to render this gorgeous video, far longer than he expected, yet a wonder to behold.

Here’s an introductory explanation of sorts starting with an explanation of the Buddhabrot’s close cousin, the Mandelbrot set:

The Mandelbrot fractal is fascinating, because it generates a point set of mind-boggling complexity from a few very simple rules. This emergent complexity seems to be a funky property of the complex plane, and many other fractals have been made using similarly simple rules over the complex numbers. One such fractal is the Buddhabrot.

The Buddhabrot uses the same iteration rules as the Mandelbrot: Points are sampled on the complex plane, repeatedly transformed using a simple function, and filtered based on whether they escape to infinity or not. The major difference, however, is which points are kept: If a point does not escape, it is thrown away; but if it does escape, the point and all of its transformed versions are stored. The transformed versions of the point correspond to its “trajectory” through space as it escapes to infinity.

If that’s too much to handle, just sit back and revel in the result. Perhaps you’ll achieve Nirvana.

Full story at Benedikt Bitterli via Kottke.

Out of this world mathematics.