December 30, 2013

Mandelbrot set of fractals in three dimensions

I found this image at NASA's Astronomy Picture of the Day site. Here's the explanation. (I'm afraid it's rather involved.)
What strange world is this? Pictured above is no real place but rather a purely mathematical visualization of a generalization of a fractal into three dimensions. Classical fractal diagrams are typically confined to the two dimensions inherent in the complex number plane, demarking regions where an iterative function diverges. Recently explored additions expand the Mandelbrot set of fractals to three dimensions with prescriptions dubbed Mandelbox and Mandelbulb sets. The results are often visually stunning creations of virtual worlds with limitless detail, some of which you can fly through. Pictured above is one such mathematical fantasy, possibly reminiscent of some sort of steam-punkian, quantum-mechanical landscape. 
Special points for using the term "steampunk". The NASA photo site I linked to above provides a new image every day. I suggest you bookmark it.

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