1 / Mandelbulb zoom
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The Mandelbulb is one of the first true 3D versions of the Mandelbrot set because you can always reveal more detail the closer in you get. When rendering on the GPU we are limited to standard floating point precision so we can't go much further in before everything breaks apart.
Update: see the blog post for more info and downloads: subblue.com/blog/2009/12/13/mandelbulb