Mandelbulbs

The geekier (or artistic) amongst you will no doubt have seen the mathematically generated beauty of Mandelbrot sets such as the below:



From a simple equation this wonderful pattern emerges again and again, no matter how far one zooms in to the image.

That's not the cool bit.

The cool bit is that a few fractal fanatics have recently been experimenting with 3D Mandelbrot sets - nicknamed Mandelbulbs. They haven't quite got the true three dimensional formula worked out yet, but the various approximations in use are already producing some fantastic graphics.

On with the pretty pictures, click for super-size (and I do mean super-size, one of these is 7000x7000px):

The basic form


Gateaux


Honeycomb Heaven


Lost Ruins


Cool or what? For those of you interested in the maths - using hypercomplex numbers - there's a bit more detail here and some pseudo-code is provided here.