Quaternion Julia Sets are four dimensional fractals. The following 2D image is the result of ray tracing a 3D slice of a 4D fractal.
Thanks to this paper and Keenan Crane I was able to implement the distance estimation formulas and improved the results of ray tracing Quaternion Julia Set images dramatically.
Click here to see some nice high resolution sample results.
The newly improved rendering method is now available in the latest version of Visions Of Chaos.
This forum post has a lot of smart nerds (and I use that as the ultimate compliment) looking for a true 3D version of the Mandelbrot Set. See here for even more ongoing research related to the Mandelbulb and variations.
Some of the results so far are amazing. These sort of images have never been seen before by human eyes. Seeing these images evolve must be similar to the experience of the first people who saw the original 2D Mandelbrot images emerge.
The following page by Daniel White includes further information on the progress so far and many more excellent example pictures.
The Unravelling of the Real 3D Mandelbulb