The Mandelbrot set is one of the most known fractal. It can be seen on many sites and images over the Internet. It was represented in many variations. Today, many fractal artists create beautiful images, which are based on it. But all this time it remained only a two dimensional fractal.
Of course, many artists created 3D images with it. Below you can see the Mandelbrot fractal (to the left) and such pseudo-3D. But as you can see, the figure to the right is the same 2D fractal, in which values of the fractal are representes as levels above the base plane.
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It remained two-dimensional until Daniel White and Paul Nylander constructed a three dimensional analog of the Mandelbrot set, using an hypercomplex algebra based on spherical coordinated, when in classic Mandelbrot set algebra of complex numbers were used. They called their creation Mandelbulb.
You can read about history of creation of Mandelbulb and many images of it at http://www.skytopia.com/project/fractal/mandelbulb.html. Here, there are very large image of the fractal wholly and images of some it's parts.
The Mandelbulb opended the door to a new class of wonderful fractals.
