There have been many attempts to find three-dimensional fractals that are as beautiful, complex, and fascinating as the classic Mandelbrot set is in two dimensions. One approach has been to use hypercomplex numbers instead of complex numbers, such as the quaternion Julia set, but all variations of this fractal have the same sort of 'linked hoops' structure; the infinite variety of forms in the original Mandelbrot set just aren't there. (Although, the quaternion Julia set can still be quite beautiful!) Another approach is to stack slices of a 2D fractal on top of each other (as in my Julia's Eye and Julia's Scaffold pieces), but although this can create beautiful 3D structures, they aren't really 3D fractals.
The Mandelbulb uses spherical coordinates to create a 3D fractal that shows the same infinite detail and variety of forms found in the original Mandelbrot set. This piece is a representation of the top half of the 8th-order Mandelbulb. I have created three versions of this sculpture in different sizes, where the larger ones are able to show the fractal greater detail. This one is the medium-sized one, about 3.5 inches (85 mm) across. There is also a two inch (50 mm) version, and a five inch (125 mm) version. All three versions are hollow.