This incredible shot is of a scale -1.7 Mandelbox. It reminds me of a giant tarantula's nest. By Jesse using Mandelbulb3d, see other pics at Jesse's gallery
By Loadus using a smaller box fold (f=0.5) and scale 1.3. More superb and atmospheric variations can be found in his gallery.
By Jesse, this is a 'Juliabox', a julia set for the standard Mandelbox. Notice how all the curves are circular (never oval) in a Juliabox.
Unlike the Mandelbrot set which is as unique and universal as the the number pi or e, the Mandelbox is comparitively arbitrary; provided the folding preserves shape and continuity there isn't really one choice of folding that is better than any other. So the possibilities for equally varied or even more varied shapes is wide open. Some of the tools in the make your own pictures section allow you to try different folding patterns.
This is a variation by blob called eye candy, it folds around a dodecahedron as well as the mandelbox folding
This image by Theli-at seems to be the first sighting of beautiful recursive spheres in a scale 1, minR 0 mandelbox
Msltoe has found an area with larger spheres and this cut-through reveals that each sphere has its own insides, wow-
Rotating the Mandelbox each iteration can look quite organic, this wonderful set by Lxh also omits the fold operation along one of the axes.