Of the different parameters you can change, perhaps the most interesting is to use a negative scale. The pictures here are of scale=-1.5, which is just small enough to prevent floating boxes on the corners, and gives a much denser box, but it produces a wonderful variety of shapes, and in fact seems to mimic some well known fractals...
This object at the corner of the Mandelbox contains a huge variety of fractal types, most of the images below are close ups of this corner object.
One of the more distinctive traits of negative scales is a "rough" look, giving it more organic features. (Parameters)
Zooming in on the right corner, a beautiful recursive structure of encrusted boxes which form on a pattern of circular lillies. It produces a pattern very similar to that of a Kleinian fractal, which is composed only of spherical inversions.
Zooming into the face of the top image shows a koch snowflake fractal. Notice the variety of other shapes too, like 5 sided star fractals. (Parameters)
Zooming in on the lower front face of the top image shows this fractal that is a bit like 1d Cantor dust as you approach the line. (Parameters)
Elsewhere at the top edge of this Mandelbox shows a border like a Parameters). This can also be seen (in great numbers!) at the right edge of the previous picture. (
See miqel's page for even more examples.
The following pictures are just to look pretty. Enjoy!
Giant oyster (by bib)