I was showing David the ability for Mandelbulber to only show partial cross-sections of a fractal.  He gave me the thought of mixing the displacement idea with slices, captured front-on.

In the end, it seemed that only 27 slices were needed before I had reached a solid form:


I further refined this gradient to 11 slices, removing redundant levels having only small additional details:

Depth Animation

This was still producing non-mirroring geometry thus, in photoshop, it was mirrored, flipped, etc.  The result was a near-perfect slice used to create a single cube side.

This side then had the sides chamfered off at 45 degrees.

Using some rotation, I combined and merged six copies of that side to form the best cube to date:

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