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A cube of side 16 defines 4096 elementary cubes. The (fractal) Hilbert curve enter and leaves each of these cubes exactly once, never crossing itself. This variant of the original (open) Hilbert curve is closed (it has no end and just loops seamlessly). This model uses a square thread and turns, a round version is also available here.
The coordinates of the 3D space-filling curve have been produced using the C code written by Doug Moore (using the Butz algorithm), available here: hilbert.c. A patch to Blender's PLY reader has also been commited in the process, to allow everybody to load 3D-curves easily in Blender.