Jason>
I don't recall if someone already posted this sculpture of trilbert: http://blog.makezine.com/archive/2010/11/math_monday_3d_hilbert_curve_in_ste...
An 8^3 (not a 4^3, Steve) in plastic would be delicate, at best. The entire weight is everywhere supported by the thickness of a single pipe, often far offcenter. Neil Bickford built a 4^3 from construction cubes that you dasn't breathe on. And the illustrated 8^3 is a quivering mass of robot intestines. (Amazingly organic, for such a seemingly crunchy and artificial concept.) Neil was investigating the connection of Trilberts with Morse (= Stutter Free = "Square" Free) sequences, and found the spacefilling property enormously underconstraining. There seem to be 2^(n+1)-1 cubes of order n, corresponding to all the ways you can reflect a subcube in the symmetry plane that contains the edge it spans. In fact, Corey's first exact map had the inverse image of (1,1,1) at 85/126 instead of 19/28. I probably missed something, but am having difficulty finding a stutter-free (no straight angles) 8^4. It seems to require a lot of searching and manual reflecting instead of a nice, clean recursion. --rwg That's no hamster--it's an illegal gerbil! Get him!