Thingiverse's Tony Buser has an amazing approach to approximating the Hilbert curve, as Make's Sean Ragan explains:
Veteran Thingiverse user Tony Buser has printed a model (intended to be an approximation of the fractal Hilbert curve) using polyvinyl alcohol (PVA) as a support material. Once everything is printed and cooled, the PVA is dissolved away in a glass of water, leaving only the polylactic acid (PLA) model. This technique, when perfected, should allow RepRap-style FFF printers to produce objects with overhanging parts that are currently very difficult, or impossible, for them to print. Tony used two of MakerBot's Mk7 extruders mounted on a Thing-o-Matic.