Hilbert Curve in 3D!

Here’s another Hilbert Curve. This one’s a photograph though. And it’s made by Carlo Séquin. You remember him?

Personally, the picture makes me squirmish - it reminds me of minced meat. And if you don’t know what a Hilbert Curve is, it’s a curve that is used to fill space. There are many kinds of space filling curves out there, but the Hilbert curve is the more popular one, discovered by David Hilbert.

An easy example of visualization is this: Remember those old games you used to play as a kid - connect the dots without lifting the pencil? Same concept. In this case, it’d be ‘fill each sector of a square/cube without lifting the pencil’. The entire thing is just one curve.

Mathematicians love the Hilbert Curve because aside from being just a space filling curve, it also exhibits a fractal nature. And stuff like that are the stuff mathematicians have wet dreams about.

You can see more hilbert curve structures (including this minced meat one) in FDM Parts.