One day I got a bee in my bonnet to make some fractal furniture with copper pipe. The Hilbert Curve was the obvious first choice.
At the time, I'd only made one other piece of furniture out of copper pipe, and was showing it off at the Fat Man & Circuit Girl show. They asked me what I was going to do next. "A Hilbert Curve coffee table," I blurted, and suddenly I was committed, though I had no idea if I could actually make it work.
So I got busy making sketches, trying to figure out if this was even possible. I didn't know much about Hilbert curves, but of course Wikipedia does. It still took me some time to get a good grasp of what's going on and how the different fractal levels relate to each other.
At PDX Dorkbot I started cutting pipe, and attempting to lay out & put together the first Hilbert curve section. I had hoped to get finer detail, but the half inch elbow fittings gave me a hard constraint on the size.
I decided to make it a 2x3 layout, with different fractal levels in a checkerboard pattern. Then I got to work fitting the pieces together, fluxing & soldering the level 3 sections, then partially assembling it to get the level 2 sections right.
Once the top was figured out, it was time to build a two-level jig to make a shelf (a Moore curve, also space-filling like a Hilbert curve).