Random Hilbert Curve - 10cm

Hilbert curves are more than pretty.

All space-filling curves allow you translate N-dimentional space down to 1 dimension. Hilbert curves are unusually good at doing that, with few "jumps" where they lunge across the space they're filling. This means that the distance between two points along the curve is fairly proportional to their Euclidean distance in N-dimensional space.

This allows all sorts of tomfoolery. Subdivide the Hilbert curve over an N-dimensional space containing points, until each occupies one "voxel" of the curve. Reorganize the points so that they're in the order you visit along the curve, and you've got a decent solution to the shortest path through every point. Other approaches will give you better estimates, but only space-filling curves allow you to do it without measuring the distance between points! Alternatively, do the above but partition the points into as many groups as you want. Now you've got a decent set of bounded volumes to characterize the entire set. Modern databases also use space-filling curves to reduce their lookup times, especially when dealing with spatial data.

This sculpture is a tribute to the practical side of Hilbert curves. Take a collection of random 3D points, sort them according to their location along the Hilbert curve, and turn those into the control points of a Bezier spline. The result is something that looks like a mess, until you look at it perpedicular to one of the sides. Suddenly, the method is revealed within the madness.

As if that wasn't cool enough, this technique allows an infinite number of variants to be generated. I'll be periodically uploading variants manually, but you've also got the option of asking for your own variant.

The only thing cooler than owning mathematical art is owning a unique piece of mathematical art.