geometry – SITMO Machine Learning

Here’s a short snippet that draws the Hilbert space-filling curve using a recursive approach.

It sounds counterintuitive. A curve normally has no area, it’s just a line. But a space-filling curve is a special type of curve that gets arbitrarily close to every point in a 2D square. If you keep refining it, the curve passes so densely through the space that it effectively covers the entire square. In the mathematical limit, it touches every point.