What are space filling curves used for in the real world?

Question

I recently watched 3Blue1Brown's video on the Hilbert Curve and Fractals, and I was wondering if the concept behind space-filling curves like the Hilbert Curve and Flow Snake could be applied in real life anywhere. I have a hunch that there's tons of ways to apply them usefully irl, but I can't think of any specific one.

Answer 1

Z-order curves are used in GPUs to preserve locality, i.e. the pixels of a texture/image when loaded into the GPU are ordered according to Z-order curve instead of ordering them line-by-line, so that if two pixels are close to each other, their locations in memory would be also close to each other, which helps in caching and therefore performance.

3Blue1Brown made a video describing a hypothetical use case, converting image into sound, where fact that a point on the curve (e.g. t=0.4) converges into a specific-point in the plane (e.g. (0.3, 0.2)) helps produce a similar sound for a similar image if the resolution has changed (the video is way better at describing it.)

Answer 2

The Hilbert curve is the foundation for S2 cells, developed by Eric Veach at Google. These cells provide a sequential covering of the surface of the Earth, at a chosen level of detail, in such a way that cells that are near to each other geographically are also near to each other in the sequence.

Probably the most widespread application for S2 cells is in Pokémon GO, which uses them for almost every aspect of geography related to proximity.

Here are some sources:
- Google’s S2, geometry on the sphere, cells and Hilbert curve, in Christian S. Perone's blog Terra Incognita;
- S2 Cells, in the technical documentation for the S2 library;
- A Comprehensive Guide to S2 Cells and Pokémon GO.