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Discussion on: Notes from Hyper-Dimensional Spelunking

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rrampage profile image
Raunak Ramakrishnan

Very well written and informative. I first came across space filling curves while learning Set theory. Cantor used a related technique to prove that points on plane have same cardinality as points on a line, similarly, any n-dim space (where n is finite) has same cardinality as a 1-D line.

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awfulaxolotl profile image
Kevin Sullivan Author

Thanks Raunak!

Ah, I think I remember that proof. If I'm not mistaken, he made the projected line do kind of a zig zag from the origin. Really cool and clever stuff.

I get the feeling space-filling curves are criminally underused -- as cool as they are. One of my favorite applications is by the big G for geospatial coordinates: github.com/google/s2geometry

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Raunak Ramakrishnan

Yes! They should be used more. 3blue1brown had an awesome video on Hilbert curves. I used S2 (python wrapper) at my previous workplace. It helped a lot in making some location calculations easy. The docs are also well written