Hilbert's Curve: Is infinite math useful?

I am not sure if you have heard of them, but space-filling curves are a way to demonstrate this. This is a great video on the Hilbert curve [VIDEO]

This is actually exactly the topic of the 3Blue1Brown video on Hilbert Curves: [VIDEO] Space-filling curves are a sort of optimal mapping strategy for compressing two dimensions down into one.

On a related note, does anyone know of a good reference of applying space filling curves as a method of dimensionality reduction? It seems like an intuitive idea since Hilbert curves [1] map points from a higher to a lower dim space but tries to preserve distance as well. [1] 3Blue1Brown video on Hilbert curves: [VIDEO]

That sounds like it would be very interesting. And while we can't extend our senses just yet, we may be able to swap them. I'm very curious if anyone has tried to use a space-filling Hilbert curve to transform vision into audio and let their brain adjust to it like suggested in this video [VIDEO]

Hilbert's curve: Is infinite math useful? by 3blue1brown [VIDEO] or skip directly to the conclusion; [VIDEO]

There's a command-line utility called pixd [1] that generates similar data visualizations on the command line. That said, it only shows static representations of binary data and is not nearly as cool as buredoranna's animated gifs showing filesystem changes over time. It can be helpful to plot these sorts of pixel arrangements on a Hilbert curve, rather than plotting pixels line by line. I learned this trick from a Ghidra plugin called cantordust [2]. 3blue1brown offers some mathematical intuition for the effectiveness of a Hilbert curve pixel arrangement [3]. [1] [LINK] [2] [LINK] [3] [VIDEO]