“This is a great video on the Hilbert curve”
Great video on the Hilbert curve.
Full comment
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 this video
Hilbert's Curve: Is infinite math useful?
2.4M views · Jul 21, 2017 · 18:18 · 4 HN recommenders · 6 mentions · discussed 2017–2024
3Blue1Brown explains space-filling curves and the Hilbert curve, and how infinite mathematical constructions connect to finite, practical approximations. It touches on mapping between dimensions and sensory ideas.
Why Hacker News points people here: Recommended as the best visual introduction to Hilbert curves, which come up in indexing, image layout and dimensionality mapping.
“This is a great video on the Hilbert curve”HN comment, 2017
What Hacker News said 6
“Space-filling curves are a sort of optimal mapping strategy for compressing two dimensions down into one.”
Covers space-filling curves as optimal 2D to 1D mapping.
Full comment
This is actually exactly the topic of the 3Blue1Brown video on Hilbert Curves: this video Space-filling curves are a sort of optimal mapping strategy for compressing two dimensions down into one.
“or skip directly to the conclusion;”
Hilbert curve video by 3Blue1Brown, with a link to the conclusion.
Full comment
Hilbert's curve: Is infinite math useful? by 3blue1brown this video or skip directly to the conclusion; this video
“3blue1brown offers some mathematical intuition for the effectiveness of a Hilbert curve pixel arrangement”
Mathematical intuition for why Hilbert curve pixel arrangement works.
Full comment
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] this video
“3Blue1Brown video on Hilbert curves”
Full comment
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: this video
“use a space-filling Hilbert curve to transform vision into audio”
Suggests using a Hilbert curve to map vision to audio.
Full comment
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 this video