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#hilbertcurve#space-fillingcurves#dimensionalityreduction

Hilbert's Curve: Is infinite math useful?

3Blue1Brown

8.7M subscribers • 42 videos on Hallway

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  • Recommended by 4 people: 4 on Hacker News.
  • A classic. People kept recommending it from 2017 to 2024.

Beginner. No background in the topic needed.

2.4M views9 years ago4 recommendations

Computer scienceGraphics and audioAlgorithmsData visualizationMath for programmers

An animated explanation of space-filling curves, focusing on the Hilbert curve and its applications in mapping dimensions.

Space-filling curves, and the connection between infinite and finite math. Help fund future projects: patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: 3blue1brown.com Supplement with more space-filling curve fun: youtu.be/RU0wScIj36o For more information on sight-via sound, this paper involving rewiring a ferret's retinas to its auditory cortex is particularly thought-provoking: phy.ucsf.edu/~houde/coleman/sur2.pdf Alternatively, here is the NYT summary: goo.gl/qNuc14 Also, check out this excellent podcast on Human echolocation: goo.gl/23f4Yh For anyone curious to read more about the connections between infinite and finite math, consider this Terry Tao blog post: goo.gl/NZ4yrW Lion photo by Kevin Pluck Music by Vincent Rubinetti: vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). Various social media stuffs: Website: 3blue1brown.com Twitter: twitter.com/3Blue1Brown Patreon: patreon.com/3blue1brown Facebook: facebook.com/3blue1brown Reddit: reddit.com/r/3Blue1Brownm/r/3Blue1Brown

Why it's here

4 people recommend this

What people say. Recommended as an exceptionally clear visual explanation of Hilbert curves and their utility in dimensionality reduction.

rhart92on Hacker News • Recommends

On “Mathematicians Measure Infinities, Find They’re Equal”

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 link to this video
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joelgon Hacker News • Recommends

On “My Sudden Synaesthesia”

This is actually exactly the topic of the 3Blue1Brown video on Hilbert Curves: link to this video Space-filling curves are a sort of optimal mapping strategy for compressing two dimensions down into one.
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91aintprimeon Hacker News • Recommends

On “Landmark computer science proof cascades through physics and math”

Hilbert's curve: Is infinite math useful? by 3blue1brown link to this video or skip directly to the conclusion; link to this video
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Cieplakon Hacker News • Recommends

On “Visualizing Ext4”

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 link to this video
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bhlon Hacker News • Mentions

On “Onion Curve: A Space Filling Curve with Near-Optimal Clustering (2018)”

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: link to this video
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vankesselon Hacker News • Mentions

On “The Human Brain Can Create Structures in Up to 11 Dimensions”

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 link to this video
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