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Hilbert's Curve: Is infinite math useful?

3Blue1Brown · 2.4M views · 2017-07-21 · 18:18

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Overview

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.

On Hacker News

Recommended as the best visual introduction to Hilbert curves, which come up in indexing, image layout and dimensionality mapping.

Recommended by 4 HN people across 4 months · HN mentions 2017–2024

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What people said

rhart92 · 2017-09 · Strong recommendation

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]

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Cieplak · 2024-01 · Recommendation

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]

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91aintprime · 2020-03 · Recommendation

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

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Sources

Video by 3Blue1Brown, played through YouTube.

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