this post was submitted on 12 Aug 2025
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submitted 3 days ago by fossilesque@mander.xyz to c/science_memes@mander.xyz
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[–] bleistift2@sopuli.xyz 5 points 3 days ago (1 children)

You can define Hilbert Curves that map n dimensions on to n−1 dimensions.

[–] IAmNorRealTakeYourMeds@lemmy.world 2 points 3 days ago (1 children)

next interesting question, how would a 3d object look if we map it to a 3d Hilbert curve, and unfold to a 2d hilbert curve.

would properties of the original object be visible, IE, if we use a sphere, would the projection look like a circle?

if the sphere is only a shell and it's empty inside, would the Hilbert projection show it?

or would the information be scrambled beyond recognition?

[–] bleistift2@sopuli.xyz 1 points 3 days ago (1 children)

Well, if you map the Mona Lisa onto a Hilbert curve and untangle the curve, you get a long sequence of random blotches of color. So I guess the horse won’t be recognizable in 2D.

[–] IAmNorRealTakeYourMeds@lemmy.world 2 points 3 days ago (1 children)

any protection to a line will be meaningless, mostly because we can't really put lots of visual information in a single extremely long line.

however,.I disagree in principle, if we flatten a bug, the end result is slightly abstract but we can still identify the bug and features. so we can theoretically agree that a 3d>2d mapping can be done so information is still positionally related a and not scrambled.

question is if the Hilbert projection would do that (i doubt that). but there must be projection methods that would actually work

[–] bleistift2@sopuli.xyz 2 points 2 days ago (1 children)

if we flatten a bug, the end result is slightly abstract but we can still identify the bug and features

I believe that you’re thinking of squishing a bug. But that’s a very lossy projection. In its 2D state you only look at the topmost portion of the bug, which is recognizable. But you’re choosing to ignore the infinitely many points that make up all the other layers of the bug. If you had to put them somewhere, too, the resulting picture would be very hard to make sense of.

[–] IAmNorRealTakeYourMeds@lemmy.world 1 points 2 days ago

I'm including all the "goo". all the internal organs will be spread out, and even though they won't be near the original place, they'll still maintain lots of proximity relations.

I'm not using it as a perfect example. but as an example that a volumetric 2d projection could maintain positional information, rather than information getting scrambled.

unless gpt fucked up (I do data science, this is far beyond my skills), this is what a sphere in a Hilbert projection looks like:

might be better to use a volume filling surface rather than a volume filling line