6 ms·

Visualize 3D hyperbolic honeycombs and sphere packings

83 points by mathgenius 5y ago

nprz 5y ago
Interesting, I was just watching this last night: https://www.youtube.com/watch?v=loCBvaj4eSg https://www.youtube.com/watch?v=loCBvaj4eSg
- _Microft 5y ago
  Would you like some shepard tone with your hyperbolic geometry, sir? https://www.youtube.com/watch?v=u9VMfdG873E https://www.youtube.com/watch?v=u9VMfdG873E Unfortunately this is not such a good example of a shepard tone, as the fade-ins of the high-pitched notes are rather audible. You can listen to other examples on the wikipedia page: https://en.wikipedia.org/wiki/Shepard_tone https://en.wikipedia.org/wiki/Shepard_tone
enchiridion 5y ago
I would pay a non-trivial amount of money to be able to move around these, and other non-Euclidean spaces in VR
- deleted 5y ago
  [deleted]
- high_byte 5y ago
  You can! :) just pay me the non-trivial amount of money. (or go here for free: https://www.youtube.com/watch?v=ztsi0CLxmjw https://www.youtube.com/watch?v=ztsi0CLxmjw)
  - enchiridion 5y ago
    I’ll pay in upvote!!
- kortex 5y ago
  CodeParade has been working on hyperbolica for a while now and doing fantastic videos on the process. https://youtu.be/EMKLeS-Uq_8 https://youtu.be/EMKLeS-Uq_8 https://store.steampowered.com/app/1256230/Hyperbolica/ https://store.steampowered.com/app/1256230/Hyperbolica/
  - enchiridion 5y ago
    So I recently heard about Jeff Hawkins 1000 brain’s theory when he was on Lex Friedman. The idea is that there is a basic unit of the brain, originally meant for mapping the environment, which was copied many times with adjustments to give us our current brain. If that is true, I wonder what brain activity while exploring hyperbolic spaces would look like.
mathgenius 5y ago
One of the creators is on twitter: https://twitter.com/neozhaoliang https://twitter.com/neozhaoliang It would be nice to understand (explicitly see) how these Coxeter diagrams give rise to these honeycomb pictures exactly.
istorical 5y ago
wish there was a modern day equivalent of medieval patronage (one rich patron you had to convince, rather than pleasing and amassing hundreds of small patrons with online astroturfing and self-aggrandizing spam marketing), I would love to spend my life creating virtual worlds you could travel through as beautiful as those fractals but with interesting things to do and discover inside. was scratching my artistic itch and self-funding exploring such things but ran out of money and had to go back to the real world: https://cmadams.itch.io/preydrivr https://cmadams.itch.io/preydrivr
- high_byte 5y ago
  you just described angel/VC investments vs. crowdsourced investment/bootstrapped income. there are thousands of ways to make a million dollars: you could ask one person for a million dollars, you could ask a million people for one dollar, or anything in between. you could start a patreon & market it through youtube because I think the concept is right.
- mandmandam 5y ago
  Basic Income would allow for this. For everyone.
- Keyframe 5y ago
  https://en.m.wikipedia.org/wiki/MojoWorld_Generator https://en.m.wikipedia.org/wiki/MojoWorld_Generator
gdubs 5y ago
Maybe a tangent but in high school we procured some … not grocery store mushrooms, and whatever it did to my brain made me see the universe as a 3d hyperbolic honeycomb lattice. Though until today, I had no idea there was a name for that particular geometry. I wonder why these shapes show up so frequently in psychedelic art and experiences (anecdotally I’m not the only one who’s had a similar visual, by a long-shot).
- nprz 5y ago
  Yeah there's this whole lecture about the hyperbolic geometry commonly seen on a DMT trip: https://youtu.be/loCBvaj4eSg?t=504 https://youtu.be/loCBvaj4eSg?t=504
  - high_byte 5y ago
    I've never seen hyperbolic geometry on not grocery store mushrooms... maybe I should try not grocery store DMT.
  - kortex 5y ago
    Also a really good blog post: https://plus.maths.org/content/uncoiling-spiral-maths-and-hallucinations https://plus.maths.org/content/uncoiling-spiral-maths-and-ha...
- tokipin 5y ago
  My guess is they are mid-layer activations in the brain that your consciousness (attention?) is connecting to, or which are being directed to the lower layers and interpreted as input.
  - gdubs 5y ago
    Are you saying that it’s the brain being conscious of the geometry of the light processing system? Kind of like the hidden layers of a neural network?
    - kortex 5y ago
gwintrob 5y ago
Any suggested reading/tutorials on how to play with OpenGL shaders?
- high_byte 5y ago
  https://thebookofshaders.com/ https://thebookofshaders.com/ and a good sandbox is https://shadertoy.com/ https://shadertoy.com/ and you should consider unity too, this is a good tutorial but also lots of good info about graphics in general: https://youtu.be/kfM-yu0iQBk https://youtu.be/kfM-yu0iQBk

83 points by mathgenius 5y ago

nprz 5y ago

Interesting, I was just watching this last night: https://www.youtube.com/watch?v=loCBvaj4eSg https://www.youtube.com/watch?v=loCBvaj4eSg

_Microft 5y ago
Would you like some shepard tone with your hyperbolic geometry, sir? https://www.youtube.com/watch?v=u9VMfdG873E https://www.youtube.com/watch?v=u9VMfdG873E Unfortunately this is not such a good example of a shepard tone, as the fade-ins of the high-pitched notes are rather audible. You can listen to other examples on the wikipedia page: https://en.wikipedia.org/wiki/Shepard_tone https://en.wikipedia.org/wiki/Shepard_tone

enchiridion 5y ago

I would pay a non-trivial amount of money to be able to move around these, and other non-Euclidean spaces in VR

deleted 5y ago
[deleted]
high_byte 5y ago
You can! :) just pay me the non-trivial amount of money. (or go here for free: https://www.youtube.com/watch?v=ztsi0CLxmjw https://www.youtube.com/watch?v=ztsi0CLxmjw)
- enchiridion 5y ago
  I’ll pay in upvote!!
kortex 5y ago
CodeParade has been working on hyperbolica for a while now and doing fantastic videos on the process. https://youtu.be/EMKLeS-Uq_8 https://youtu.be/EMKLeS-Uq_8 https://store.steampowered.com/app/1256230/Hyperbolica/ https://store.steampowered.com/app/1256230/Hyperbolica/
- enchiridion 5y ago
  So I recently heard about Jeff Hawkins 1000 brain’s theory when he was on Lex Friedman. The idea is that there is a basic unit of the brain, originally meant for mapping the environment, which was copied many times with adjustments to give us our current brain. If that is true, I wonder what brain activity while exploring hyperbolic spaces would look like.

mathgenius 5y ago

One of the creators is on twitter: https://twitter.com/neozhaoliang https://twitter.com/neozhaoliang It would be nice to understand (explicitly see) how these Coxeter diagrams give rise to these honeycomb pictures exactly.

istorical 5y ago

wish there was a modern day equivalent of medieval patronage (one rich patron you had to convince, rather than pleasing and amassing hundreds of small patrons with online astroturfing and self-aggrandizing spam marketing), I would love to spend my life creating virtual worlds you could travel through as beautiful as those fractals but with interesting things to do and discover inside. was scratching my artistic itch and self-funding exploring such things but ran out of money and had to go back to the real world: https://cmadams.itch.io/preydrivr https://cmadams.itch.io/preydrivr

high_byte 5y ago
you just described angel/VC investments vs. crowdsourced investment/bootstrapped income. there are thousands of ways to make a million dollars: you could ask one person for a million dollars, you could ask a million people for one dollar, or anything in between. you could start a patreon & market it through youtube because I think the concept is right.
mandmandam 5y ago
Basic Income would allow for this. For everyone.
Keyframe 5y ago
https://en.m.wikipedia.org/wiki/MojoWorld_Generator https://en.m.wikipedia.org/wiki/MojoWorld_Generator

gdubs 5y ago

Maybe a tangent but in high school we procured some … not grocery store mushrooms, and whatever it did to my brain made me see the universe as a 3d hyperbolic honeycomb lattice. Though until today, I had no idea there was a name for that particular geometry. I wonder why these shapes show up so frequently in psychedelic art and experiences (anecdotally I’m not the only one who’s had a similar visual, by a long-shot).

nprz 5y ago
Yeah there's this whole lecture about the hyperbolic geometry commonly seen on a DMT trip: https://youtu.be/loCBvaj4eSg?t=504 https://youtu.be/loCBvaj4eSg?t=504
- high_byte 5y ago
  I've never seen hyperbolic geometry on not grocery store mushrooms... maybe I should try not grocery store DMT.
- kortex 5y ago
  Also a really good blog post: https://plus.maths.org/content/uncoiling-spiral-maths-and-hallucinations https://plus.maths.org/content/uncoiling-spiral-maths-and-ha...
tokipin 5y ago
My guess is they are mid-layer activations in the brain that your consciousness (attention?) is connecting to, or which are being directed to the lower layers and interpreted as input.
- gdubs 5y ago
  Are you saying that it’s the brain being conscious of the geometry of the light processing system? Kind of like the hidden layers of a neural network?
  - kortex 5y ago

gwintrob 5y ago

Any suggested reading/tutorials on how to play with OpenGL shaders?

high_byte 5y ago
https://thebookofshaders.com/ https://thebookofshaders.com/ and a good sandbox is https://shadertoy.com/ https://shadertoy.com/ and you should consider unity too, this is a good tutorial but also lots of good info about graphics in general: https://youtu.be/kfM-yu0iQBk https://youtu.be/kfM-yu0iQBk