Visualize 3D hyperbolic honeycombs and sphere packings | Hacker News Reader

Visualize 3D hyperbolic honeycombs and sphere packings

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83 pointsmathgenius22 comments

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).

Yeah there's this whole lecture about the hyperbolic geometry commonly seen on a DMT trip: https://youtu.be/loCBvaj4eSg?t=504

I've never seen hyperbolic geometry on not grocery store mushrooms... maybe I should try not grocery store DMT.

Also a really good blog post:

https://plus.maths.org/content/uncoiling-spiral-maths-and-ha...

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.

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?

Essentially, yes (we theorize).

> It turns out that hallucinations comprising spirals, circles, and rays that emanate from the centre correspond to stripes of neural activity in V1 that are inclined at given angles. Lattices like honeycombs or chequer-boards correspond to hexagonal activity patterns in V1.

https://plus.maths.org/content/uncoiling-spiral-maths-and-ha...

The shapes showing up during psychedelic experiences probably have to do with the geometry of our visual perception apparatus:

Uncoiling the spiral: Maths and hallucinations

https://plus.maths.org/content/uncoiling-spiral-maths-and-ha...

One of the creators is on twitter:

https://twitter.com/neozhaoliang

It would be nice to understand (explicitly see) how these Coxeter diagrams give rise to these honeycomb pictures exactly.

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

You can! :) just pay me the non-trivial amount of money. (or go here for free: https://www.youtube.com/watch?v=ztsi0CLxmjw)

I’ll pay in upvote!!

CodeParade has been working on hyperbolica for a while now and doing fantastic videos on the process.

https://youtu.be/EMKLeS-Uq_8

https://store.steampowered.com/app/1256230/Hyperbolica/

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.

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

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.

Basic Income would allow for this. For everyone.

https://en.m.wikipedia.org/wiki/MojoWorld_Generator

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

Would you like some shepard tone with your hyperbolic geometry, sir?

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

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

https://thebookofshaders.com/

and a good sandbox is 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

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