Hyperbolic space in Poincaré ball model {4,3,5} cut in half.

Hyperbolic space in Poincaré ball model {4,3,5} cut in half.

[@lolzsicka9454]

Brain: this shit too complicated so goodbye im gonna die

[@erikkollar66]

Looks like Kaleidoscope.

[@debblez]

this makes me want to see a hyperbolic penrose tiling

[@marytepes8437]

Wonderful...!

[@FraktalyFraktsal2024]

cool, i understand what's happening.

[@erawanpencil]

What would you see if you were in the center of the ball looking out towards the boundary?

[@ZenoRogue]

Not sure whether I understand your question... you mean hyperbolic space (Poincaré ball), filled like in this video (cubes of the {4,3,5} honeycomb), you are standing in the center of a cube? You would see only the walls of the cube you are in, and since the hyperbolic perspective works generally like the Beltrami-Klein model, it would look just like a cube.

[@erawanpencil]

@@ZenoRogue Oh, no I meant if you were in the center of a Poincare Ball generally, nothing to do with cubes. In other words, is our universe a Poincare Ball, and we're all in the center (at zero?) looking out at ourselves? I saw Penrose say that 'celestial spheres are Reimann Spheres' and I'm trying to picture that, or understand how extensive this math goes into reality. I'm still new to the subject.

[@ZenoRogue]

@@erawanpencil If you were in the center of a Poincare Ball, you would see nothing, because you would be in an empty universe. You would not even see the boundary of this Poincare ball, because it represents "ideal points" which are infinitely far away from you, it is not a real thing to you, so to say. If you assume that the boundary of Poincare Ball is a painted, real thing, and you can see it somehow (despite it being infinitely far away from you), see the "cohomology fractals" on Henry Segerman's channel -- it is a good representation of how the painting changes how it looks as you move.

[@77GOD77]

​@@ZenoRogueBasically like the sky then? We can see the blue sky but it is literally unapproachable! But we are living in a simulation we are a simulation of the Universe itself.

[@Zi7ar21]

Mafs

[@tristenarctician6910]

THIS IS SO SAD