Our brain reconstructs the 3D scene based on the angles perceived by both eyes. So (under some natural assumptions) a human in hyperbolic space would perceive it as the Beltrami-Klein ellipsoid model -- their eyes would be at the foci of this ellipsoid!

Note that, in the picture in [2/3], for clarity, the distance between foci was much larger than the distance between the eyes of the Princess. Here is a picture that is more accurate to the size of HyperRogue characters. The cutting plane is more "flat" and the perceived shape of hyperbolic space is closer to a B-K ball than obvious ellipsoid.

(This was inspired by @theking's 2019 post https://www.reddit.com/r/Hyperrogue/comments/aq4i7k/euclidean_depth_perception_in_the_hyperbolic_plane/ abut what hyperbolic space looks like, and the "stretched B-K" result was originally proven by Magma in the HyperRogue discord -- however, Magma's proof only used continuity to show that the ellipsoid model is azimuthal in two points -- but not that they are actually foci.)

[3/3] #hyperrogue #vr #RogueViz #nonEuclidean #noneuclideanGeometry #mathart #geometry

This game is indirectly based on #Borges' "The Library of Babel", and it's cleanly done. I appreciate that it can be played with the keyboard.

I played for 3 days wanting something to happen, then I stopped sleeping - it gets dark. Morale dropped soon, and then I jumped. There is a ground. You need to climb a bunch of floors so that it kills you. I started holding down keys but didn't bother killing myself many times. Finally, I rerolled characters for a short walk.

Would've been pretty cool if it were sorted like #Hyperrogue's turtle challenge, but that would defeat the point. Excellent adaptation.

#7drl #roguelike #gamejam