Hyperbolic Geometry in HyperRogue

Jacob demonstrates some of the interesting properties of the hyperbolic plane through a video game that exemplifies them.
You can get HyperRogue at www.roguetemple.com/z/hyper/ for free, or the Steam-integrated, latest updated version at store.steampowered.com/app/342... for $2.99.

[@ZenoRogue]

Thanks for the video! There are several more nice hyperbolic features in the game which are not covered nor mentioned in the video, like the lands based on horocycles (e.g., Temple of Cthulhu, Whirlpool), the Princess Quest (navigation, solvable with probability ~1), infinite tree-like structures which would not fit in Euclidean (e.g. Zebra, Palace, Vineyard), etc.

[@marcopolo8584]

"What does this do?" "I guess we'll never know." Oh yeah, it's a roguelike.

[@huangkeqi8263]

You forgot that these lands are not large, But TECHNICALLY INFINITY. by this there's also one infinity large-enemy in Clearings, The infinite mutant ivy.

[@SimonClarkstone]

@Electro_blob 2 Indeed. In most games the hub world needs teleporters. In Hyperrogue it is simply adjacent to everything.

[@igorjosue8957]

and i dont know but i think the camelot is the only whose land isnt infinity, but it still very big, like, u cant see the walls from the middle of it

[@TheRMeerkerk]

Wouldn't it be cool to have a 3D hyperbolic FPS game. Admittedly it would be harder to find others and you get lost pretty quickly, but it still sounds like something someone should try to make for fun.

[@AlgolZ]

There's a hyperbolic VR available (elevr), and admittedly it'll be very cool to have any sort of game that uses it in 3D, though because the amount needed to render increases exponentially as render distance increases, the amount of computing power needed would be substantial to say the least. Sniping would be also be neigh impossible in FPS as well given its nature.

[@ZenoRogue]

Yeah, elliptic geometry is cool in VR/FPP -- you see the same things in front of you as behind you (unless they are covered by something else). Just created a spherical VR video (with HyperRogue's engine): kzbin.info/www/bejne/qoWbYZWlg8-DlaM

[@ChristopherKing288]

That's possible in the newest version. Just set dimensions to three, perspective to first person, and combat to shooter.

[@_Iscream]

Actually.... kzbin.info/www/bejne/e36ufZiJYrqklZo

[@TheRMeerkerk]

@@_Iscream Yeah I saw the video a couple of days ago too.

[@kshinji]

This game is awesome. I love how the idea was so smoothly turned reality. For such an eccentric game I would have expect less pleasant experience, but it was very, very nice.

[@paulfoss5385]

When I leave the Icy Lands I usually let the wolves live to block further attacks from that world.

[@alan2here]

Kickass video, please keep making ones on the mathematical properties of hyperbolic space with reference to this incredible game. Also, your killing me with mouse navigation all video like this! After a while start using (the number-pad)/(a game controller) etc...

[@TheRojo387]

The main problem is the tidal forces that try to rip you apart as you move.

[@gracefool]

You're okay so long as you don't go too fast. You'd feel the forces growing gradually.

[@Hampardo]

Awesome!

[@AdlerMow]

I want a VR Lovecraft game where I can enter the hyperbolic space. In normal space you can be strong and a hunter but in hyperbolic you are the prey, and had to follow their rules in their lair. Also, motion sickness and insanity of the non-euclidian geometry!

[@greshengaines7099]

Thank you, I underestimated this game

[@Dragoniiia]

Nice video btw

[@marcosssocram]

Escher like this.

[@robelicit]

Marcos Socram ..Yes, very very Escher like, definitely the game designers and artists were Escher fans ✌👊📐📏🍺🍸

[@ynntari2775]

I'll strongly wait for an immersive hyperbolic game, in which you move like in console videogames instead of clicking in where you can't to go with turns.

[@Norsilca]

Look up Hyperbolica.

[@ynntari2775]

Isn't Hyperbolica like just a test? Like, just a world with some stuff to see and nothing to do?

[@Norsilca]

@@ynntari2775 Not sure, but yeah it seems like less of a traditional game like HyperRogue. At least you can experience actual 3D hyperbolic space. But the holy grail, a 3D hyperbolic shooter, is still nowhere to be seen. Man, I was just thinking, how would aiming even work? It seems like it would basically be impossible, since any tiny error would cause the bullet to miss wildly!

[@gracefool]

@@Norsilca Worse than that, if it had realistic physics the bullet would pull itself apart before it even left the barrel, because the faster something moves, the faster the different sides of it move away from each other.

[@igorjosue8957]

continuous space of hyperrogue only press V then M then S to activate the continuous space mode, and u can play like it

[@igorjosue8957]

the game was made in 2015 but i only liked when i notice a gameplay of it in 2019

[@AlexandrePorto]

Nice

[@alansmithee419]

1:18 Isn't it asymptotic? Doesn't that faint blue ring represent infinite area? 2:55 You pretty much confirm it here.

[@leonardovergara5620]

1:18 I hear Exponentially watch memes.

[@Dragoniiia]

I am. Confused.

[@bld691]

./net

[@the_hanged_clown]

wow... Portal I could manage but this is absolutely nauseating.

[@leonardovergara5620]

I just ignore the expanse-ness and play it linearly.

[@jessfucket]

The hyperbolicity is unnecessary; just play on a Euclidian hexagonal grid seen from above and put a 180º fisheye lens in the virtual camera. The essential nature of the Poincare disk is that faraway things are tiny. But that is not relevant here, since the player always moves locally, and all manifolds are locally Euclidean. Or am I WAY off?

[@thomashall1236]

even locally parallel lines diverge quite quickly which would not happen with lensed euclidian space

[@glitchy9613]

it wouldn't have any of the interesting effects hyperbolic space has

[@godlyvex5543]

Hard disagree. I tried playing on euclidean mode, which is basically exactly what you described, without the fisheye lens. The problem is that it's way harder to find new areas. There just isn't enough space. You can only see 7 or so tiles away in hyperbolic space, yes, but you still see way, WAY more tiles. In euclidean mode you sometimes spend several minutes walking and not finding any new lands, while in hyperbolic space you are constantly seeing new lands. In euclidean space, you can easily run out of treasures to collect, as the land is usually finite and small. In hyperbolic space, every land is infinitely large. This isn't even mentioning lands that simply don't function in euclidean geometry, like the temple of cthulhu. It has infinite layers of concentric circles that you delve into. In euclidean geometry, this isn't possible. Lands like camelot would also be quite boring. The challenge of camelot is finding the center of a hyperbolic circle, but finding the center of a euclidean circle is trivial.

[@ophello]

You’re pronouncing “hyperbolic” wrong. The “o” in hyperbolic should rhyme with the “a” in “bawl.” Not the “o” in “bowl.” Hyper-BAWL-ick. Not “hyper-BOWL-ick.”

[@infiniteplanes5775]

On the other hand, it is spelt with an o rather than an a

[@ZenoRogue]

Thanks for the video! There are several more nice hyperbolic features in the game which are not covered nor mentioned in the video, like the lands based on horocycles (e.g., Temple of Cthulhu, Whirlpool), the Princess Quest (navigation, solvable with probability ~1), infinite tree-like structures which would not fit in Euclidean (e.g. Zebra, Palace, Vineyard), etc.

[@coopergates9680]

+ZenoTheRogue I assume that Euclidean space is used to model the hyperbolic plane in this game, so how are all these features stored when they are not in the range being rendered?

[@ZenoRogue]

+Cooper Gates This page describes roughly how HyperRogue is implemented: www.roguetemple.com/z/hyper/dev.php (it is a bit outdated, but the general idea did not change). Does this answer your question?

[@coopergates9680]

+ZenoTheRogue Why is it more convenient to run the computations in the hyperboloid model, which needs an extra dimension, as opposed to half-space or disk models, or even the Klein model with "straight" geodesics?

[@ZenoRogue]

I have answered this question here: steamcommunity.com/app/342610/discussions/0/535151589910869886/ Having a third dimension is not a problem, and I don't see how having straight geodesics would help.

[@coopergates9680]

+ZenoTheRogue It's interesting to read about algorithms for approximating horocycles in a 6,6,7 tiling of H^2, but I don't see how it answers my question. My point about dimensions was that, if you are limited to modeling in 3-space (x, y, z), the hyperboloid model represents H^2, but a half-space or Poincare ball would handle H^3 (3D hyperbolic space) in that same set of coordinates. Maybe your main argument for the hyperboloid model is the formula for the hyperbolic distance between two points (more complex in other models), although that's only one parameter.