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HyperRogue 3 - a non-Euclidean roguelike

sgc_meltdown

Arcane
Joined
May 8, 2003
Messages
6,000
http://www.roguetemple.com/z/hyper.php

You are a lone adventurer trapped in a strange non-Euclidean world. Collect as much treasure as possible before being caught by monsters. The more treasure you collect, the more monsters come to hunt you, as long as you are in the same land type. You can fight most monsters by moving into its location. The monster could also kill you by moving into your location, but the game automatically cancels all moves which result in that.

HyperRogue III features:
  • a new structure of the map (most roguelikes allow 8-directional movement, like Rogue, recently there are many new roguelikes which explore changing this geometrical structure: some games use 4-directional movement, and there are also some based on a hex grid; Hyperbolic Rogue tries hyperbolic geometry, which is very different)
  • a perspective with objects drawn smaller and smaller as the distance from the PC increases
  • when the PC moves, the perspective rotates to catch them
  • eleven original worlds to explore, and powerful magical orbs and other objects
  • find the Orb of Yendor to win the game
Click to expand...



http://zenorogue.blogspot.sg/2012/03/hyperbolic-geometry-in-hyperbolic-rogue.html
HyperRogue takes place on a hyperbolic plane. You can read more about it on
Wikipedia. This is not a sphere,but rather a hyperboloid (but also not in a normal space). The 3D object you see when you activate the “eye distance”option is this hyperboloid.

Normally the game presents the world in the so called Poincaré disc model.
http://en.wikipedia.org/wiki/Poincaré_disc_model
http://en.wikipedia.org/wiki/Hyperbolic_geometry#Models_of_the_hyperbolic_plane

The closer you are to the edge of the disc, the bigger distances are (five pixels close to the edge is a much bigger distance than five pixels in the center). On the Euclidean plane, the boundary of a circle of radius r is linear in r. On the hyperbolic plane it is exponential. This means that it is very hard to return to a place where you have already been in HyperRogue. You would have to return almost the same way.

Triangles in hyperbolic geometry have angles which sum to less than 180 degrees. For example, if you take two hexagons and one heptagons next to each other on the HyperRogue map, the sum is (360/6) + (360/6) + (360/7) = 171.4 degrees. The bigger the difference with 180 degrees is, the bigger such a triangle. (Similar thing happens on a sphere: a triangle with a vertex on a pole and two on the equator has 90+90+90 = 180+90 degrees, which is π/2 more than 180 degrees, and the total area of the sphere is 4π, which corresponds to eight of our triangles.)

This is the map structure I have found most suitable for a roguelike (or other similar grid-based game). Three hexagons would sum up to 180 degrees and we would get a plane. Three heptagons in each corner would be possible, but they would be too big (each of them would take the space of one heptagon in HyperRogue plus 1/3 of each hexagon surrounding it).

Now how does this relate to the actual gameplay? As already mentioned, an important result of using the hyperbolic plane is that you almost never get into a place where you have been before. Some of the areas make other aspects of the hyperbolic geometry important, and some are just for fun.
Click to expand...


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Last edited by a moderator:
Zeriel

Zeriel

Arcane
Joined
Jun 17, 2012
Messages
13,428
I feel like this is what Prosper would have made if he was high-functioning.
 

Citizen

Guest
This is like that thing prosper was talking about
 
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