So you remember that whole “non-euclidean geometry” thing that purportedly is characteristic to various eldritch locations and the like?
What if you could actually be inside this kind of world?
Welcome to HyperRogue.
You will never run out of space
You are Rogue, of course, and somehow found yourself in this strange world full of treasures, countless Lands (including R’yleh, because of course), each with its own special properties, strange enemies… and terrible, terrible sense of direction.
Game milks it’s unusual geometry for all it’s worth. Many game mechanics take advantage or rely on differences between world of HyperRogue – hyperbolic plane – and standard Euclidean space. Combat is simple, though some enemies have puzzle elements. There are almost no traditional RPG system elements – “upgrading” your character is done almost exclusively by using various magical orbs that you can find in Lands (and sometimes on Crossroads existing between Lands) as long as you find sufficient amount of treasures.
First thing first: there is a lot of space there, quite literally. A lot more than in normal space. It has many interesting implications.
Simplest one: on Euclidean plane, if two enemies next to each other run after you, then without obstacles and with equal speed you will have two of them forever after you. In hyperbolic space under exactly same conditions sooner or latter one will drop behind other one without any funneling.
It also works in other direction, though. It is extremely hard to get from point A to B, and then back to A. One wrong turn and you will find yourself very far from intended destination. In fact, so far you practically have no chance to stumble on it by accident… unless you can mark your way somehow.
At least in many Lands directions are hinted by color and item patterns.
Looks can deceive
If you get impression that you are on sphere, you are mistaken! What you see is projection. There is no straightforward way to present surface of globe on two-dimensional flat patch of paper. In same way, you have to show surface of hyperbolic plane in certain way if you want to at least make some sense of it at all. Due to non-euclidean nature of this place, making readable map of bigger areas is literally impossible.
Straight lines exist in this world, but due to projection they will look curved. At least circles still look like circles… but a lot of other things also look like circles, but they aren’t really them (like so-called horocycles – closest equivalent in standard geometry is straight line, since it is only way to represent border of circle that have infinite radius).
It is infinite
This game has so, so many infinities (at least potential ones). World itself and Lands are infinitely large. Entire game is balanced around that fact. Resources are endless, but difficulty rises so sharply you won’t live long gathering treasure of one Land (some Lands have it easier than other, though). Any upgrades and bonuses are always temporary and getting more only prolongs their active time. There is almost no grind, but you certainly will be walking a lot. Interestingly enough, if you could trace your movement through entire game (not counting safe orbs), it almost always will be roughly straight line – yet another consequence of having a lot of space “in” space.
Live and learn
It is little fun game. It is also closest I will ever get nearby this kind of mathematical concept.