History VideoGame / HyperRogue

* NoobCave: Each normal game starts in the Icy Land, an area designed for new players with no real gimmicks (aside from the meling walls) and two enemies with simple behaviors (Yetis and Icewolves). It can still become difficult to survive in it once you collect enough Ice Diamonds, though.

The game is free software, with the music released under CC BY-SA 3.0 and everything else released under GPL2, and can be downloaded for free or compiled from source. However, a purchase on UsefulNotes/{{Steam}}, the Play Store or the App Store will give access to the platform-specific leaderboards and achievements, ''may'' include features not yet freely released, and of course, supports the developer. [[http://www.roguetemple.com/z/hyper/download.php The official website]] explains this in more detail.

You can buy it on UsefulNotes/{{Steam}} [[http://store.steampowered.com/app/342610 here,]] or get the free version [[http://www.roguetemple.com/z/hyper/download.php here.]] The free version is complete, but it's updated less frequently.

* '''Apeirogons''': polygons with an infinite amount of sides (you start with one side of X length, then add two sides connecting it that are, say, half the length of the first side, then two more sides half again in length, and so on). If the sides are short enough, a regular apeirogon approximates a horocycle.

* '''Ultraparallel''' lines, which can be said to have a point where they're "closest" to each other, and beyond it, diverge.

* '''Apeirogons''': polygons with an infinite amount of sides. If the sides are short enough, a regular apeirogon approximates a horocycle.

* '''Hypercycles''', "circles" with ''more'' than infinite area and radius. On the disk model, they look like circles intersecting the disk at non-right angles; if they intersected at right angles, they would be straight lines. They can be generated by including all points that are a given distance from a straight line, and as such, are sometimes also known as '''equidistants'''.

Hyperbolic geometry is a type of non-Euclidean geometry, meaning that it does away with some of Euclid's postulates. In particular, it does away with the parallel postulate, stating that given a line and a point, there is exactly one line parallel to the line and going through the point; in hyperbolic geometry, there is an infinite amount of them (see AlienGeometries below for the non-Technobabble explanation).

Hyperbolic geometry is a type of non-Euclidean geometry, meaning that it does away with some of Euclid's postulates. In particular, it does away with the parallel postulate, stating that given a line and a point, there is exactly one line parallel to the line and going through the point; in hyperbolic geometry, there is an infinite amount of them.

** In later versions, this was expanded to a full-on "experiment with geometry" menu, which gives you a lot more options for geometry, including spherical, Euclidean, hyperbolic, triangles, squares, pentagons, octagons, whatever you fancy. You aren't limited to two dimensions, either: want to play in a grid of dodecahedra? You're the king. It even includes geometries that work in three dimensions but not in two, such as Solv (explanation: [[spoiler:XY and XZ planes are hyperbolic, but oriented orthogonally, so receding objects will appear to stretch.]]) and Nil (explanation: [[spoiler:moving forward, then left, then backward, then right results in net movement up, allowing "impossible" Penrose staircases to exist.]]).
** Version 7.0 also adds Shoot-'em-up mode, where you have a ranged attack, your movement (and movement of monsters) no longer needs to follow the grid, and the game plays in real-time, with most mechanics kept unchanged.

** Hyperbolic space has completely unintuitive (for us) relations between linear size and area. For example: if you consider that an edge of the game's tiles is around 1 meter long, then a circle whose radius is merely 91.6 meters will have greater area than ''Earth''. And yet, any two points will be less than 200 m apart. If it had a radius of 152 m, it would surpass the surface area of a sphere with the radius of Earth's orbit! A circle with radius 1 km would then have an absolutely insane area of 1.65 x 10^140 km2. This is showcased by the Round Table, a circle of a radius
of 28 tiles. In Euclidean space, it would have an area of a few thousand tiles; here, it takes up over 30 ''million''.

** The Vineyard has a regular arrangement of hyperparallel lines.

** The Round Table is a circle of radius 28. In Euclidean space, it would have an area of a few thousand tiles; here, it takes up over 30 ''million''.

** Less obviously, the Running Dogs follow you on a path always one step to your left or your right (since they can't walk on tiles you've walked on). If you run in a straight line, you'll slowly outpace them, due to the above mentioned factor of parallel lines diverging by necessity in a hyperbolic world (for them to catch up with you they would need to be following on the exact tiles you've been walking in, but they can't, so they can only run in a line parallel to yours).

** Hyperbolic space has completely unintuitive (for us) relations between linear size and area. For example: if you consider that an edge of the game's tiles is around 1 meter long, then a circle whose radius is merely 91.6 meters will have greater area than ''Earth''. And yet, any two points will be less than 200 m apart. If it had a radius of 152 m, it would surpass the surface area of a sphere with the radius of Earth's orbit! A circle with radius 1 km would then have an absolutely insane area of 1.65 x 10^140 km2.

* HubLevel: The Crossroads. Unusually, it doesn't teleport you to distant lands -- hyperbolic geometry lets it get away with just having a lot of borders.

* {{Infinite}}: The mutant ivy in the clearing. The mutant ivy is an infinitely large monster who's center is infinitely far away. You aren't supposed to actually defeat, just try and take some of its apples.
** The world itself is infinite too, and has many infinitely large regions (duh!).

* '''Hypercycles''', "circles" with ''more'' than infinite area and radius. On the disk model, they look like circles intersecting the disk at non-right angles; if they intersected at right angles, they would be straight lines.

Because hyperbolic geometry, much like the surface of a sphere, cannot be represented on a flat screen while preserving both angles and areas, a projection must be used. [=HyperRogue=]'s default is the Poincaré disk model, which preserves angles, but does away with areas; even though tiles closer to the edge of the disk appear smaller, in hyperbolic geometry, they are exactly the same size. In fact, the entire hyperbolic plane fits in the disk, including points which are infinitely far away (mathematically known as '''ideal points'''.

The game is set on a hyperbolic plane, which has a lot of strange geometric properties. A regular grid of hexagons and heptagons, triangles whose angles add up to less than 180 degrees, straight lines that seem to curve away from you, infinitely large circles. Returning to the same place twice is very unusual. The creator was inspired by Creator/MCEscher's hyperbolic tilings for some of the graphics.

* AlienGeometries: The [[DeconstructedTrope Deconstruction]] of this trope is the main point of the game; ''actual'' non-Euclidian geometries don't suck out your sanity and summon EldritchAbominations, they're just a MindScrew. Specifically it uses Hyperbolic Geometry, which is a critical concept for understanding this game. To wit: Compared to Euclidian space (the kind we experience in the real world), in a hyperbolic universe, space itself has more actual space "stuffed in" so to speak, such that if you draw two parallel lines on the ground and extend them indefinitely, they gradually diverge, despite each remaining straight relative to itself. In a euclidian universe like ours, you can only fit four squares to a corner. However a hyperbolic universe could (depending on the size of the squares and the degree of hyperbolic-ness) fit five or more. In this world, such squares would need to have a side length of 1.25374 absolute units (According to the developer, an "absolute unit" is [[TechnoBabble "the "natural" unit of length, in which the Gaussian curvature is -1."]] ...Whatever that means.)

* UnexpectedGameplayChange: Euclidean Mode shows how the game would play on a regular hexagonal grid, with none of the hyperbolic weirdness. This changes several things, making various parts of the game easier or harder and some areas completely unplayable.
** Running away becomes more difficult, especially from multiple enemies at a time. You have to use walls to bottleneck them, you can't rely on walking across heptagons any more. And some Lands don't have walls.
** Obstacles become more substantial. In many lands, solid lines of impassable terrain will block off entire directions from you. This is still true in hyperbolic mode, but as the creator puts it, "there are many more directions".
** Several Lands flat-out don't work because they require hyperparallel lines that simply don't exist in Euclidean geometry. This includes the Great Walls and the Crossroads, so travelling from Land to Land is usually impossible.
** Mirages get much more useful, since they'll stay in the same position relative to you, allowing you to accumulate truly massive armies.
** The Yendor Quest gets much easier.

* DamselInDistress: A Princess is held prisoner in the Palace and there is a sidequest to find and rescue her. (Female [=PCs=] will rescue a Prince instead.)

* AlienGeometries: The [[DeconstructedTrope Deconstruction]] of this trope is the main point of the game; ''actual'' non-Euclidian geometries don't suck out your sanity and summon EldritchAbominations, they're just a MindScrew. Specifically it uses Hyperbolic Geometry, which is a critical concept for understanding this game. To wit: Compared to Euclidian space (the kind we experience in the real world), in a hyperbolic universe, space itself has more actual space "stuffed in" so to speak, such that if you draw two parallel lines on the ground and extend them indefinitely, they gradually diverge, despite each remaining straight relative to itself. In a euclidian universe like ours, you can only fit four squares to a corner. However a hyperbolic universe could (depending on the size of the squares and the degree of hyperbolic-ness) fit five or more.

* CrazyJealousGuy: If you manage to save two Princes, they will ''also'' murder each other until only one is left.

* AlienGeometries: The main point of the game, specifically the real life case of Hyperbolic Geometry, which is a critical concept for understanding this game. To wit: Compared to Euclidian space (the kind we experience in the real world), in a hyperbolic universe, space itself has more actual space "stuffed in" so to speak, such that if you draw two parallel lines on the ground and extend them indefinitely, they gradually diverge, despite each remaining straight relative to itself. In a euclidian universe like ours, you can only fit four squares to a corner. However a hyperbolic universe could (depending on the size of the squares and the degree of hyperbolic-ness) fit five or more.

* AlienGeometries: The main point of the game, specifically the real life case of Hyperbolic Geometry, which is a critical concept for understanding this game. To wit: Compared to Euclidian space (the kind we experience in the real world), in a hyperbolic universe, space itself has more actual space "stuffed in" so to speak, such that if you draw two parallel lines on the ground and extend them indefinitely, they gradually diverge, despite both remaining straight. In a euclidian universe like ours, you can only fit four squares to a corner. However a hyperbolic universe could (depending on the size of the squares and the degree of hyperbolic-ness) fit five or more.

* AlienGeometries: The main point of the game, specifically the real life case of Hyperbolic Geometry, which is a critical concept for understanding this game. To wit: Compared to Euclidian space (the kind we experience in the real world), in a hyperbolic universe, space itself has more actually space "stuffed in" so to speak, such that if you draw two parallel lines on the ground and extend them indefinitely, they gradually diverge, despite both remaining straight. In a euclidian universe like ours, you can only fit four squares to a corner. However a hyperbolic universe could (depending on the size of the squares and the degree of hyperbolic-ness) fit five or more.

* AlienGeometries: The main point of the game, specifically the real life case of Hyperbolic Geometry, which is a critical concept for understanding this game. To wit: Compared to Euclidian space (the kind we experience in the real world), in a hyperbolic universe, space itself has more actually space "stuffed in" so to speak, such that if you draw two parallel lines on the ground and extend them indefinitely, they gradually diverge, despite both remaining straight. In a euclidian universe like ours, you can only fir four squares to a corner. However a hyperbolic universe could (depending on the size of the squares and the degree of hyperbolic-ness) fit five or more.

** Less obviously, the Running Dogs follow you on a path always one step to your left or your right (since they can't walk on tiles you've walked on). If you run in a straight line, you'll slowly outpace them... somehow.

* AlienGeometries: The main point of the game, specifically the real life case of Hyperbolic Geometry, which is a critical concept for understanding this game. To wit: Compared to Euclidian space (the kind we experience in the real world), in a hyperbolic universe, space itself has more actually space "stuffed in" so to speak, such that if you draw two parallel lines on the ground and extend them indefinitely, they gradually diverge, despite both remaining straight.

* AlienGeometries: All over the place, due to the hyperbolic geometry, and the main point of the game.