''HyperRogue'' is a
free and open-source
Free and open-source software (FOSS) is software available under a Software license, license that grants users the right to use, modify, and distribute the software modified or not to everyone free of charge. FOSS is an inclusive umbrella term ...
independent video game developed by Zeno Rogue. It is a
roguelike
Roguelike (or rogue-like) is a style of role-playing game traditionally characterized by a dungeon crawl through procedurally generated levels, turn-based gameplay, grid-based movement, and permanent death of the player character. Most ro ...
inspired by the puzzle game ''
Deadly Rooms of Death'' and the art of
M. C. Escher
Maurits Cornelis Escher (; ; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made woodcuts, lithography, lithographs, and mezzotints, many of which were Mathematics and art, inspired by mathematics.
Despite wide popular int ...
, taking place in the
hyperbolic plane
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
:For any given line ''R'' and point ''P' ...
.
Gameplay

''HyperRogue'' is a
turn-based
Timekeeping is relevant to many types of games, including video games, tabletop role-playing games, board games, and sports. The passage of time must be handled in a way that players find fair and easy to understand. In many games, this is don ...
game in which the player controls one character exploring a world based on
hyperbolic geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or János Bolyai, Bolyai–Nikolai Lobachevsky, Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
:For a ...
, with cells arranged as a
truncated order-7 triangular tiling by default (with a few exceptions). The player can also choose to play on some other tilings and honeycombs in two and three dimensions, in all eight
Thurston geometries, along with a variety of
quotient spaces. It borrows
procedural generation
In computing, procedural generation is a method of creating data algorithmically as opposed to manually, typically through a combination of human-generated content and algorithms coupled with computer-generated randomness and processing power. I ...
and
permadeath
Permadeath or permanent death is a game mechanic in both tabletop games and video games in which player characters who lose all of their health are considered dead and cannot be used anymore. Depending on the situation, this could require the p ...
from the
roguelike
Roguelike (or rogue-like) is a style of role-playing game traditionally characterized by a dungeon crawl through procedurally generated levels, turn-based gameplay, grid-based movement, and permanent death of the player character. Most ro ...
genre, and puzzle-based combat of ''
Deadly Rooms of Death''.
The world consists of 72 lands, each of which has a different theme, treasure, enemies, mechanics, and a magical power; the lands are usually separated by hyperbolic straight lines ("Great Walls") and change as one travels, thus allowing monsters and magical powers to interact between the different lands. The world is
procedurally generated
In computing, procedural generation is a method of creating data algorithmically as opposed to manually, typically through a combination of human-generated content and algorithms coupled with computer-generated randomness and processing power. I ...
on the fly; some of the lands must be unlocked by fulfilling a prerequisite in the given play (e.g., collecting a certain number of treasures).
The main goal of the game is to collect treasures while avoiding entrapment by enemies. Other than simply collecting the treasures, there are several major quests to undertake (Yendor quest, Prince(ss) quest, Hyperstone Quest and the
Holy Grail
The Holy Grail (, , , ) is a treasure that serves as an important motif in Arthurian literature. Various traditions describe the Holy Grail as a cup, dish, or stone with miraculous healing powers, sometimes providing eternal youth or sustenanc ...
).
The gameplay is inspired by ''Deadly Rooms of Death''. The basic enemies alternate their turns with the player; in their turn, the player or an enemy can stay in place, move or attack an adjacent cell. The player and basic enemies can be killed with a single hit. Similar to the
check rule in
chess
Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arran ...
, the game does not allow the player to make moves which would lead them to be immediately killed. While defeating a single enemy is not a problem, tactical planning is essential for winning fights with multiple enemies at once. This basic formula is altered in many ways: there are monsters of varying speeds, multi-tile monsters such as Ivies,
sandworms, snakes and dragons, and monsters which have to be attacked in a specific way.
The game has many special modes, allowing the player to take on a specific challenge (Pure Tactics Mode, Yendor Challenge), or changing a crucial aspect of the game (Chaos Mode where lands change very quickly as you travel, Shoot'em Up Mode which is continuous rather than turn-based and grid-based, and Orb Strategy Mode where orbs can be used at any time instead of being picked up in the world). The source code also contains a visualization engine, called RogueViz.
Hyperbolic geometry
The world of ''HyperRogue'' is characterized by its
non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean ge ...
, precisely
hyperbolic geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or János Bolyai, Bolyai–Nikolai Lobachevsky, Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
:For a ...
; this affects many aspects of the game.
Basic gameplay. The player can use the negative curvature to escape situations which would be impossible to escape in a similar game in the Euclidean grid. Specifically, any monster following the player will get further and further behind unless directly behind the player; this is because following an equidistant to a specific path takes longer than following the original path.
Art. The game is displayed in the
Poincaré disk model
In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines are either circular arcs contained within the disk t ...
by default; it is also possible to select other projections from the special modes menu. The graphics are inspired by the art of
M. C. Escher
Maurits Cornelis Escher (; ; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made woodcuts, lithography, lithographs, and mezzotints, many of which were Mathematics and art, inspired by mathematics.
Despite wide popular int ...
, particularly the
Circle Limit series using hyperbolic geometry.
Balance. One property of hyperbolic geometry is that the amount of cells in distance at most ''d'' from the starting point is exponential in ''d''; there are centillions of cells in distance 1000 from the starting point. This makes the world of ''HyperRogue'' practically infinite. The traditional RPG formula of getting stronger by collecting equipment had to be changed, in order to prevent
grinding strategies from being effective. New lands and magical powers are unlocked by collecting treasures, but on the other hand, the amount of monsters spawning depends on the number of treasures collected in the given land, thus making it impossible to grind indefinitely.
Quest design. Many challenges in the game would be trivial in a Euclidean world, but are made harder by the exponential expansion of the hyperbolic plane. At the same time, other challenges would be practically impossible in Euclidean, but are relatively easy in the hyperbolic world. Getting to the center of a moderately sized circle and returning to where you were prior are two examples of tasks that are almost impossible in hyperbolic geometry, while both are much easier in Euclidean geometry.
Level design. Obstacles and other objects in the game world use shapes that are impossible in Euclidean geometry, like infinite trees,
equidistants and
horocycles, and straight lines which never cross. There is also one land that relies on the
holonomy
In differential geometry, the holonomy of a connection on a smooth manifold is the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported. Holonomy is a general geometrical consequence ...
of hyperbolic geometry: when the player returns to a tile after making a few steps, the world has rotated around the player.
The in-game tutorial allows the player to learn about hyperbolic geometry and the game's basic mechanics.
Release
The first version of ''HyperRogue'' was created in November 2011, and contained only a single land and very simple monsters. A new version was made in March 2012 for the
Seven Day Roguelike Challenge, with more lands and the introduction of magical orbs. In January 2015, ''HyperRogue'' was released on
Steam
Steam is water vapor, often mixed with air or an aerosol of liquid water droplets. This may occur due to evaporation or due to boiling, where heat is applied until water reaches the enthalpy of vaporization. Saturated or superheated steam is inv ...
.
Version 12.0, released in June 2021, added support for
virtual reality
Virtual reality (VR) is a Simulation, simulated experience that employs 3D near-eye displays and pose tracking to give the user an immersive feel of a virtual world. Applications of virtual reality include entertainment (particularly video gam ...
through
SteamVR
Steam is a digital distribution service and storefront developed by Valve Corporation, Valve. It was launched as a software client in September 2003 to provide video game updates automatically for Valve's games and expanded to distributing thir ...
.
Reception
''HyperRogue'' was called "one of the most interesting roguelikes to come around lately" in the book ''Exploring Roguelike Games''. ''Pocket Tactics'' stated that it was reminiscent of
Roger Zelazny
Roger Joseph Zelazny (May 13, 1937 – June 14, 1995) was an American fantasy and science fiction writer known for his short stories and novels, best known for '' The Chronicles of Amber''. He won the Nebula Award three times (out of 14 nominatio ...
's ''
Chronicles of Amber'' series.
References
External links
* {{Official website, https://roguetemple.com/z/hyper/
Official wikiOnline demo using WebGL
2011 video games
Mathematical education video games
Linux games
MacOS games
Turn-based tactics video games
Roguelike video games
Video games developed in Poland
Video games using procedural generation
Windows games
Open-source video games
Video games with gender-selectable protagonists
Free software that uses SDL
Multiplayer and single-player video games
Free software programmed in C++
Free and open-source Android software
Video games inspired by M. C. Escher
Hyperbolic geometry
Commercial video games with freely available source code