Uploaded June 2015 | Updated September 2026, 2 weeks ago
HyperRogue is normally played as a turn-based and grid-based game. However, since Version 7.0, you can forget about the discrete spacetime, and play it as a shoot'em up!
Watch the video or play the game to see how a shoot'em up works in the hyperbolic plane. Also featured is the Caribbean (a new land in 7.0) and the Temple of Cthulhu (new in 6.2).
HyperRogue website: roguetemple.com/z/hyper
HyperRogue is normally played as a turn-based and grid-based game. However, since Version 7.0, you can forget about the discrete spacetime, and play it as a shoot'em up!
Watch the video or play the game to see how a shoot'em up works in the hyperbolic plane. Also featured is the Caribbean (a new land in 7.0) and the Temple of Cthulhu (new in 6.2).
HyperRogue website: roguetemple.com/z/hyper



![Trapped in a 3-sphere, crocheting Euclidean planes!
In the hyperbolic plane there is more area than in the Euclidean one in fact, the area of a circle of radius r is exponential in r. However, if you fold a small fragment of the hyperbolic plane, you can fit it in three-dimensional Euclidean space this can be done in the real world (see hyperbolic crocheting or beads [1]) or simulated [2].
This was negatively curved surface embedded in a flat space but what about embedding a flat surface into a positively curved space? Again, there is not enough space to do this without folding, In this video, we try to fit a fragment of a Euclidean plane into a three-dimensional sphere, S³ (imagine a two-dimensional sphere, e.g., the surface of Earth but add one extra dimension, and imagine light rays sticking to the surface).
It might appear that something strange is happening things that seem to be close are obscured by ones that seem to be distant... this is a weirdness of S³ we are in. All the rays coming out of your eyes will meet again at the antipodal point, causing things close to that antipodal point appear just as if they were next to you. Furthermore, all these rays will hit the back of your head (head not shown); this means that things you have walked past will appear in front of you again. These effects are visible in the video.
Want to explore S³ yourself (as in this video)? This will be possible in HyperRogue 10.3.
HyperRogue: http://roguetemple.com/z/hyper/
[1] https://www.youtube.com/watch?v=7mqnd5aGWpw
[2] https://www.youtube.com/watch?v=GegO9ysaaio
See also: https://archive.bridgesmathart.org/2018/bridges2018-551.pdf Trapped in a 3-sphere, crocheting Euclidean planes!](https://i.ytimg.com/vi/L0QczgEH3IU/mqdefault.jpg)




![Bad Apple, but rendered with hyperbolic planes
Our take on the famous Internet meme! If something can display something, it will display Bad Apple. If it cant, people will make it display Bad Apple. LiterallySomeOne, [2]
By the Riemann Mapping Theorem, every simple-connected shape can be conformally mapped to a hyperbolic plane, and thus be used as a model* of hyperbolic geometry.
Made with newconformist: https://github.com/zenorogue/newconformist (modified to allow animation)
Want to know more? Follow us and comment for a making of video! [3]
[1] original Bad Apple animation by Anira (uploaded to YouTube by kasidid2): https://www.youtube.com/watch?v=FtutLA63Cp8
[2] Bad Apple explained by Megapig9001: https://www.youtube.com/watch?v=6QY4ekac1_Q
[3] The making of video is ready! https://youtu.be/NGixk6jVVNM
* rather a projection than a model... but people call them models, so lets call these anime-girl models
Download video without YouTube compression: (also fixes the missing frames at 0:41 and at the end, causing music desync)
https://drive.google.com/file/d/1TqZo1AyeU7a4N9zcr32bIzVxT0vUNwxo/view?usp=sharing
#badapple #mathart #noneuclidean #mindbending #visualization #mathisbeautiful #mathgenius #mathisfun #mathisawesome #newconformist #conformal #hyperrogue #rogueviz Bad Apple, but rendered with hyperbolic planes](https://i.ytimg.com/vi/P9EZy8ZzlVU/mqdefault.jpg)

