Uploaded September 2021 | Updated September 2026, 3 weeks ago
This video combines earlier videos related to both non-Euclidean geometry and portals.
While gamers often call portals "non-Euclidean geometry", non-Euclidean geometry is more about parallel lines diverging, rectangles not existing, triangles summing up not to 180, things like that. All this causes the perspective to work weirdly, and other cool effects that could not be achieved with portals.
We start with an Euclidean portal (but still quite cool since it is knotted), then explore some non-Euclidean portals, then we make scaling portals actually non-Euclidean, and finally, we attempt to recreate non-Euclidean geometry using portals.
See the earlier videos for more detailed descriptions. Or play HyperRogue or visit the HyperRogue discord to learn more! (Some scenes were posted on Twitter but not on YouTube.)
This is mostly done because apparently YouTube prefers to recommend videos that are about 10 minutes long -- let's see if it works! Don't forget to subscribe and like this video, as they often say...
Still useful for those who want to watch everything at once. (Well, at least if there are no... interruptions.)
All made using RogueViz (aka the HyperRogue engine). Music from the HyperRogue soundtrack by Shawn Parrotte, Will Savino and Lincoln Domina.
Short descriptions and links to original videos with more details in the description:
0:00 "Blocky Knot Portal v2"
youtu.be/eb2DhCcGH7U -- a knotted portal in Euclidean space
1:41 "Self-Hiding Knot Portal"
youtu.be/vFLZ2NGtuGw -- like the above but self-hiding
2:32 "Cat Portal: non-Euclidean portal in Solv"
youtu.be/CGiSxC9B6i0 -- a portal in Solv geometry
3:22 "Spherical Portal"
youtu.be/PerPeQFu5gw -- a portal in spherical geometry
4:59 "non-Euclidean portal (in Nil geometry)"
youtu.be/2K-v8tK68AE -- a portal in Nil geometry
6:09 "non-Euclidean recursive house"
youtu.be/Tf1wgYdjf_Q -- a recursive house (first scene) realized in S2xE geometry (second scene)
7:14 "Right-angled pentagon", looping animation
an example of a scene that cannot be achieved with portals -- twitter.com/ZenoRogue/status/1304130700870901761
(note that the period is 20 seconds -- can you see why the scenes after 4 and 5 seconds are different?)
7:34 "Right-angled pentagon"
youtu.be/c3BTm3t4Gw0
7:54 "Can we simulate spherical geometry in Euclidean space"
youtu.be/XUIYga-AfLI -- an attempt to simulate spherical geometry using portals
8:22 "too many shapes to see all of them"
youtu.be/3-jRAVUXWgw -- an attempt to simulate hyperbolic geometry using portals
9:32 some extra scenes to "too many shapes"
from Twitter: twitter.com/ZenoRogue/status/1423663341944377345
This video combines earlier videos related to both non-Euclidean geometry and portals.
While gamers often call portals "non-Euclidean geometry", non-Euclidean geometry is more about parallel lines diverging, rectangles not existing, triangles summing up not to 180, things like that. All this causes the perspective to work weirdly, and other cool effects that could not be achieved with portals.
We start with an Euclidean portal (but still quite cool since it is knotted), then explore some non-Euclidean portals, then we make scaling portals actually non-Euclidean, and finally, we attempt to recreate non-Euclidean geometry using portals.
See the earlier videos for more detailed descriptions. Or play HyperRogue or visit the HyperRogue discord to learn more! (Some scenes were posted on Twitter but not on YouTube.)
This is mostly done because apparently YouTube prefers to recommend videos that are about 10 minutes long -- let's see if it works! Don't forget to subscribe and like this video, as they often say...
Still useful for those who want to watch everything at once. (Well, at least if there are no... interruptions.)
All made using RogueViz (aka the HyperRogue engine). Music from the HyperRogue soundtrack by Shawn Parrotte, Will Savino and Lincoln Domina.
Short descriptions and links to original videos with more details in the description:
0:00 "Blocky Knot Portal v2"
youtu.be/eb2DhCcGH7U -- a knotted portal in Euclidean space
1:41 "Self-Hiding Knot Portal"
youtu.be/vFLZ2NGtuGw -- like the above but self-hiding
2:32 "Cat Portal: non-Euclidean portal in Solv"
youtu.be/CGiSxC9B6i0 -- a portal in Solv geometry
3:22 "Spherical Portal"
youtu.be/PerPeQFu5gw -- a portal in spherical geometry
4:59 "non-Euclidean portal (in Nil geometry)"
youtu.be/2K-v8tK68AE -- a portal in Nil geometry
6:09 "non-Euclidean recursive house"
youtu.be/Tf1wgYdjf_Q -- a recursive house (first scene) realized in S2xE geometry (second scene)
7:14 "Right-angled pentagon", looping animation
an example of a scene that cannot be achieved with portals -- twitter.com/ZenoRogue/status/1304130700870901761
(note that the period is 20 seconds -- can you see why the scenes after 4 and 5 seconds are different?)
7:34 "Right-angled pentagon"
youtu.be/c3BTm3t4Gw0
7:54 "Can we simulate spherical geometry in Euclidean space"
youtu.be/XUIYga-AfLI -- an attempt to simulate spherical geometry using portals
8:22 "too many shapes to see all of them"
youtu.be/3-jRAVUXWgw -- an attempt to simulate hyperbolic geometry using portals
9:32 some extra scenes to "too many shapes"
from Twitter: twitter.com/ZenoRogue/status/1423663341944377345
