Cat Portal: Non-Euclidean Portal in Solv

Yet another non-Euclidean portal, this time in Solv geometry (the honecomb based on the mapping torus of Arnold's cat mapping).
As usual, the algorithm works as follows:
* we start with a basic scene (here, a 8x8x3 manifold with a loop put in it)
* create all possible paths not hitting the walls in this space
* two paths are the same if they are homotopic (one can be continuously deformed into another)
* two paths are the same under some extra rules (here, we identify paths which go 6 times around the loop)
* create a new space where every group of paths which are "the same" becomes a cell
Wihout extra rules we get the universal cover; with extra rules we get just a cover. Can you guess the extra rules here?
Made with the HyperRogue engine aka RogueViz
Source code: github.com/zenorogue/hyperrog...
A playable Windows exe at roguetemple.com/z/sims/notknot... (works in VR too!)

[@Kaiveran]

Broke: sticking portals in something and calling it non-Euclidean
Woke: making actual non-Euclidean geometry
Bespoke: making actual non-Euclidean geometry WITH portals in it

[@igorjosue8957]

i hate when it happens at my house by accident, once i make non euclidean geometry with portals in it, but each axis where a different curvature, like, y was spherical, x was flat and z was hyperbolic, and this becuz i accidentaly make 2 more dimensional axis on my house, i needed to clean all later the incident

[@cheeseburgermonkey7104]

@@igorjosue8957 this comment is cursed

[@einekartoffel2490]

This is gonna be one hell of a trippy game.
I love how watching all this videos is kinda easing one in into the slowly increasing weirdness of alternative geometry, portals and other spatial interventions.

[@mastermenthe]

RUclips interaction + 1

[@tylerwilliams33]

Taking shrooms then tripping and falling into the tezzeract.

[@zfm1097]

If the Qoocam Ego 3D camera/viewer becomes as popular as it should (given that we might as well view footage in 3D if we're not printing out) ...perhaps you could create & share 3D renders of non-Euclidean landscapes/forms.

[@kaidatong1704]

there's so much space that I'm waiting for a plot twist: didn't actually travel thru portal to pocket space; just built diorama to fake u out

[@bengineer8]

*hums the Cthulhu temple theme while watching*

[@pretzelboi64]

How hard would connecting two geometries with portals be? I imagine some arbitrary choices might be necessary to make it work but it seems like a hyperbolic quadrilateral could map to a Euclidean rectangle.

[@EvilStreaks]

I'd like to see AI enemies manage pathfinding in this

[@willieforty15]

I wouldn't dare become enemies with native pathfinders in this space.

[@Solotocius]

So wherever you go, you end up in the same area?

[@kylaxial]

I slightly understand spherical space, but I cannot understand spherical space with different curves per axis or something like that...

[@ZenoRogue]

Solv is more like hyperbolic spaces with different curvature per axis. I do not know any easier explanation of Solv than www.roguetemple.com/z/hyper/geoms.php (which is still probably quite difficult).

[@columbus8myhw]

@@ZenoRogue If Nil and SL2R are twisted E^2xE and twisted H^2xE, is there a twisted S^2xE?

[@ZenoRogue]

@@columbus8myhw With the right amount of twist, you get S^3. With incorrect amount, this geometry is called Berger sphere.
(Berger sphere is not one of Thurston geometries, because Thurston geometries are the ones that are useful to geometrize closed manifolds, and anything with Berger sphere geometry can be made more regular and given S3 geometry.)

[@columbus8myhw]

​@@ZenoRogue Ah. So Thurston's eight geometries are not a complete taxonomy of homogenous geometries

[@ZenoRogue]

@@columbus8myhw Indeed, there are also less symmetric variants of Solv, which are not Thurston geometries because there are no closed manifolds with that geometry (only infinite ones).

[@theespatier4456]

I know nil but how’s this place work?

[@ollllj]

step 1, get a cat drunk.

[@tylerwilliams33]

Ah yes, the fine game of nil...

[@columbus8myhw]

Hey here's a random question, if you glue two (Euclidean) spheres of the same size by their boundaries, what happens?
It'll be homeomorphic to S^3 but with zero curvature aside from a sphere's worth of nondifferentiable points

[@columbus8myhw]

Does every portal lead to the same place?

[@ZenoRogue]

They are different places (as shown by different fog colors), but the walls are arranged in the same way.

[@mymyscellany]

I know this is nitpicky, but you do make a ton of videos like this one so it could be something to work on- it would be better if the camera's path was preprogrammed to minimize shakiness. Or if there was a smoothing algorithm used to remove small bumps.

[@melwugon3687]

I’d assume that this is prob real time and Zeno is controlling the camera with a mouse. Not sure though

[@mymyscellany]

@@melwugon3687 that's what I'm assuming as well (minus the mouse)

[@ZenoRogue]

@@mymyscellany No, this was how first videos were made and it was more shaky. Generally it is quite difficult to go smoothly without hitting any walls.
The current method waits for a keypress, and goes one step (1/10s), adding rotation depending on the keypress. It is quite smooth when the direction is constant, here it was quite difficult to get into the portals, so it is more shaky. There are also some methods for smoothening, although they were not used in this video.
Definitely some things to improve, would be great to have camera control on the level of the recent viral drone bowling video :)

[@columbus8myhw]

(The reference: ruclips.net/video/VgS54fqKxf0/видео.html)

[@melwugon3687]

@@ZenoRogue The more you know

[@Invalid571]

😵 😵 😵
Edit:
Do not watch this if you have drunk.
(Barf)

[@kaidatong1704]

ymmv

[@TomtheMagician21]

I do not understand solv at all

[@igorjosue8957]

well, i also not, i searched and my surprise is that the second link that appears literally goes to one of his video