Self-Hiding Knot Portal

Guess what happens in the end!
In • Blocky Knot Portal v2 we had a knot portal.
In that video, looping around the knot 3 times brought us back to the same room ("order-3 branching cover"). We had 24 rooms with 4 separate knots (each of them twice as long as it appears).
With order-4, we have 96 rooms, and 6 knots, each of them four times as long.
What if we remove one of these knots, collapsing the spaces?
Well, 24 rooms remain, with 1 knot of 1x length and 1 knot of 4x length.
In the video, we start from a viewpoint from where we can see both of these knots, and we end at a viewpoint from where only the longer knot is visible. Thus, the knot portal hides a part of itself!
(With order-5, 120 out of 600 rooms remain, 1 knot of 2x length and 2 knots of 10x length. With order-6, there are infinitely many rooms.)
The self-hiding knot portal is based on an idea by Magma.
Made with the HyperRogue engine, aka RogueViz
Source code: github.com/zenorogue/hyperrog...
A playable Windows exe at roguetemple.com/z/sims/notknot... (don't go into the walls; works in VR too!)

[@pretzelboi64]

This would have made a really cool Windows screensaver back when people still cared about screensavers.

[@mendelovitch]

The tiling feels like a bath house. It needs a few pools, jacuzis, saunas and splashing sound effects.

[@protonagaiako6201]

That is really cool! How do you even make stuff like that? It looks like a vonfusing mess to program!

[@ZenoRogue]

Thanks! The program itself is not that confusing / hard to understand if you know a bit of algebraic topology. It is the result of that program which is confusing. I do not understand it either. :)

[@jasondelong83]

@@ZenoRogue The camera itself is following the topology right? If the camera was purely locked in 3-D would you be able to get to those hidden angles? I don't know if any of this is accurate, just a hunch.

[@ZenoRogue]

@@jasondelong83 Not sure what you mean, but yes, the camera follows the topology (it follows paths in the manifold, without suddenly jumping to another sheet).

[@noahnaugler7611]

That portal most have it's own fun geometry

[@Bonewerkz]

New mathematic science: portal geometry.

[@alexanderthomas1869]

What would you see if you tried to trace the knot/portal from beginning to end?

[@ZenoRogue]

I think this is something that one should try themselves, difficult to make a video.

[@lukatolstov5598]

Cool!

[@alan2here]

Does it hide itself even more than that with more moving around it?
This seems similar to passing connected square portals through themselves, in either 2 or 3 dimensions, where they have rigid hairline frames that cannot pass through each other. Some angles and movement would seem to have both portals vanish, like someone eating them-self.

[@columbus8myhw]

Oh that's strange. So the branch points depend on what sheet/world you're on. (Or something, I'm not a topologist)
Is this what people call a "non-abelian cover"?

[@columbus8myhw]

Have you seen this, by the way? (Same person who did the Möbius portal thing) ruclips.net/video/fWkAfa96OmI/видео.html

[@ZenoRogue]

@@columbus8myhw I thought I have seen it, but it is much cooler than I remember, so maybe I have seen some older version? Thanks!
No idea about "non-abelian cover".

[@theespatier4456]

In the year 2154 someone will watch this and actually understand it

[@chasemarangu]

Pls do a 360° render

[@ZenoRogue]

Good idea, although it requires some work to do well, and IMO a version that you can explore yourself is even better (especially in VR), and easier to create:
roguetemple.com/z/sims/notknot.zip