ZenoRogue | Self-Hiding Knot Portal @ZenoRogue | Uploaded February 2021 | Updated October 2024, 2 hours ago.
Guess what happens in the end!
In youtu.be/eb2DhCcGH7U 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/hyperrogue/blob/master/rogueviz/notknot.cpp
A playable Windows exe at roguetemple.com/z/sims/notknot.zip (don't go into the walls; works in VR too!)
Guess what happens in the end!
In youtu.be/eb2DhCcGH7U 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/hyperrogue/blob/master/rogueviz/notknot.cpp
A playable Windows exe at roguetemple.com/z/sims/notknot.zip (don't go into the walls; works in VR too!)
