Non-Euclidean recursive house
HTML-код
- Опубликовано: 14 июн 2024
- Several recent games use this trick where a scene contains a smaller copy of itself. Sometimes called non-Euclidean, although it is more of an affine (similarity) manifold rather than non-Euclidean. So let's make it actually non-Euclidean!
0:00 To make the animation smooth, our speed is proportional to the distance from the center. We can assume that that's how the distances in our space work: distances are larger and larger as we
come close to the center. However, in this scene, the light rays travel still according to the rules of Euclidean / affine geometry.
0:15 Here we make the geometry work according to the metric outlined above! For example, when the blue person wants to reach the purple person, they won't go through the center, because the distances
are larger closer to the center. Because of this, if you want to reach the point in the same distance from the center, it is useless to come closer (or further), and the closest path would be a spherical
arc around the center.
The light rays also always take the shortest path, so for example, when we are above the head of the purple person, we see the blue torso in every direction orthogonal to the
central direction! This is because the light rays travel in spherical arcs and hit the blue person.
0:45 The Euclidean scene again.
Recent games based on this trick include:
Patrick's Parabox: store.steampowered.com/app/12...
Maquette: store.steampowered.com/app/76...
Spaceflux: store.steampowered.com/app/13...
Also e.g. glkitty.itch.io/spheres and this Minecraft video / since_the_trend_seems_...
This geometry is called S2xR or S2xE. Discuss this stuff and non-Euclidean geometry in general in the #geometry channel in the HyperRogue discord: / discord
Music: "Palace" by Will Savino, from the HyperRogue soundtrack (CC BY-SA 3.0) 
Наука
Our house, in the middle of our
house
ruclips.net/video/k55FYtqtXXU/видео.html
0:16 Our house, in the middle of our trip
Madness, I tell ya.
♪♫♪
ah, the contractors finally finished building my infinite house. now to open the front door and-
U r stuck
Now you will open the front door and-
There is a way to escape - just push the house such that it is on the edge. Then escape from that edge. You will come out of ∞.
(Patrick’s Parabox perspective)
You finally manage to beat the escape room. However, you are now in a bigger escape room with the same layout.
to exit the house, u need to exit the house
yes.
The Corner of Peace has been the place where all treaties are negotiated and conflicts are ended. It was built in the time when all the spaces where built by the Men of the Last Epoch. The Corner of Peace is said to have been designed by Larry the Trickster.
According to legend, Larry the Trickster was due to be punished for the havoc caused by the other spaces he had built. When asked for a plea he offered the High Magistrate that he should be forgiven and released on the condition that he builds a space where there would always be peace and asylum as violence would be impossible. The High Magistrate reluctantly agreed to the offer. Three days later Larry the Trickster presented the High Magistrate with the Corner of Peace. The High Magistrate was deeply underwhelmed. The Corner of Peace is a very simplistic space which lacked all of the intricate hallmarks of Larry the Tricksters previous work. The High Magistrate did not understand how this space would disallow violence and suspected Larry the Trickster was playing yet another trick. He decided to put the Corner of Peace to the test in order to reveal the trick and punish Larry once and for all. The High Magistrate picked up a very large stone and threw it as hard as he could. Larry the Trickster ducked and the stone missed him and continued on its path until it went straight into the back of the High Magistrate’s head killing him instantly.
Here in the Corner of Peace the path of all projectiles quickly return to where they began. The High Magistrate is the first and only person to ever be killed here. In his blood is written the one law of the corner. What goes around comes around.
Tat is looooooooooooooooooong
@@flamesdiamond I get that a lot.
gaming
But why make lore when you have recursion?
Another game this reminds me of is "Infinite Pizza" by Toco Games
*points flashlight at house centerpoint*
*eviscerated*
you wouldn’t since a non-zero fraction of the photons miss the house each time, so the resulting total number of photons that make it is approximately a convergent geometric series, so only a finite amount of light actually makes it to infinity
@@paradoxica424 laser pointer, then.
@@benthomason3307 Doesn't work, same issue. The only way you would be able to have an infinite number of photons aimed at the "house at infinity" is to have a perfect point source of light. Now here's the problem: such a thing doesn't exist.
@@paradoxica424 Pretty sure that the light coming from outside would be shifted towards red too.
*grabs the house off the house and throws it as hard as i can*
WHEEEEEEEEEEEEEEEEEEE
Interesting.. Would you want to live in a house like this?
The bathroom is in the bathroom and then to the right.
It's not like you can escape.
@@SimonClarkstone you can escape to a larger house
Yes
No cuz I don’t want to make a paradox
What is the geometry of this house-self-world?
S2xE
I am wondering how the game engine is storing the coordinates and rendering these.
ray tracing magic?
And how would gravity work ?
Green, Green Grass of Home
Is this S2xR?
looks pretty spherical yeah
Yes (it is mentioned in the description).
This is related to the complex exponential map, isn't it?
The two-dimensional analog would be indeed the complex exponential map (the original R^2\{0} world would be the complex exponential of the S1xR reshaped world).
U r Stuck in there forever or u just bend space-time and then „Exit“ it
Yes, if the logic of Patrick’s Parabox is right, you can exit it by ∞-exiting (move the house to the edge and ∞ exit)
the discord invite in the description is not working
It seems to work for me...
AAAAHHHHH THE INFINTE TWIDDLES AAAAAAHAHHHHHHH
actually, it's S²xS¹ because it loops
Yes, this space is S²xS¹, but the geometry is S²xR¹ (S²xS¹ and S²xR¹ have the same geometry but different topology; the geometry is named after the simple connected space).
I have got yet another idea. What if you generalize non-Euclidian portals to allow Mobius transformations?
They are used in simple lense calculations. A portal to the distorted world beyound the lense. Transformations can be defined by 4x4 matrix in uniform coordinates with full 15 degrees of freedom unlocked.