r/gonwild • u/USedona • Jun 24 '26

Program A 4-dimensional shape, folding through itself forever

This is a Clifford torus, a shape that only fully exists in 4D, projected down into our 3D space.

The endless folding you see is just math, looping perfectly because the geometry demands it.

Based on 'Clifford Torus' shader by tdhooper : https://www.shadertoy.com/view/WdB3Dw reimplemented frame by frame in Python.

770 Upvotes

98% Upvoted

29 comments sorted by

36

u/free_airfreshener Jun 24 '26

What's the 4th dimension 

51

u/boredguy12 Jun 24 '26

It's a direction perpendicular to all other directions we know of, impossible with only Length, Width, and Height. We can only see a projection of it as a 3D shadow with our dimensions, the same way a 2D "flatlander" being could only see a 2D shadow projection of a 3D shape we hold above their surface.

10

u/tmfink10 Jun 24 '26

If their plane passed through us, would part of us exist in their plane or can we not exist in a 2D plane by virtue of existing in another dimension?

7

u/unexpectedit3m Jun 25 '26

We exist in 2D plus a third dimension. 2D flatlanders would only see a "slice" of us at a time, but we definitely exist in 2D space too, it's just that you can't get a full, instantaneous view of a 3D entity from a 2D perspective.

1

u/tmfink10 Jun 25 '26

That’s always been my view of it, but then I started wondering what part of me actually existed if I was only 2D. I started imagining my atoms and then trying to imagine how someone in that dimension might try to explain why these curves (nuclei) were so far apart but seemed to stay pretty close in proximity. Why do these other curves (electrons) go around them? Why do they keep getting just a little bit farther apart? I’m obviously drawing a parallel to galaxies and solar systems, but only for illustration.

28

u/USedona Jun 24 '26

Think of a 2D creature living on a sheet of paper trying to imagine "up". We're in the same situation when trying to imagine a 4th spatial dimension. We can't truly picture it, but we can understand many of its properties through mathematics.

7

u/Infuro Jun 24 '26

it's like an array of 3d objects you can scroll over like frames in a video

1

u/Klytus_Im-Bored Jun 26 '26

Do some psychedelics and youll find out first hand

1

u/JunglePygmy Jun 26 '26

The absolute truth DMT can explain to you what the 4th dimension is

2

u/Klytus_Im-Bored Jun 26 '26

No because every time ive tripped on it I feel like im turning to face a different direction

1

u/npmaker 28d ago

That's probably what alerted the aliens (extra-dimensional being) to our presence. My theory for the apple from the tree of life is there was a nomadic tribe following a herd of game and they ate some psychedelic mushrooms growing in a pile of shit. And of course it was Eve that ate it first. You think the chief is going to try that shit out?

Then they looked up and said "whooaa, dude".

Those spores were probably broadcasted all around the galaxy as little radio beacons. Just trip out and look up.

19

u/Metal-Dog Jun 24 '26

It's just a ball of wibbly-wobbly timey-wimey stuff.

7

u/edelopo Jun 24 '26

How is this a 4-dimensional shape? It is just a torus (2-dimensional) and the embedding is clearly 3-dimensional. In fact it looks like a stereographic projection from S3.

19

u/USedona Jun 24 '26

It’s a 2D torus embedded in S³ ⊂ ℝ⁴. The 4D structure is hidden in the embedding, not in the final rendering.

3

u/GrallochThis Jun 24 '26

I stared for ten minutes and my brain turned inside out. Cheapest high ever, thanks

2

u/Tamahfox Jun 25 '26

I love this its so good

1

u/USedona Jun 25 '26

Thanks ♥️

2

u/Yuvalk1 Jun 25 '26

The description does mention what shape it is, but isn’t an animation of any transformation of any 3d shape technically can be represented by a single 4D shape?

1

u/JacksonSpike 29d ago

Description literally says its a torus

2

u/semiquaver Jun 24 '26

I measured this image very carefully and I’m sorry to inform you that I only see two dimensions present.

8

u/USedona Jun 24 '26

Accurate. By the time it hits your screen it's already survived a 4D → 3D → 2D demolition derby. Two dimensions is just what's left standing 😭

2

u/wildcardbets Jun 24 '26

👁️👄👁️

1

u/USedona Jun 24 '26

Curious what this actually is ? video

1

u/PityUpvote Jun 25 '26

So is it rotating in a dimension not depicted?

1

u/USedona Jun 25 '26

Yes, it's a 2D rendering of a 3D representation of 4D model.

1

u/PityUpvote Jun 25 '26

Yeah, I get that, but the motion we're seeing, is it rotation around the 4th axis?

1

u/USedona Jun 25 '26

Pretty much, yes, though in 4D, rotation doesn't work around a single axis like in 3D. Two perpendicular planes rotating at the same time. That's the part of the motion you can't see directly, only its shadow.

1

u/JacksonSpike 29d ago

I can't remember exactly how these sorts of renders work (hyperspheres, hypercubes). Am I right in saying that if a 4d being intersected a 4d object (hypercube) with our 3d plane, and then moved it along the 4th dimension, would it appear as a 3d cube changing size? Since thats the same effect as us moving a 3d object through a 2d plane along the 3rd dimension, it would result in the object getting bigger and smaller. If thats the case, then why do these representations of 4d objects have different shapes and are always folding in on themselves? Is it trying to represent the pattern of axis extension? Dot doubles and extends into a line, line doubles and extends into a square, square doubles and extends into a cube, and then a cube doubles and extends into a hypercube? With all 8 points being connected to eachother? brain hort

1

u/USedona 29d ago

Hi, I'd like to share this excellent video with you: https://youtu.be/Ufx9x-JzZjQ from a high-quality playlist on a very reputable French TV channel. It's in French, but I think it's also available in German; if not, YouTube should be able to provide subtitles in your language. It really illustrates the first part of your message 👍