4 Dimentional Objects!!! <33

[bluhmaster]

MAN I LOVE THEM WHEN THEy ROTATE especially along the w axis X33

Spoiler: these r gifs

tessaract

duocylinder

this is probably not 4D but i still like it anyway

 

[Raggamuffin]

The first reminds me of this Win 95 screensaver.

Ed

 

[Nervous Rex]

Here is how to draw my favorite rendition of a 4-D cube, or tesseract:

1. Start by drawing points at: (-1,1), (0,1), (1,1), (1,0), (1,-1), (0,-1), (-1,-1), and (-1,0). This makes the small square at the in the middle of the image below.
2. Draw 4 points around the square - above, below, to the left, and to the right at (0,3), (0,-3), (-3,0), and (3,0).
3. Draw 4 points diagonal from the square at (-2,2), (2,2), (-2,-2), and (2,-2).

Your diagram should look like this, without the numbers:

Now, connect the dots as shown below. I usually do this by:
1) Connecting the 8 inner points in an 8-pointed star.
2) Connecting the 8 outer points in an octagon.
3) Connecting each outer point to two inner points in a V shape.

Now here's the fun part. I drew this one with four colors, one for each dimension. If you remove any single color, you will see that the other three colors form two unconnected cubes. If you remove any two colors, you will see that the other two colors form four unconnected squares (some slanted).

Whenever I have to go to meetings, I always bring a notepad and a pen. Sometimes I actually take notes and sometimes I just draw this or other shapes.

Sometimes I will draw all the partial versions:
Four versions, each with only one colors line, so I can see the four different sets of eight parallel edges.
Six versions, each with only two colors, so I can see the 24 different squares.
Four versions, each with only three colors, so I can see the eight cubes.

 

[Nervous Rex]

View attachment 102894 this is probably not 4D but i still like it anyway[/SPOILER]

I actually have that exact animation saved in my Instagram account because I want to figure out how to build a physical version of this.

I think I could make it work by having the cube connected at the top and bottom to two question-mark-shaped wires and then covering those wires with a piece of rubber or fabric, so that the visible "band" could flex and turn while the wire keeps everything in place. Rotating those wires would give me the rotating cube suspended in the air.

Then, the sides would have to have a wire inside the first half of each ribbon - enough to guide the ribbon to go over the cube for one rotation then under for the next.

I find these kinds of animations transfixing and hypnotic. I could stare at them for hours. That's why I chose the animation that I did for my avatar here.

 

[MildredHubble]

I really like those! Visual stims I think! I find 4D geometry fascinating but I'm not entirely sure my brain can make the quantum leap (pun absolutely intended) to perceiving what the 4th dimension actually is. I thought it was time, but how on earth is the 4th dimension of the cube showing it? I'm sure I probably need to learn more here.

I saw a really entertaining YouTube video on 4D geometry and basically concluded that the ancient Greeks were on to something after all!

 

[Misery]

Now I'll admit I dont understand like, ANY of this stuff, but through a certain game I play a lot of I've been exposed to an awful lot of hyperbolic geometry in particular, which has... some number of dimensions. Or something. It doesnt make a whole lot of sense to me, like you've got infinite within infinite which is just confusing, and all sorts of other screwy aspects. Lots of... twisting.

So here's a couple of things:

And now here's a game on Steam:

https://store.steampowered.com/app/342610/HyperRogue/
The two videos up there are using the engine that this game uses. What gets me about the game itself is that the geometry weirdness isnt just some graphical fluff, it is directly connected to the actual gameplay, and dealing with it is the main challenge, and different areas use the geometry in different ways, or twist it in different ways. So you do all that while not getting eaten by flaming dogs or hyperdimensional pirates or whatever the heck is happening in it. One of my favorite games of all time, actually. It has like a zillion modes and things to do.

Also if you watch the trailers there, you can do all of this in VR, which... yeah, dont actually do that, that's not a very good idea. Not unless you're already 100% immune to VR side effects, and even then, be careful.

 

[Ronald Zeeman]

I personally think the universe is four spatial dimensions plus time. Kaluza Klien suspected this years ago which in turn led to string theory. which in turn led the community down the wrong path. Hard to change directions as long as us baby boomers still alive.

 

[bluhmaster]

Now I'll admit I dont understand like, ANY of this stuff, but through a certain game I play a lot of I've been exposed to an awful lot of hyperbolic geometry in particular, which has... some number of dimensions. Or something. It doesnt make a whole lot of sense to me, like you've got infinite within infinite which is just confusing, and all sorts of other screwy aspects. Lots of... twisting.

So here's a couple of things:

And now here's a game on Steam:

https://store.steampowered.com/app/342610/HyperRogue/
The two videos up there are using the engine that this game uses. What gets me about the game itself is that the geometry weirdness isnt just some graphical fluff, it is directly connected to the actual gameplay, and dealing with it is the main challenge, and different areas use the geometry in different ways, or twist it in different ways. So you do all that while not getting eaten by flaming dogs or hyperdimensional pirates or whatever the heck is happening in it. One of my favorite games of all time, actually. It has like a zillion modes and things to do.

Also if you watch the trailers there, you can do all of this in VR, which... yeah, dont actually do that, that's not a very good idea. Not unless you're already 100% immune to VR side effects, and even then, be careful.

oml i love non euclidean geometry!!! my favorite geometries has to be spherical geometry! ill explain it breifly!

so you are a flatlander on a sphere, the horizon is the ground. you look up and you see a rock. if you were 3D you would see a giant rock instead of sky! theres more detailed explanations on youtube, but i just wanted to make the reply brief :3

 

[SusanLR]

@Misery Now I can see where your strange dreamscapes come from.
Maybe I'll go to bed now and see if my brain tries to process this.

 

[Nervous Rex]

Okay. Because my art skills suck and my Excel skills rock, I made a chart in Excel that will draw the tesseract for me. I can also turn off any dimension and show just parts of it.

Here is the full tesseract:

And here are the cubes you can get by turning off one color at a time:

I can also turn off two colors at a time and show all the squares, or turn off three colors at a time and just show lines of a single color.

 

[Nervous Rex]

Fun trivia:

A four dimensional cube is called a "tesseract". After that, you add the "tesse", "pente", "hexe", etc. for however many dimensions you want. So it goes "point", "line segment", "square", "cube", "tesseract", "penteract", "hexeract", etc. Generally, they're all called "hypercubes".

An n-dimensional triangle is called a "simplex", but they don't have any fancy names. "4-simplex" is a four dimensional, "5-simplex" is 5 dimensional, etc. So it goes "point", "line segment", "triangle", "tetrahedron", "4-simplex", "5-simplex", etc.