Hypertorus

4D hypertorus rotations. This is what the shadow of a 4D torus would look like. The rainbow colors are to help in the visualization: +x = red, +y = green, +z = blue, and +w axis = gray.

Category:

Education

Tags:

• 4D
• Hypertorus

[ChrisCDXX]

this should be called the silly rainbow wire frame torus, just because its rotating doesnt mean its 4d lol

[WildStar2002]

@ChrisCDXX You're right - just because it's rotating doesn't make it 4D, and it's hard to visualize because of the loss of information with the step down to 3D. Well, actually, it's *impossible* to visualize - but I trust the math behind it. This is what the shadow of a 4D torus would look like. The rainbow colors are to help in the visualization: +x = red, +y = green, +z = blue, and +w axis = gray. :-)

[ChrisCDXX]

@WildStar2002 dude, you need to put that in the description. makes a lot more sense now that you said that, I bet a lot of ppl would benefit from an explanation.

[WildStar2002]

@ChrisCDXX Good idea - done! :-)

[MrNitt]

Just because we can make a fancy illusion doesn't necessarily mean it's the fourth dimension.

[WildStar2002]

@MrNitt True - but in this case, I had no idea what it would look like, I trusted the math. I created a program that revolved a sphere around an imaginary axis perpendicular to the volume in which it was created (like revolving a circle around an axis in it's plane). Then I used a perspective projection technique from an imaginary 4D viewpoint, and rotated the object along various random axes - and here it is! :-)

[Dathgarion]

@MrNitt i know this is a very old comment but just feel i should say it seems a lot of people have a missunderstand of these type of objects. This is a shadow of A 4 Dimensional object. The Object has 4 dimensions to it. A lot of people think of time as a dimension the only problem is we can not move time back and forth, it is fluid atm. otherwise if we could move time along an axis in our universe time would become a very valid dimension and we would have discovered we are in 4 dimensions.

[MrPianoman6651]

You probably shouldn't watch this if you have motion sickness...

[Meb8Rappa]

@SharkRetriver a 3-torus is defined as what you get when you try to fold the opposite sides of a cube together. So it is more like a 2-torus revolved around a circle.

[SharkRetriver]

@Meb8Rappa It's like connecting the ends of a spherical cylinder...there're multiple types of 4d tori, and i can't rly ask wildstar which type it is because he's not on anymore.

[Meb8Rappa]

@SharkRetriver it more looks like a sphere around a circle but i don't know.

[Meb8Rappa]

Is this a duocylinder or what kind of hypertorus is this?

[oaney]

Actually after thinking about the topic a bit more, and then thinking back to the story of flatland. If I saw this floating and morphing in my living room in 3 dimensional space, I would be seeing the shadow of a 4 dimensional shape that is outside my 'plane' of existance (cube of existance is more accurate I suppose.) Would it be a shadow or 'slices' of the 4d shape passing through my 3d 'plane', similar to a finger appearing like a morphing circle when passing through flatland.

[oaney]

I have a quick question before I ask a more in depth question: At the beginning and end the shape appears like a 3d torus. Is it possible to rotate this 4d shape such that it would rotate in on itself in the same fashion as a 3d torus like a vortex? Think like how smoke rings move. In what ways could we make this 4d shape behave like a smoke ring?

[lilrocker1053]

Ok, from what I'm understanding from this (besides the part where I'm getting high all the time from this) is that considering the lack of knowledge the human brain has, will only allow us to see a certain dimension (2D) but imagine 3D? So if the human used more than 10%, wouldn't that allow us to see in more dimmensions?