Hypercube Manual Rotationsby DovSherman

Someone requested a hypercube which could be manually rotated so I threw this together. Drag any of the sliders to rotate the hypercube around each of the six planes of rotation. You may notice that some rotations seem to have no effect when seem in orthographic or 3D perspective because the rotation is happening in directions which are not represented in those views when seen from some angles.

A hypercube (or tesseract) is the 4-dimensional analogue of a cube. It has 16 corners, 36 edges, and 24 sides. All corners are right angles although they may seem like acute or obtuse angles when seem from a different viewpoint, just as the corners of a cube may seem sharper or wider depending on your viewpoint.

Rotation is achieved through a simple 4x4 transformation matrix which allows the hypercube to be rotated along a single plane at a time. In 3-dimensional rotation, rotation usually occurs around a linear axis but 4-dimensional rotation occurs around a planar axis.

You can check/uncheck the box to see the hypercube with solid sides or empty sides. Click on "Perspective" to select different methods of display.

The Artist has requested Critique on this Artwork

jambawolfflipnote Featured By Owner Dec 6, 2013  Student General Artist
Guess who's confused!
Featured By Owner Feb 7, 2013  Professional General Artist
HOLYSH'OOT IM FAVE THIS, I was looking for something like this! *gaps*
Featured By Owner Dec 10, 2012  Hobbyist Digital Artist
Never would I imagine that someone would take the tme to conjure this up. Thumbs up!
Featured By Owner Dec 10, 2012  Hobbyist Digital Artist
Never would I imagine someone would take the time to make this. Thumbs up!
Featured By Owner Dec 4, 2012  Hobbyist Digital Artist
Damnit. I'm trying to rotate it into the angle that the projection in my avatar shows, but it doesn't seem to be possible with a perspective projection. Obviously my projection is orthographic. I got it really close but then the meanings of different rotation planes in 4D confuse me and I can't continue without messing it up.
Featured By Owner Edited Apr 27, 2015
I think that you're avatar is showing a cross-section of a hypercube, rather than a rotation
Featured By Owner Apr 27, 2015  Hobbyist Digital Artist
No, it's actually just an ortographic wireframe. I just now realized that in this hypercube with interactive rotations, you can actually select ortographic projection and rotate the hypercube to the angle that it's projected on in my avatar. You can in fact rotate it in all 4 dimensions so that it ends up looking like my avatar.
Mark-y-pin Featured By Owner Jul 1, 2012  Student Traditional Artist
uh fun !!
Featured By Owner May 23, 2012
This is really clever. Strange to think that you're the same person who makes sissy drawings and also hypercubes. Hehe. Who'd have thought that they were in the same galery.
Featured By Owner Feb 11, 2012  Hobbyist Writer
The rotation of the ana and kata directions. Freaking awesome. I just wish I could see this in three dimensions.
Featured By Owner Dec 13, 2015   General Artist
You can but you can't
It's got an extra dimension thrown into the mix of shapes
Featured By Owner Dec 23, 2011  Hobbyist General Artist
It's... amazing!
Featured By Owner Dec 12, 2011
Such a simple concept... a cube inside a cube... but what the hell is the W dimension!?
1st Dimension: Length
2nd Dimension: Width
3rd Dimension: Hight
4th Dimension: ?
Featured By Owner Jul 25, 2012  Hobbyist Digital Artist
Time?
Featured By Owner Jul 25, 2012
Featured By Owner Nov 28, 2011
mind=blown
rockman296 Featured By Owner Nov 3, 2011
wierd, but AWESOME!
Featured By Owner Oct 12, 2011  Hobbyist General Artist
this... is... freaky... it's awesome, but freaky...
Featured By Owner Oct 11, 2011  Hobbyist General Artist
Featured By Owner Aug 21, 2011
Cooool!
Featured By Owner Jul 29, 2011  Hobbyist Digital Artist
...I...don't...get it...
missy22673 Featured By Owner Jul 29, 2011
WHHEE!!!! I dont get it :3
Im justr making it randomly spin...WHEE!
Featured By Owner May 7, 2011
my brain is asploding...
Featured By Owner Apr 7, 2011
nice work o3o
Featured By Owner Feb 26, 2011
awesome!
Featured By Owner Feb 24, 2011  Student General Artist
I don't understand the 4th dimension. I'm very much into science, but I have trouble understanding these concepts
Featured By Owner Mar 31, 2011  Hobbyist Photographer
you can't understand it because you live in the 3rd dimension
Featured By Owner Dec 13, 2015   General Artist
Exactly,
Wait wtf =-O
loopnana Featured By Owner Feb 13, 2011  Student
holy shiiiit im trippin balllz.
Featured By Owner Dec 7, 2010  Hobbyist Digital Artist
Witchcraft!

I love it.
Featured By Owner Oct 2, 2010
wow this is trippy to look at. (and to think about)
Featured By Owner Oct 2, 2010
So... confusing o.o love it!
Featured By Owner Oct 2, 2010  Student Digital Artist
great
Featured By Owner Sep 7, 2010
transforming rectangle, duh. also, it has to be transparent
Featured By Owner Sep 7, 2010
IVE FINALLY REALIZED EXACTLY WHAT THIS IS!!!
This a 4-D cube that can rotate in the 4th dimension, as seen from exactly "above" in the 4th dimension! We, however are seeing it as 3 - dimensional beings. Think of it like this. A rectangle, rotating along the x-axis, as seen above from a 2D being, would look a heck-of-a lot like a transforming square. Only when we can mathematically find exactly where the "w" axis is and somehow create an image of it with it actually look like it is spinning and not transforming. That, alas, is where it all breaks down.
Featured By Owner Dec 13, 2015   General Artist
Why does my brain feel like every nuke on earth just went off.
It hurts so much!
Featured By Owner Sep 10, 2010  Professional Digital Artist
Actually, we're not even seeing it as 3D. We're seeing it as 2D since it is on a computer screen.

Imagine a 3D wireframe cube hanging in the air. Now imagine a light shining on it from above. Look at the shadow it casts on the ground. That shadow is the way we represent a 3D object on a 2D surface like a computer screen.

Now imagine a 4D wireframe hypercube hanging in 4D space. A light casts it's shadow onto the 3D "ground", creating a 3D shadow which, to a 3D human, looks like the 3D wireframe in the previous example.

So this simulation is showing you the the 2D shadow of the 3D shadow of the 4D hypercube.
Featured By Owner Sep 10, 2010
actually, we cant see that shadow the way they would see it
I find it is much easier to imagine the 4th dimension by making comparisons from 2d to 3d. a 2d person would see the 2d "shadow" of a cube much more differently then we do. So what does it actually look like? The world may never know...
Featured By Owner Sep 13, 2010  Professional Digital Artist
A 2D person can only see 1D so, to them, a shadow of a cube would look like a line segment when seen straight on, or like two shorter line segments when seen at an angle.
Featured By Owner Jul 26, 2010
Awsome, very good work.
Featured By Owner Jun 11, 2010
Featured By Owner Jun 11, 2010  Professional Digital Artist
I don't think you normally can download Flash SWF files. It might be possible if you can hack into your browser's cache but I don't know if you would be able to run the SWF file directly, anyway, unless you have the full Flash development kit with the stand-alone player.
Featured By Owner Apr 21, 2010
I just realized one thing: You have created the new Rubik's cube!
Kansheera Featured By Owner Apr 10, 2010
Furthermore, can you visualize this thing? Can you picture the W axis? Is it even possible for a human to do it?
Featured By Owner Apr 10, 2010  Professional Digital Artist
Hard to say. I know I have tried to visualize 4D and, for a moment, I think I have it, and then it slips away. While I don't think it is impossible for a human to visualize 4D, I do think that our brains develop pathways primarily for interpreting 2D and 3D. Since we are not constantly exposed to a 4D environment, we don't develop the pathways for interpreting it. But, perhaps, if a human were raised in a 4D environment, they would develop the pathways to understand it naturally.
Featured By Owner Jun 25, 2011  Hobbyist General Artist
sometimes stuff happens for only a split second and we're not prepared for it so we can't really see it, so it's more like a flicker in your eye instead of you actually seeing it
Kansheera Featured By Owner Apr 10, 2010
You should totally include a mode that makes the "surface" opaque! This it the best thing ever, even though it makes my brain cringe
Featured By Owner Apr 10, 2010  Professional Digital Artist
I'm not sure if the term "surface" applies to a 4D object. I'd have to think about that.
Featured By Owner Feb 1, 2010  Hobbyist Traditional Artist
my mind just blew up!
Featured By Owner Jan 23, 2010  Hobbyist Traditional Artist
This is my new favorite toy~ ... thanks so much for makin it~ ^w^

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Submitted on
November 26, 2005
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