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DovSherman — Hypercube Manual Rotations
#4d #hypercube #fourdimensional
Published: 2005-11-27 04:36:25 +0000 UTC; Views: 35734; Favourites: 214; Downloads: 1511
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Description
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.
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Comments: 105
HOLYSH'OOT IM FAVE THIS, I was looking for something like this! *gaps*
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Never would I imagine that someone would take the tme to conjure this up. Thumbs up!
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Never would I imagine someone would take the time to make this. Thumbs up!
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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.
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I think that you're avatar is showing a cross-section of a hypercube, rather than a rotation
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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.
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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.
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The rotation of the ana and kata directions. Freaking awesome. I just wish I could see this in three dimensions.
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You can but you can't
It's got an extra dimension thrown into the mix of shapes
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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: ?
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this... is... freaky... it's awesome, but freaky...
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WHHEE!!!! I dont get it :3
Im justr making it randomly spin...WHEE!
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I don't understand the 4th dimension. I'm very much into science, but I have trouble understanding these concepts
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you can't understand it because you live in the 3rd dimension
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wow this is trippy to look at. (and to think about)
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transforming rectangle, duh. also, it has to be transparent
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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.
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Why does my brain feel like every nuke on earth just went off.
It hurts so much!
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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.
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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...
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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.
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I am having trouble downloading this item and Hypercube Rotations. Can you advise?
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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.
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I just realized one thing: You have created the new Rubik's cube!
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Furthermore, can you visualize this thing? Can you picture the W axis? Is it even possible for a human to do it?
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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.
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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
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You should totally include a mode that makes the "surface" opaque! This it the best thing ever, even though it makes my brain cringe
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I'm not sure if the term "surface" applies to a 4D object. I'd have to think about that.
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This is my new favorite toy~ 
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This is my new favorite toy~
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