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Hypercube Computer Animation


Computer animated movie of a rotating four-dimensional hypercube, perspectively projected into 3D as stereoscopic left and right images, to be viewed cross-eyed. Animation was performed at Bell Labs in the mid 1960s.

Channel: Film & Animation
Uploaded: November 30, 1999 at 12:00 am
Author: computerartist

Length: 01:41
Rating: 4.71
Views: 52929

Tags: animation  hypercube  

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Video Comments

blackfractal (November 30, 1999 at 12:00 am)
It's a thought experiment: a 1D line is two points with infinite points between them a 2D square is two lines with infinite lines between them a 3D cube is two squares with infinite squares between them a hypothetical 4D hypercube is two cubes with infinite cubes between them, lined up in a hypothetical 4th spatial dimension.
blackfractal (November 30, 1999 at 12:00 am)
the video shows stereoscopic imagery. The two pictures are indeed different -- stop it on any frame and simply look at the two cubes and you can see they are different. When crossing your eyes you are changing the convergence point from the screen to somewhere in front of the screen. You can find the exact point of convergence by placing your finger on the screen in the middle and below the cubes. Focus on your finger and bring your finger toward you until the cubes fuse.
EvilHeadBoy (November 30, 1999 at 12:00 am)
well, it is possible to view a 3d object on a 2d surface; the video has the right idea of crossing our eyes, but it would only make it true 3d if each of the two pictures were different, (same way both eyes see a different angle, which makes it 3d instead of 2d with one eye i suppose)
zipatriarc (November 30, 1999 at 12:00 am)
259 great explanation of what we are seeing here but i you forgot the fact that you can't even view a true 3d object on a computer so what this video shows is a 3d shadow shown in 2d of a 4d shadow shown in 3d. The only true 4d shadow that can be seen in 3d is if you have one of those glass "klien bottles". Either way still a good video. Check out how to turn a sphere inside out.
ecreif (November 30, 1999 at 12:00 am)
you dont even see 3d things.. because you have a 2d eye... thing about it.. when you did you are able to understand how to "get" a 3d eye and even a 4d "eye2
MPS186282 (November 30, 1999 at 12:00 am)
in the same way as a shadow of your hand appears to be passing through itself as your hand rotates, this 3-d "shadow" of a 4-d hypercube appears to be passing through itself as the actual 4-d object rotates. hope that explaination clears things up.
FerHivore (November 30, 1999 at 12:00 am)
Wow, if we were in the fourth dimension that would be the most boring video ever.
259 (November 30, 1999 at 12:00 am)
No, it is not "changing shape" or "morphing", it is just merely rotating. It only appears to change because it is an unavoidable consequence from projecting a 4D object into a 3D space. What you are seeing here is not an actual 4D object, as that would be impossible since we are all restricted to 3 dimensions. What you are seeing is a "shadow", or a projection of it.
xXGoDxiSxdEaDx666Xx (November 30, 1999 at 12:00 am)
ahahahaha...technically u can visuallize it...it takes a pure mind however to accomplish it; since ours are contaminated with the 3-d shit...its going to be pretty hard
SilkOlive (November 30, 1999 at 12:00 am)
it looks like a square donut that keeps rolling in on itself...so is the negative space the inner cube? or the outer cube?

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