Hypercube 3D Computer Animation
Вставка
- Опубліковано 4 лис 2006
- Computer animated movie of a rotating four-dimensional hypercube, perspectively projected into 3D as stereoscopic left and right images, to be viewed cross-eyed. The computer animation was performed at Bell Labs in the mid 1960s. This is one the first stereoscopic digital computer animations. The image quality became degraded during the process in which the original 16-mm film was digitized.
In order to fully (if that's possible) understand 4 dimensional objects, it really helps to understand 3 dimensional objects interacting with a 2 dimensional surface. Take for example a sphere passing thru Flatland. It would first appear as a point, then as a circle, expanding gradually until it reaches its full diameter, then shrinking back down to a point and vanishing, as the sphere passes thru the plane. Extrapolating, a four dimensional sphere as it passes thru 3 dimensional space would appear as a point, expanding as a sphere to its maximum at its midpoint, then shrinking back to nothingness as it completes its passage. A cube passing thru flatland would look vastly different from their perspective depending on the angle of the intersection; just picture the different shapes possible by slicing thru a cube at different angles, shape in this case being the face of the cut surface. At the simplest level, passing thru perpendicular to the surface, it would appear as a full square for a while until it disappears suddenly when its passage is complete. Tilt it a bit first, and you'll have an expanding triangle until one of the vertices passes thru the plane, then things start to get complicated, but the angles and shape of the changing polygon can be calculated easily. A tesseract passing thru 3d space would similarly appear vastly different depending on its angle of intersection, but I believe those angles can be calculated as well. I don't know if this simulation has ever been written, but I'd love to see it.
This is the coolest thingy ever!! I'm holding a hypercube between my fingertips!
I understand some people are having trouble seeing it.
-Sit directly in front of your screen.
-Don't tilt your head.
-Hold your arms out in front of you.
-Point your index fingers at each other a few centimeters apart. Each finger should block 1 image.
-slowly pull your fingertips toward your eyes while focussing on them.
-The hypercube images will merge in between them at the right distance.
-Now focus on it.
XD
It's worth enduring the effort of crossing your eyes for the stereo effect. How amazing that stereoscopic animations were such an early part of CGI.
These videos are very hard to find! I have read about them for years but never viewed them.
Took a while to get the knack of crossing your eyes without losing focus - but this is great - better than any 3D film I've seen no glasses required!
That is the best hyper cube video I've ever seen. Thank you!
In 3D it looks so awesome and mind-twisting!!!
I love those cross eye animations!
The 4d object has a 3d shadow, that's what we see and it's really difficult to imagine how it really looks like. I think it's a rich structure, with too much volume. A 3d object has a 1 m^3 volume, so a 4d, a 1m^4,it's space is filled with cubes...
This is so awesome! I love how from one perspective it can seem like small cube after cube after cube is continually passing through a tunnel, but by looking at it in 3D you can see that at any given point in time the small cube could rotate through any of the 6 sides of the bigger cube, and then my brain tries to grasp the concept that it's all connected and there really isn't any small or big cube but one 4D object.
It's so confusing, I love it!
thanks helped to understand how the movie cube 2 was about.
beautiful, thank you so much for posting this!
To anybody saying time is the 4th dimension... time can be seen as an analogy to a dimension, and works well as an introduction, but I think the implications are pretty clear that we are talking about a spatial dimension here. Maybe we can try to model reality as 3D space and 1D time, but when someone shows a video of a cube rotating, people don't assume it's a representation of 2D area with 1D of time. Why should you in this case?
wow it's really cool when you look at it stereoscopicly.
Man, I couldnt see the 'shape' before, but with this, I can see it, and understand it completely
The 4d cube has 3d cubes as surfaces (like 3d cube has squares as surfaces). The small cube we see in 3d as we cross the eyes, is not small, it's just the (or the shadow of the) surface of the 4d cube that's further away and as it comes to our 3d world, and then enters the 4d world again (disappears from here). Thank you, it's clearer when it's seen in 3d!
Pretty cool. Nice 3d w/ crossed eyes
a 3d representation of a 4d object. Priceless.
I'm well aware that time is the fourth dimension in which things exist and move; videos on hypercubes are not about the 4th dimension being a temporal one, but a hypothetical extra spatial one, so objects exist within the normally observed ones x, y & z, but adding in another one; w to models and equations.
this is a 4th euclydian dimension (spatial) as opposed to the concept of the 4th dimension being time, (temporal) so for the purpose of this concept, shift time up to the 5th dimension.
oh hell man, this is tripping, good stuff
Exactly, it's a 3 dimensional 'shadow' of a 4d object. The same way as a 3d cube can be drawn on 2d paper.
that's how i seem to understand it, a cube within a cube, rotating as you said, in on itself.