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4D-Hypercube/Tesseract

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screenshot of the scene

Author: FRA32

Group: Technical

Filesize: 130.4 kB

Date added: 2015-12-13

Rating: 6.1

Downloads: 1708

Views: 511

Comments: 16

Ratings: 3

Times favored: 0

Made with: Algodoo v2.1.0

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This scene contains yet another of my mathematical algodoorythms, this time featuring a tesseract constructor and -rotator.

Yellow lines mark the "outer cube", blue lines the "inner cube", and the red lines mark the "connection lines", adding to a total of 32 lines. Note that these names are relative, when looking at the tesseract in a very specific angle, since at this view it looks like a cube inside another cube connected via 8 diagonals.

The code was quite complicated to find out, and used to be a bit bugged with displaying, as noticable when looking on the code snippets. Yet the result was worth the work, since this is actually the very first time I managed to display ANY type of highter-dimensional shape in ANY type of enviroment *yay*

I hope you'll enjoy this little view into the highter dimensions.
Last edited at 2016/07/03 21:52:09 by FRA32
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WOW! Very nice! :tup: _o_ :tup:


EDIT: I noticed a minor problem with the scene. Once a box is clicked to make the cube rotate, it cannot be "unclicked". So, if I wanted to go back to rotating the cube manually, I cannot do that.:o
Last edited at 2016/01/08 18:28:16 by Xray
Huh? I am very sure the boxes automatically disable automation once clicked again. I checked again, and they do return to normal mode when I left-click them:huh: . Are you left-clicking? and if yes have you tried clicking them while their selected or de-selected?
OOPS! My bad! :blush: I clicked on a box to rotate the cube, and then I clicked on other boxes which added other axes rotation. Then thinking that I have the cube rotating on only one axis, I clicked only one box, and of course the cube continued to rotate on the axes that I auto-rotated. I did not notice before that the boxes turn blue when in auto-rotation mode. Now I see that I can click on all the blue boxes which will take all of them out of auto-rotation mode.

Sorry for my verbose reply, but that's just how I am!

Again, very nice work!
i added to my strange movement thing
WOOW !!! =D incredible!!!
Cool!

Is it possible to do this with the other 4d shapes? like the 5-cell hyper-tetrahedron, or the other 4d analogues of the platonic solids? Look at this guy in the wikipedia, he made lots of the animations: https://commons.wikimedia.org/wiki/User:JasonHise

Also, would it not have been easier to connect the points with springs? Just set the length to some big number, and the thing will look like a transparent line. http://imgur.com/iCax8AM
Last edited at 2016/02/28 04:18:22 by icrls984
@icrls984
Wow, thanks for commenting on this scene despite it's age. About your question to the 4D-shapes. It would in fact be possible, if I change the amount of points and the absolute position of them. so if I take 5 and position them in the shape of a "Tessermyd"(My name for 4D Pyramid), and then just connect them with springs(thanks for the suggestion btw), it could work.
:tup::tup::tup::tup::tup::tup::tup::tup::tup::tup::tup:

OMG AWSOME
Amazing Illusion :lol:
This isn't just an illusion, this is basically the 2D projection of a real 4D Cube:D
Interesting my friend, how could yo do this?

IS that take a long time to make?

I have too many questions to ask!

But I have one think to say before leaving;

PERFECT!
Before I made this scene, I got to know with some formulas to apply rotation and dimension transformation to Data points, which would allow me to "camera render" 3D bodys from any angle. I applied these formulas to the 4th dimension by continuing the pattern in which these formulas work. Then I started scripting these formulas in this scene while creating the angle wheels and defining 16 vertices. The worst problem for me was how exactly the 6 rotation motions had to be stacked to properly result in the rotation style I wanted. Then I just sent these coordinates to the 16 circles and boom! Projected 4D cube.
I love it! How does it work? And how long did it take you to make that code?!
Yikes, i got hypnotized by it.
The code propably took me a few days in total, mostly due to long lasting fixing of the applied formula, which wasn't producing the exact effect I desired. It works by taking a point in 4D space, applying all 6 rotations to it in a specific order(The typical ZXY order plus the three new rotation planes) and then double-transforming the 4D coordinates down to 2D. these 2D coordinates are then used for the 16 circles that make up the figure. This last part is where most spacial information regarding 4D is lost, due to the fact that I basically cast a shadow of a shadow, which sounds illogical already, but is the only method of bridging the 4th and 2nd dimension.
If you turn on XW and ZW rotation it looks like it’s changing rirection