# 4D Hypercube Animation

By on June 6, 2006, with 70 Comments

Ok, we both know this isn’t a real 4D Cube (also known as Hypercube). Never the less, this animation really blew me when I first glazed my eyes on it. If you are interested more in mathematics behind 4D spaces, be sure to browse Wikipedia. In the meantime, enjoy!

70 Responses
1. marry says:

boring I can make that

2. jolovesthisanimation says:

That is so wicked!!!!!!!!!!!!!

3. mg says:

wow

4. Connor says:

That’s not even 4D, what a gay image

5. niki says:

it’s just a box inside a box… *stares blankly*

6. zippy the turtle says:

click on the link for the animation! its not just a box in a box people learn to READ

7. sbredflag says:

Pretty cool!

• CoaCo says:

Its just a 4D version of a 2D square ore 3D cube rotating

8. NIC says:

zzzzzzzzzzzzzZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ BORING!

9. kristen says:

ok…what you do is READ THE STATMENT OBVE THE PIC click on the link AND WATCH THE ANIMATION omg DUH

oooooohh!! i always wondered what made hypercubes special!

11. rae says:

maybe I’m missing something…(yes I did see the animated version), but couldn’t this object be made in RL with some sort of stretchy/gummy material?

12. Rachael says:

That’s almost hypnotizing. Aren’t those called tesseracts?(don’t know how it’s spelled)

• Josiah says:

I think that this is awesome
(and you spelled it right.

13. Kim says:

I dont see the animation, what is it supposed to do?

14. Kim says:

nevermind :p, cool stuff

15. Me says:

cool

16. Bob says:

It is not possible to visualize a 4D object with 3D imaging no matter how fancy the animation. The visual concepts are beyond the abilities of the human brain. All we can visualize is the shadow of a hypercube presented as a 3D object just as a square is a 2D representation of a cube.

it is however a very pretty animation

If you’re interested in the fourth dimension, might I recommend “And He Built a Crooked House” by Robert A. Heinlein. Very cool short story if you’re geeky like me

18. alana says:

if u see the animation, it almost puts you to sleep. not of boredom, just cuz its relaxing and hypnotizing

19. me says:

zomg thats amazing!

20. DUDE! says:

This is so wicked!!!!
you have to go to the link above it!!!!

21. BurninRubber says:

MY BRAIN!!! AARRRGGGH!! SMART PEOPLE MAKING IT WORSE… ARRGH!

22. intrested says:

what does this cube represent? 4D. BUT can it be applied to anything? this doesnt explain 4D because it’s only a cube. but my question is: can anything be in 4D? or does it only have to be a cube? and isnt 4D time?

23. Cool says:

Each edge of the cube is the same length, you cant reallly tell but if you think about it they would have to be, the cube inside is smaller because the cube could not only move up, down, left, right, in and out it can also move to seem smaller or bigger (shrink or expand). And to answer your question no it doesnt have to be a cube, yes 4D is time and this is basicly an example of 4D it is not what 4D IS but just an animation made to aid you in understanding it.

Thats my opinion, pretty good stuff.

24. loser says:

just a box..inside a box…kinda boring..*stares* *not interested*
=^.^=

25. Anonymous says:

yes Rachel, it is…

26. idontlikeanything says:

That is not even an animation, wrong category

27. Anonymous says:

LOOK AT THE ANIMATION, DANGIT! I don’t mean to be rude, but really, people…

28. Anonymous says:

*staring blankly* a box..wow..this fails to amaze me..

29. Anonymous says:

u dumbasses need to click the link to the animation… dumbass

30. jrgruntly says:

LOOK AT THE ANIMATION STUPID!!!!!!!!!! omg u ppl have tumors in ur brain

31. Anonymous says:

i used to have this mind toy that was put together exactly like that. using tubes and elastic string. or something similar O.o fuuuuun

32. Anonymous says:

am i suposed to be amazed
BORING!!!

33. Sandoras says:

Makes a lot of sense after taking it and watching it frame-by-frame in my cheap photoshop program…Still, excellent illusion

34. The AMBINATOR _u m ok,BORING!!!!!! says:

That is not an illusion!! I can make that out of magnetix!!!!!!!!!!
All the people that think this is an illusion are dumbasses! The rest of’em are on my side=^^=
o

Ok, Anyone who thinks this is NOT a illusion is WRONG.
DID YOU EVER LEARN TO READ AND LISTEN?
YOU HAVE TO SEE THE ANIMATION

36. Cory says:

cool it makes me think of the mist games for some reason!

37. Politikally Paranoid says:

Tat iz so kewl. I wanna know how dat happened yo!

38. Griffin says:

i dont know about anyone else, but all i see is just a stupid picture of a shape that anyone can make out of magnetix sticks!!

39. www.yourgay.co.u-gay says:

that hyperpube sux!
geddit! hyperpube! lol

40. Anonymous says:

The picture did nothing. I clicked on “animation” and found an advertise window. Is this why we were asked to click on -animation- link? Please find other ways to advertise.

41. Anonymous says:

Yes, this cube IS really called a tessaract, and yes, it IS really four dimensional. Look it UP!
And don’t click on the picture, click on the link. Pay attention!

• Laura says:

Yes, I thought it was a tesseract. The fourth dimension is time.

42. Anonymous says:

Alothough, no, I’m pretty sure it’s not actually a real illusion.

43. Schunki says:

it IS a 4d Hypercube… there are also 5D, 6D … and so on

44. Anonymous says:

well if it is an advertisement then it is a great way to do it.

45. chris flucture says:

its amazing,ihave never seen this ever before

46. Nigel says:

Why can’t people read The Time Machine by H.G. Wells? The fourth dimension is time, all objects are in the fourth dimension. Time, duration, call it what you will, have you ever seen a cube in only 3d? An instantaneous cube?

47. Anonymous says:

dats awsome!!!!!!!!!!!!!!!!!!!!!

48. Coolio says:

i think of marshmallows when i c this…..maybe im just hungry.

49. Amber says:

Nigel – You’re not really getting dimensions. Yes, the fourth dimension we, the common public, experience is time, but for mathematicians, who know there’s more, it would be bad practise to label time as the “4th” dimension when there are more spacial dimensions after the 3rd.

50. Silver says:

I must get one of these in RL. I will play with it for hours!

51. steve says:

its from that movie called “The Flatlands”

• Allison says:

haha i watched that in geometry class.

52. Noone says:

I luv this

53. javacuzi says:

thats too cool

54. Guido de Mossimo says:

it kind of folds into itself…….. coolio tho

55. derek says:

it looks kool, but i think its being turned round and round.

• Sparky says:

You’ve got to be kidding me-it’s so transparnetly clear now!

56. SefronZ says:

the 4° dimension is the time :)
the 5° dimension is the light :)
and maybe there is 6 more dimensions

• anonamus says:

those rnt dementions stupid all the dimentions are of a phyical mesurement length width highth time isnt a dimention and neither is light or else the original mario would be 4d which its not

57. Mathematically four-dimensional space is simply a space with four spatial dimensions, that is a space that needs four parameters to specify a point in it. For example a general point might have position vector a, equal to

\mathbf{a} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \\ a_4 \end{pmatrix}.

This can be written in terms of the four standard basis vectors (e1, e2, e3, e4), given by

\mathbf{e}_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix}; \mathbf{e}_2 = \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix}; \mathbf{e}_3 = \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix}; \mathbf{e}_4 = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix},

so the general vector a is

\mathbf{a} = a_1\mathbf{e}_1 + a_2\mathbf{e}_2 + a_3\mathbf{e}_3 + a_4\mathbf{e}_4.

Vectors add, subtract and scale as in three dimensions. The dot product also generalizes to four dimensions, like so:

\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3 + a_4 b_4.

It can be used to calculate the norm or length of a vector,

\left| \mathbf{a} \right| = \sqrt{\mathbf{a} \cdot \mathbf{a} } = \sqrt{{a_1}^2 + {a_2}^2 + {a_3}^2 + {a_4}^2},

and calculate or define the angle between two vectors as

\theta = \arccos{\frac{\mathbf{a} \cdot \mathbf{b}}{\left|\mathbf{a}\right| \left|\mathbf{b}\right|}}.

The cross product is not defined in four dimensions. Instead the exterior product is used for some applications, and is defined as follows

\mathbf{a} \wedge \mathbf{b} = (a_1b_2 – a_2b_1)\mathbf{e}_{12} + (a_1b_3 – a_3b_1)\mathbf{e}_{13} + (a_1b_4 – a_4b_1)\mathbf{e}_{14} + (a_2b_3 – a_3b_2)\mathbf{e}_{23} + (a_2b_4 – a_4b_2)\mathbf{e}_{24} + (a_3b_4 – a_4b_3)\mathbf{e}_{34}.

This is bivector valued, with bivectors in four dimensions forming a six-dimensional linear space with basis (e12, e13, e14, e23, e24, e34). They can be used to generate rotations in four dimensions.

thats the math behind it! =]

58. ps info from wiki

59. Bunnasaur says:

That’s so cool! It kinda makes a cube in the middle :P

60. Trent says:

Never the less, this animation really blew me when I first ….
Am I the only one who caught this??

61. unknown says:

no i got it the out gets in and then the in gets out

62. toni says:

MATH 4D is real, when it comes to “math” concepts only. Animating it is stupid as the real world is 3D, you only need to specify x, y, z, to get the point you want.

any nD space is OK in math, but not in reality, the above image is silly, it’s just a 3D object anyway.

63. Kam says:

Imagine looking at a video of a normal 3D cube rotating. Because of perspective the side away from you looks smaller. As the cube rotates it appears that different sides are getting smaller or larger.

The animation above shows the same effect for a 4D cube. The perspective projection of the 4 dimensional cube onto a 2D surface means different edges will appear shorter or longer. The hypercube is not stretching. In four dimensions all of its edges are the same length and all the angles are 90 degrees. But as it rotates, the perspective projection makes it appear that parts are shrinking and that one cube is moving inside the other.

64. LOLMAN says:

all lies! a hypercube is real I watched a documentary about 4d things