Wednesday, April 02, 2014

4D Hypercube Animation

On Cheezburger, of all places, I saw this cool animated visualization of higher dimensionality.

It shows the progression from a 1D line> to a 2D square> to a 3D cube> to a 4D hypercube.

Of course, since we cannot directly experience a 4-dimensional object, we are only seeing a 3D "shadow" of the theoretical form.


This same time last year, I posted about a 3D rendering I had made of Salvador Dali's "Crucifixion (Corpus Hypercubus)".

The Monkey Buddha Archives: 

3D "Dali's Crucifixion" 
by Paul Micarelli

I had also posted a rendering I created, of a similar progression of dimensional forms- to show how each dimension that we perceive is a "shadow" of a higher one.

(click to enlarge)
https://picasaweb.google.com/MonkeyBuddha.com/TheMonkeyBuddha03#5860825739888514066

• The 0-dimensional point is a shadow of a line...
• The 1-dimensional line is a shadow of a square...
• The 2-dimensional square is a shadow of a cube...
• The 3-dimensional sides of a cube are the shadow of an (unfolded) hypercube.

3 comments:

David Watson said...

I recently came across your blog and have been reading along. I thought I would leave my first comment. I dont know what to say except that I have enjoyed reading. Nice blog. I will keep visiting this blog very often.

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Lorri said...

Wicked Blog. Very interesting content. Will be back tomorrow to delve some more.

paul_mic said...

Thanks for reading, I appreciate the positive feedback!