Perspective sketches from 4D to 3D?

[Curl]

Just like we can draw 3D-looking images on paper, has anyone tried to "draw" out a 4D image onto 3D space? It's not really drawing, more like building. Since nobody can visualize 4D, it would have to be done mathematically. I've seen projections of hypercubes onto 3D, but it was still 2D since it was still a picture.A 3D hologram of 4D would be cool, although it might not be possible since light is limited to 3D space.

Has anyone studied higher dimension geometry to tell me more about this?

 

[TylerH]

It's possible to draw a certain perspective of a 3d image in 2d while preserving the 3rd dimension. There are some graphing programs that map the 4th dimension to time, and the other 3 to lwh. Lorenz attractors are graphed this way. I've thought about how to graph higher dimensions, but I can't really visualize it.

 

[Bill Simpson]

There is a book that deals with exactly this subject.

http://www.google.com/search?q=heiserman+experiments+in+four+dimensions

If you do as he says and actually do the exercises as he works up from 1D to 2D to 3D to 4D you can understand the methods.

15 or 20 years ago I had a copy of that, but have no idea where it is now.