Math and Art

[Forecast]

M.C. Escher has motifs that repeat in his work, where you can re-paste his images right, left, up, or down the image and it'll all fit together. I know there's some mathematical, geometrical reason it works, but does anyone here know how to do it? They talk about lattices, but a lot of their terminology and explanations are confusing.

Here's the example from one of my math textbooks: http://www.auburn.edu/~hameswe/Horsemen.jpg

How does it work? I want to start doing this... my math teacher shrugged me off when I asked him and didn't take me seriously because I'm a poor math student. I really want to learn how to do this.

Thanks in advance (this can turn into a math/art idea thread as well)

:yum:

[•Lindsay•]

http://www.mathacademy.com/pr/minitext/escher/index.asp

[H.Evans]

Pattern Design by Lewis F. Day explains how to create various pattern systems.
It's online here:
http://www.cs.arizona.edu/patterns/weaving/books/dlf_patx_1.pdf
http://www.cs.arizona.edu/patterns/weaving/books/dlf_patx_2.pdf
...and Dover books recently reprinted it.
Tesselation is around page 68 of pdf 1.