I am learning about a special topic in complex analysis called conformal maps. It is an extremely geometric and visual topic. A lot of nice art can be done with them. I wanted to show you the nice art that comes out of them.
You can see some nice maps here, just look near the top of the page at the pictures. Note, all the intersections between the curves are orthogonal (that is a property of these maps).
Also you can see some animations here and here.
If anybody is interested I can explain how what is going on here. The explaination uses just very basic complex analysis, in case you want to draw these curves yourself.
Does Mathematica or any one of those serious math programs have a conformal map feature?