I had some time recently to mess about in Processing. For your consideration: sketch_2008_04_28_diagonal_lines2. Stare at it for a while and everything starts to make sense.

Update: I posted a few shorts to Vimeo: diagonal_lines2 / diagonal_lines3.

I’ve always enjoyed these patterns, so I decided to generate them. Someday I’ll be savvy enough to make it interactive. For your consideration: sketch_2007_12_11a