Toilet Paper Problem

What would it look like if you marked each perforation on a roll of toilet paper and rolled it all back up?  A striped pattern?  A spiral pattern?  I wondered about that in college, and wrote a program to answer the question - here's it's latest incarnation:
(The link above goes to a Processing app requiring Java - if it doesn't work, try this Flash version).

Of course, the pattern depends on the sheet thickness and the sheet length.  Try clicking different places on the screen - the farther your mouse is to the right, the thicker the sheet, the farther down, the longer the sheet.  I was surprised at what a difference small changes in these values had on the overall pattern.  My fractal sense is tingling - is yours?

At one point I found an article about this type of pattern (an Archimedean spiral marked at fixed intervals), but have since lost track of it - can you help me out?