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? 


  1. This is awesome Nathan! Have you found any 'sweet spots' where you get very striking patterns? Your 'poster frame' is certainly very nice.

    1. Is that you, Naylor? I've found all kinds of 'sweet spots' but always lose them!


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