When I moved my blog to a new host a couple weeks ago, I had the opportunity to spruce up the design a bit. Our IT guru Ross suggested I come up with a graphic for my header, which he just put in place for me yesterday. I believe my new header graphic is suitably nerdy to fit my personality — I’ve chosen a Penrose tiling as the pattern you see at the top of this page (assuming you are viewing this as a web page). Credit goes to Wikipedia for each of the images you see in this blog post.
Penrose tilings are cool because they are totally aperiodic over an infinite plane. I’m not sure I could understand the the mathematical proof of this at this point, but back when I was a Symbolic Systems major at Stanford taking the dreaded Logic 160 A&B Series, we had to once prove the four-color map theorem and Gödel’s Incompleteness Theorem, and I would assume similar techniques would apply to proving the aperiodicity of the known Penrose tilings.
While poking around the Wikipedia entry for Penrose tilings I not only found a photo of Penrose tiles covering the MCS building floor at the University of Western Australia, but I also discovered that Penrose actually licensed the Penrose tilings to Pentaplex Ltd, a company in Yorkshire, England controlled by Sir Roger Penrose. Pentaplex actually sued Kimberly-Clark for using Penrose tilings on quilted Kleenex toilet paper. Apparently some licensing agreement was reached. Who knew that arcane mathematics and toilet paper would intersect in the commercial marketplace? Given my partner Brad’s well-reported fondness for bathrooms, I’m sure he will find this fascinating.