Sir Roger Penrose, himself, standing on a Penrose tiling at Texas A&M University.
Penrose tilings (Wikipedia), named for British mathematical physicist Sir Roger Penrose, who investigated them in the 1970s, are interestingly “aperiodic,” or, simply put, do not repeat themselves no matter how far you extend the pattern. All Penrose tilings are aperiodic, but not all aperiodic tilings are Penrose tilings.
Lots of bright creative folks have installed custom Penrose tile floors. Here’s a selection of a few of my faves from around the web. I couldn’t find anybody selling pre-cut Penrose prototiles, so it looks like anybody who wants to do it themselves has to cut their own. At least until some motivated entrepreneur comes along…
The atrium floor at Meredith College in Raleigh, NC.
One of three mathematically curious tiled floors in the home of UC-Davis professor Greg Kuperberg. Note that this floor is actually not a Penrose tiling per se. “Rather,” Dr. Kuperberg writes, “it’s a Penrose-like tiling discovered by Robert Ammann.”
Shower floor by Eric Osman of Portland, OR.
Chemistry building floor at the University of Western Australia.
Did I miss a good one? Let me know, below!