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
— via MAKE