When I was a kid I used to read Scientific American at the local library. I loved Martin Gardner‘s Mathematical Games column, and I vividly remember his description of Roger Penrose‘s then recent discovery of two shapes that force a nonperiodic tiling of the plane, an aperiodic tiling, a kind of visual music.
Only later did I learn of Penrose’s important contributions to General Relativity, including topological arguments to demonstrate the inevitably of gravitational collapse leading to astrophysical black holes. And earlier this month I was excited to hear that Penrose — in his 90th year — shares the 2020 Nobel Prize in physics!
So I got out my Penrose tiles (thanks Woody) and assembled a small pattern. It’s not easy, but a combination of local edge and vertex rules (or a global inflation rule) can extend the aperiodic pattern to infinity.