Penrose Tilings, Quasicrystals, and Islamic Architecture

What do the floor of the Oxford mathematics department and Medieval Islamic architecture have in common? They both feature a particular kind of mathematical pattern called aperiodic tilings. In the 1960s and 1970s, mathematicians found different sets of shapes that could be put on a flat surface in such a way that the pattern never exactly repeats, so matter how many tiles you use. Roger Penrose created one of the most famous of these tilings, involving just two different shapes: a kite and a dart. Though Penrose is credited for this discovery, a version of this very same mathematical tiling appears in Medieval Islamic architecture dating to the 1400s. Additionally, in the same way that a set of cubes is the three-dimensional version of a tiling of squares, these aperiodic tilings provide the basis for the atomic structure of newly discovered set of materials called quasi-crystals. In this talk, we explore how this one mathematical idea appears in surprising and beautiful places.

Catherine Blume is currently pursuing her Ph.D. in astrophysics at the University of Colorado Boulder. She earned her B.A. in physics from Princeton University in 2018, where she studied Earth's magnetosphere. At CU, she studies the solar interior using fluid simulations. When she is not buried beneath equations, she enjoys crocheting cat sweaters, being outside with friends, and baking banana cupcakes with (what some would say is too much) chocolate frosting.

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