Prof. Andrew Vince together with his coauthor Michael Barnsley were recipients of a 2018 Mathematics Association of America Paul R. Halmos – Lester R. Ford Award for their paper “Self-Similar Polygonal Tiling” . The Paul R. Halmos-Lester R. Ford Awards recognize authors of articles of expository excellence published in The American Mathematical Monthly.
The award citation read in part: Many mathematicians are familiar with the magical beauty of Penrose tilings. These famous aperiodic tilings of the plane involve two primitive shapes: the “kite” and the “dart.” They are non-local in the sense that one cannot distinguish between the uncountably many distinct Penrose tilings based upon examining any finite region of the plane. What about similar tilings that involve only one primitive shape? This fantastic article investigates the fascinating possibilities. It begins with a careful study of the tilings that arise from the “Golden Bee,” an unusual six-sided polygon closely related to the Golden Ratio. The authors then proceed to a general construction of self-similar polygonal tilings. Remarkably, many of their polygons are irregular in appearance and some are not even convex. Nevertheless, they still manage to tile the plane in startling and unusual ways. Many examples are studied, each of which is accompanied by dazzling full-color artwork.