The Pinwheel Tiling

Sometime around 1991, Charles Radin commissioned John Conway for a substitution tiling for which the tiles appeared in infinitely many orientations, and soon John obliged with the Pinwheel. The Pinwheel is formed from right triangles,


The trilobite and cross tiles clearly generalize to higher dimensions. Though a simpler method soon appeared”Threelobites” were a first early graphic / mathematical exploration. Here’s a nice pic of a tiling by the trilobite and


This window, in Champions Hall at the University of Arkansas, illustrates a particular twelve-fold tiling substitution scheme: each individual tine may be refined into an arc of smaller tines, and itself sits within a larger