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 Math Factor

In the fall of 2003 (as a strategic move to have the department seem more community minded) I began putting a weekly puzzle problem on the University of Arkansas campus wide listserv. This caught the

Symmetry here and there

All of these photos were taken in 2022, for the upcoming The Magic Theorem of the Symmetries of Things, a second edition of the first part of the book, with expanded exercises and examples, in

A few groovy images

All of these groovy pix use maps from the plane to itself, taking a periodic pattern into the plane in a distorted way. Don’t stare into the middle for too long…

Double Triamond, w/ Hexastix!

“Double Triamond, w/ Hexastix!” created in collaboration with Eugene Sargent, was assembled at the eighth Gathering for Gardner, at Tom Rodgers’ and Sarah Garvin’s beautiful Japanese style gardens and home in Atlanta in 2008. The


You’ll have to cross your eyes or use a stereoscope to see these stereoscopic images, photographed with a stereopi . Tubing and 3D printed connecters are a great way to make models with lots of


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

Self-assembly of Robinson tiles

Through a local self-assembly rule these tiles are forced to form arbitrarily large patches of Robinson tilings, with some extra markings that are used to manage the process. In the animation, at each green dot,

Orbifold Geometrization

I was curious about the actual algorithm for geometrizing an orbifold — it’s only lightly sketched at in Thurston’s Three Dimensional Topology and Geometry. Hence the app. The details are now inside some javascript: Check