Automating Escher’s Combinatorial Patterns

Rick Mabry, Stan Wagon, and Doris Schattschneider

The use of replacement rules to implement transformations of the plane and equation-solving to determine colors allows the automation of some early tiling techniques of M. C. Escher.

Everyone knows about Escher’s beautiful tilings based on the hyperbolic plane, Angels and Devils being one of the most famous. But he preceded this work with highly original investigations into repeating patterns in the more familiar Euclidean plane. In this column we show how Mathematica can be used to automate the generation of such patterns.

This material will be covered in two forthcoming Mathematica projects: [Wagon  (in press #1)] and [Wagon  (in press #2)].