Factor Group Transformations on Escher Patterns

Joshua Jacobs
Renaissance Banff: Mathematics, Music, Art, Culture (2005)
Pages 457–462


The artist M.C. Escher intuitively expressed many mathematical concepts in his graphic designs. One of these concepts was that of transformations between different factor groups over the complex plane. We describe a method whereby any tiling that can be expressed as a rectangle system can be mapped to a multiplicative factor group over the complex plane.