Complex Symmetries in Repeating Hyperbolic Patterns

Abstract

One often uses complex symmetry transformations in order to create art in the hyperbolic plane, producing repeating patterns with corresponding complex symmetries. We explore such transformations for a specific pattern, but these transformations are characteristic of many hyperbolic patterns, including those of M.C. Escher. We also explore the use of color symmetry in creating these patterns, which adds another degree of complexity to the transformations.