Symmetry and Art

Abstract

We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can have rotational, translational, or mirror symmetry according to our chosen mapping functions. An appealing feature of these designs is how they reveal important properties of Euclidean and non-Euclidean geometries. We can also generate animations of our designs. Our goal is to create designs and animations having significant artistic content.