  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.
