Symmetry and Art
Metric Geometry
2020-08-27 v1 Complex Variables
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.
Cite
@article{arxiv.2008.11311,
title = {Symmetry and Art},
author = {Emily J. Gullerud and James S. Walker},
journal= {arXiv preprint arXiv:2008.11311},
year = {2020}
}
Comments
This paper is accepted for publication in the proposed Handbook of Complex Analysis, edited by Steven G.~Krantz