Complex Polynomial Mandalas and their Symmetries

Konstantin Poelke, Zoi Tokoutsi and Konrad Polthier
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014)
Pages 433–436 Short Papers


We present an application of the classical Schwarz reflection principle to create complex mandalas—symmetric shapes resulting from the transformation of simple curves by complex polynomials—and give various illustrations of how their symmetry relates to the polynomials' set of zeros. Finally we use the winding numbers inside the segments enclosed by the transformed curves to obtain fully coloured patterns in the spirit of many mandalas found in real-life.