Complex Polynomial Mandalas and their Symmetries

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Konstantin Poelke, Zoi Tokoutsi and Konrad Polthier: Complex Polynomial Mandalas and their Symmetries. In: Bridges 2014. Pages 433–436



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.

Extended Abstract


Used References

[1] Z. Nehari. Conformal Mapping. Dover Books on Mathematics. Dover Publications, 1975.

[2] H.A. Schwarz. Ueber einige Abbildungsaufgaben. Journal für die reine und angewandte Mathematik, 70:105–120, 1869.


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