Gielis's Superformula for Complex Shapes

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The superformula proposed by Gielis [1], a generalization of Piet Hein's superellipse, can be used to describe a wide range of forms, many of which are similar to natural structures.

Contributed by: Ernesto Iglesias-Rodríguez, José Alejandro Mesejo-Chiong and Julián Bravo-Castillero (April 2020)
Open content licensed under CC BY-NC-SA



In polar coordinates, the superformula can be represented by



[1] J. Gielis, "A Generic Geometric Transformation That Unifies a Wide Range of Natural and Abstract Shapes," American Journal of Botany, 90(3), 2003 pp. 333—338. doi:10.3732/ajb.90.3.333.

[2] Wikipedia. "Superformula." (Apr 28, 2020)

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