Superformula
Equation in polar coordinates / From Wikipedia, the free encyclopedia
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This article is about a generalization of the superellipse. For the Japanese formula racing series, see Super Formula Championship.
The superformula is a generalization of the superellipse and was proposed by Johan Gielis around 2000.[1] Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature. Gielis has filed a patent application related to the synthesis of patterns generated by the superformula, which expired effective 2020-05-10.[2]
In polar coordinates, with the radius and the angle, the superformula is:
By choosing different values for the parameters and different shapes can be generated.
The formula was obtained by generalizing the superellipse, named and popularized by Piet Hein, a Danish mathematician.