Butterfly curve (algebraic)

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x 6 + y 6 = x 2

The butterfly curve singularity link

In mathematics, the algebraic butterfly curve is a plane algebraic curve of degree six, given by the equation : $x 6 + y 6 = x 2 .$ Another curve, this one a transcendental curve, is also called a butterfly curve. The butterfly curve has a single singularity with delta invariant three, which means it is a curve of genus seven. The only plane curves of genus seven are singular, since seven is not a triangular number, and the minimum degree for such a curve is six, so the butterfly curve aside from its appearance is possibly interesting as an example.