butterfly curve

An animation based on the butterfly curve: video.

The area of the algebraic butterfly curve is given by (with gamma function )

The butterfly curve has a single singularity with delta invariant three, which means it is a curve of genus seven.

Butterfly curve may refer to:

Butterfly curve (transcendental)

The butterfly curve is a transcendental plane curve discovered by Temple H. Fey.

The butterfly curve has branching number and multiplicity two, and hence the singularity link has two components, pictured at right.

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.