Butterfly curve (transcendental)

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The butterfly curve is a transcendental plane curve discovered by Temple H. Fay. There is another curve called the butterfly which is an algebraic curve. The transcdendental curve is given by the parametric equations:

[x = \sin t \left [ e^ - 2cos 4t - sin^5 right ]]

[y = \cos t \left [ e^ - 2cos 4t - sin^5 right ]]

or by the following polar equation:

[\rho=e^ - 2 \cos (4 \theta ) + sin^5 (2 \theta - \pi)}]

References

External links

[Butterfly Curve from MathWorld]
An animation based on the butterfly curve: [video]. The script to reproduce it with gnuplot: [script]

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