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 transcendental curve is given by the parametric equations:

The butterfly curve.
The butterfly curve.
x = \sin t \left [ e^{\cos t} - 2\cos 4t - \sin^5 {t \over 12} \right ]
y = \cos t \left [ e^{\cos t} - 2\cos 4t - \sin^5 {t \over 12} \right ]

or by the following polar equation:

r=e^{\sin \theta} - 2 \cos (4 \theta ) + \sin^5 {{1 \over 24} (2 \theta - \pi)}

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