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\left({t \over 12}\right)\right)
y = \cos(t) \left(e^{\cos(t)} - 2\cos(4t) - \sin^5\left({t \over 12}\right)\right)

or by the following polar equation:

r=e^{\sin \theta} - 2 \cos (4 \theta ) + \sin^5\left(\frac{2 \theta - \pi}{24}\right)
An animated construction gives an idea of the complexity of the curve (click for larger image).
An animated construction gives an idea of the complexity of the curve (click for larger image).

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