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:
- <math>x = \sin t \left [ e^{\cos t} - 2\cos 4t - \sin^5 {t \over 12} \right ]</math>
- <math>y = \cos t \left [ e^{\cos t} - 2\cos 4t - \sin^5 {t \over 12} \right ]</math>
or by the following polar equation:
- <math>\rho=e^{\sin \theta} - 2 \cos (4 \theta ) + \sin^5 {{1 \over 24} (2 \theta - \pi)}</math>
[edit] References
- Fay, Temple H. (May 1989). "The Butterfly Curve". Amer. Math. Monthly 96 (5): 442–443.
[edit] External links
- Butterfly Curve from MathWorld
- An animation based on the butterfly curve: video. The script to reproduce it with gnuplot: script
