Butterfly curve (transcendental)

The butterfly curve.

The butterfly curve is a transcendental plane curve discovered by Temple H. Fay. The curve is given by the following parametric equations:

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

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

or by the following polar equation:

$r=e^{\sin \theta} - 2 \cos (4 \theta ) + \sin^5\left(\frac{2 \theta - \pi}{24}\right)$

See also

• Butterfly curve (algebraic)

References

• Fay, Temple H. (May 1989). "The Butterfly Curve". Amer. Math. Monthly 96 (5): 442–443. doi:10.2307/2325155. JSTOR 2325155.
• Weisstein, Eric W., "Butterfly Curve", MathWorld.

External links

• An animation based on the butterfly curve: video. The script to reproduce it with gnuplot : script