Butterfly curve

The parametric equations of the butterfly curve can be given by 

$x=\sin t(e^{\cos t}-2\cos 4t-si{n}^5{\displaystyle \frac{t}{12}})$ 

$y=\cos t(e^{\cos t}-2\cos 4t-si{n}^5{\displaystyle \frac{t}{12}})$ 

 In polar coordinates the equation of a butterfly curve is given by 

$r=e^{\sin \theta }-2\cos \left(4\theta \right)+{\sin }^5\left[{\displaystyle \frac{1}{24}}(2\theta -\pi )\right].$

Source: en1gm4th5