Butterfly curve

The parametric equations of the butterfly curve can be given by 

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

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

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

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

Source: en1gm4th5