WOLFRAM|DEMONSTRATIONS PROJECT

Butterfly Curve and Variations

​
u
10
a
4
The butterfly curve (
a=4
) is a transcendental plane curve discovered by Temple H. Fay. The parametric equations are
x=cos(θ)-2cos(aθ)-
5
sin
θ
12
+
cos(θ)
e
,
y=sin(θ)-2cos(aθ)-
5
sin
θ
12
+
cos(θ)
e
.