The butterfly curve is a transcendental plane curve discovered by Temple H. Fay of University of Southern Mississippi in 1989.
For , the curve is given by the following parametric equations:
or by the following polar equation:
The term has been added for purely aesthetic reasons, to make the butterfly appear fuller and more pleasing to the eye.
In 2006, two mathematicians using Mathematica analyzed the function and found variants where leaves, flowers, or other insects became apparent. New developments regarding such curves are still under research by mathematicians.