Butterfly curve (transcendental)

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An animated construction gives an idea of the complexity of the curve (Click for enlarged version).
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:

or by the following polar equation:

See also[edit]


  • 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.