Butterfly curve (transcendental) - Alchetron, the free social encyclopedia

The butterfly curve is a transcendental plane curve discovered by Temple H. Fay. The curve is given by the following parametric equations:

x = sin ⁡ ( t ) ( e cos ⁡ ( t ) − 2 cos ⁡ ( 4 t ) − sin 5 ⁡ ( t 12 ) ) y = cos ⁡ ( t ) ( e cos ⁡ ( t ) − 2 cos ⁡ ( 4 t ) − sin 5 ⁡ ( t 12 ) )

or by the following polar equation:

r = e sin ⁡ θ − 2 cos ⁡ ( 4 θ ) + sin 5 ⁡ ( 2 θ − π 24 )

References

(Text) CC BY-SA