Simone

The Simone Attractor is named for physicist Simone Conradi. It displays chaotic behavior. You can learn more about him and some of his art and formulas here.
To obtain the behavior shown, parameter b is held steady at 1.0, and parameter a varies incrementally between 3.0 and 6.0 as the following formulas are iterated and the resulting values (orbit) plotted:
x_n+1=sin(x_n²- y_n²+a)
y_n+1=cos(2xy+b)