Henon

The Henon map displays chaotic behavior. You can learn more about it here.

The following formulas are iterated, and the orbit generated is plotted in the xy plane:
x_n+1=1-ax_n²+y_n
y_n+1=bx_n

To obtain the rich and complex behavior shown in this animation, parameter b is held steady at -0.9998, and parameter a varies incrementally between -0.6 and 0.9.

Note that this display looks very different from the Henon Map that most people are familiar with, which is frequently based on parameter a = 1.4 and b = 0.3, making it appear assymetric and less complex.