The following image is a Pickover inspired strange attractor.
x_{n+1} = sin(y_{n}*b) + c*sin(x_{n}*b)
y_{n+1} = sin(x_{n}*a) + d*sin(y_{n}*a)
x_{n+2} = sin(y_{n+1}*b) + c*sin(x_{n+1}*b)*(-1) y_{n+2} = sin(x_{n+1}*a) + d*sin(y_{n+1}*a)

As you can see, two symmetrical overlapping attractors are produced.
I'll try to modify the code to make this more interactive. Source
code for this image. A lot of points (a,b,c,d) provide degenerate
images. I haven't figured out why, yet. Perhaps someone will
tell me. Would you like to see more items like this? Send
opinions.