A long time ago I came across a chaotic sequence of the form
x[n+1] = f(x[n], y[n])
y[n+1] = g(x[n], y[n])
If I remember correctly, f and g are simple polynomials of maximum order 3, but I am not sure if they also included other functions. The functions also had a number of parameters that could be varied.
Plotting the points (x[n],y[n]) produces intersting patterns that grow around a center point, often creating flower-like shapes. The shapes have no exact symmetry but typically an odd number of similar regions that are rotated around the center point, but in a distorted way.
I am not sure where I originally found a description of that system but it could have been a very old Scientific American article probably from the late 1980s.
Not much information, I know, but hopefully sufficient for someone who knows that system.