where f x,n is an attractor
For an infinite recurrent parabola
y = ax (1-x) we can compute the possible function values, as function of the parameter a.
The resulting pattern is a bifurcation 1),
a forklike ramification. The shown bifurcation belongs to the above mentioned parabola.
For other polynomials sometimes symmetry around the x-axis be reached.
The generalization for the bifurcation to the complex numbers is the Mandelbrot set.
1) furca (Lat.) = fork, bis (Lat.) = twice