You see iterations of f oN(x) = f(f(...f(x)))
for N = 2 below
Controls: Click mouse to zoom in 2 times. Click mouse with Ctrl to zoom out. Hold Shift key to zoom in the R (vertical) direction only. Max number of iterations = 4000. See coordinates of the image center and Δx, ΔR in the text field. The vertical line goes through x = 1/2 (see Bifurcation diagram for quadratic maps for more detailes).
Chaotic region zoom of the map
You can test that the map is chaotic for R < 0 too.
I made this page for Wiki users as since I can't put Java applets here yet.
By a linear substitution the logistic map is reduced to the quadratic map xn+1 = xn2 + c (see Iterations of quadratic maps).