You see iterations of *f ^{ oN}(x) = f(f(...f(x)))*
for

*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.

*Comments*:

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
*x _{n+1} = x_{n}^{2} + c*
(see Iterations of quadratic maps).

M-set anatomy