Interactive Logistic map

Iteration diagram

Iteration diagram for nonlinear logistic map   xk+1 = f(xk ) = R xk (1 - xk )

Controls: Drag the blue curve by mouse to change R value. Press <Enter> to set new parameters from the text fields.

You see iterations of   f oN(x) = f(f(...f(x))) for N = 2 below

Bifurcation diagram

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).

M-set anatomy
updated 18 Nov 2005