First, create an example of a bifurcation diagram by clicking the "Bifurcation" button
(to the left). Once the applet is loaded, click on the "Plot" button to make a
bifurcation diagram for
This will take a short while to calculate and display because the algorithm which produces the diagram requires many iterations of .
Bifurcation Diagram Algorithm
The idea is that after the first 30 iterates the values of are either fixed points or points on a periodic orbit. Note: this is not true when convergence to a fixed point or a periodic point is slow, such as for µ = 1 and µ = 3 -- observe the "smearing" around these values of µ.
Remark: it is good to use the critical point x = 0.5 as the iteration seed since it is
always attracted to an attracting periodic point. However, you get qualitatively the same diagram by starting
with any point in (0, 1).