# Bifurcation Diagrams

 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 Start with µ = 0, x = 0.5. Calculate the first 30 iterates of . Plot the value of for iterates 31 through 120. Increment µ a little, reset x = 0.5. If µ <= 4, go to step 2, else exit. 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). Next: Follow the "As µ Increases" link.