COPYRIGHT 2008, PRINCETON UNIVERSITY PRESS

discrete & continuous nonlinear dynamics 2951Logistics Map Bifurcation Diagram0.80.6X*0.40.80.20.43.82 3.84 3.8601 2 3 3.5 4Figure 12.2 The bifurcation plot, attractor populations versus growth rate, for the logistic map.The inset shows some details of a three-cycle window.µ12.5.1 Bifurcation Diagram ImplementationThe last part of this problem is to reproduce Figure 12.2 at various levels of detail.(You can listen to a sonification of this diagram on the CD or use one of the appletthere to create your own sonification.) While the best way to make a visualization ofthis sort would be with visualization software that permits you to vary the intensityof each individual point on the screen, we simply plot individual points and havethe density in each region determined by the number of points plotted there. Whenthinking about plotting many individual points to draw a figure, it is importantto keep in mind that your screen resolution is ∼100 dots per inch and your laserprinter resolution may be 300 dots per inch. This means that if you plot a pointat each pixel, you will be plotting ∼3000 × 3000≃10 million elements. Beware: Thiscan require some time and may choke a printer. In any case, printing at a finerresolution is a waste of time.C D12.5.2 Visualization Algorithm: Binning1. Break up the range 1 ≤ µ ≤ 4 into 1000 steps and loop through them. Theseare the “bins” into which we will place the x ∗ values.2. In order not to miss any structures in your bifurcation diagram, loop througha range of initial x 0 values as well.3. Wait at least 200 generations for the transients to die out and then print thenext several hundred values of (µ, x ∗ ) to a file.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 295