Cobweb of the logistic map
Explore chaos in the logistic map (cf. http://en.wikipedia.org/wiki/Logistic_map) using the sliders below. x represents the population relative to its maximum value. Vary r to explore different models. Vary the initial x value (red dot) to see what the stable populations (x values) are. Vary N to see how the cobweb is constructed. For instance, start at N=1 and work up slowly to see what the simulation is doing.
What values of r are interesting? Can you find the bifurcation points (r-values at which the number of stable populations doubles)? Use http://en.wikipedia.org/wiki/File:Logistic_Bifurcation_map_High_Resolution.png to help you.