Applet: Robert May bifurcation movie

Here is an animation to illustrate the bifurcation in a slightly different way.

Here, the successive values of x in the iterative calculation of

are plotted on a 120-point-per-turn radial graph, to show the successive points more clearly. This is animated over r, for values of r between 2.5 and 4.

The animation oscillates back and forth between 2.5 and 4, just for fun.