Click the Action button to plot iterations 1000-1255. There should be a white box outlining an area of interest after plotting. If you do not see it, just move the mouse a bit. I suspect this is a manifestation of a mismatch between the Java language version in which the applet was written and the Java machine installed on your computer. We are hoping to resolve this with the next revision to the web site.
Clearly the nature of a chaotic attractor is fundamentally different than where the attractor is single valued or periodic. We may think of the different attractor regions as having different degrees of tolerance for aberrant behavior on the part of the function. Where it is single valued, the attractor is not content until it has drawn the function to that one value. Where the attractor is periodic the function may settle sequentially on two or more values. Where it is chaotic, the function may take any of a large number of values as long as it stays in bounds.