The applet requires Java 1.4.1 or higher to run. It will not run on Windows 95 or Mac OS 8 or 9. Mac users must have OS X 10.2.6 or higher and use a browser that supports Java 1.4 applets (Safari works, IE does not). On other operating systems, you may obtain the latest Java plugin from Sun's Java site.

Suggestions: Click "setup" to begin. In fact, you MUST click "setup" first to avoid errors. Then, if you wish, adjust the sliders "R-min" and "R-max" to define the interval of the control parameter "R" that you want to explore (resp. 0 and 4 if you want the entire response diagram).

The "transient" slider determines how many iterations will be computed before beginning to draw. After "clipping the transient" in this way, the "attractor" slider determines how many more iterations to compute and actually plot (in red). The green locus shows the initial value for each computation, 0.5. The horizontal axis scale is from R-min to R-max. The vertical scale is from 0 to 1.

This applet has been created with NetLogo 2.1.0.

To view/download the model file: logisticresponse03.nlogo

Logistic Response by Ralph Abraham, www.visual-chaos.org.

This model is a gymnasium for studying the response diagram of the logistic family of
one-dimensional maps: X --> f(X, R) = RX(1-X), with X in [0, 1], and R fixed in [0. 4].

You select minimum and maximum values for the control parameter, R. Click the buttons
"setup" and "go", and then see the response diagram drawn in the Graphics Window.

Experiments are suggested in the companion web page: www.visual-chaos.org/lab.

NetLogo is a marvelous tool for experiments in chaotic dynamics, as many trajectories
may be calculated in parallel.