Discrete Dynamical Systems

Given a function f, define fn to be the composition of f with itself n times: f°f°f°...°f.

The orbit of a point x0 is the sequence x0, x1=f(x0), x2=f(f(x0)),...,xn=fn(x0),...

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

The preset function in the applet is f(x)=4x(1-x). You may want to try other functions such as:
f(x)=kx(1-x) (for different positive values of k)
f(x)=x2-k (for different nonnegative values of k)
f(x)=sin(x)

Enter a new function in the input box by typing, for instance, f(x)=2*x^2-2.

Note: you can double-click on the applet to open it in a new window.

Created by Dave Richeson using GeoGebra.