## Discrete Dynamical Systems
Given a function f, define f^{n} to be the composition of f with itself n times: f_{°}f_{°}f_{°}..._{°}f.
The *orbit* of a point x_{0} is the sequence x_{0}, x_{1}=f(x_{0}), x_{2}=f(f(x_{0})),...,x_{n}=f^{n}(x_{0}),...
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)=x^{2}-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. |