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)),...,x_n=fⁿ(x₀),...

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.