This applet shows the iterates of x₀ versus time for the Logistic map f(x) = x (1 - x).

Initially x₀ = 0.5 and = 2. If you move the horizontal slider, changes, and its value is shown in the function description on top. You can change x₀ by dragging the blue dot on the vertical axis. The number of iterates shown is given in the upper right corner. Initially this is set to 100, and you can change it by typing.