One Dimensional Maps - Demo 1

Iterating the Map

The basic scheme of iterating one-dimensional maps is shown by the applet. Hitting "Step" will perform one iteration of the map.

From the initial value x0 of x the value of y=F(x0) (a vertical "step" on the plot) gives the value of the next iterate. The horizontal "tread" on the plot graphically changes this y to an x value i.e. gives x1. Successive iterations are then given by repeating the "step-tread" sequence.

For a=2.8 repeatedly hitting step will eventually lead to x converging onto a value that no longer changes under iteration. Such a point is known as a fixed point. Any fixed point is located at the intersection of F(x) with the diagonal line. After stepping the iteration a few times, you can watch how the iterations behave by by hitting Start to start a running iteration. (Set the Speed to a convenient value.) To study the behavior for different initial conditions click somewhere in the plot while the iterations are running to start a new iteration with initial condition given by the value of x at the mouse position.

[Demos Introduction] [Next Demonstration] [Introduction]
Last modified Sunday, November 28, 1999
Michael Cross