This Demonstration allows you to explore the effect of iterating a selection of polynomial and rational functions, showing three types of fixed points, :

1. attracting: . Iterations of nearby values converge to attracting fixed points.

2. repelling:. Iterations of nearby values are repelled.

3. indifferent:. The iteration behavior is difficult to predict.

Experiment with different initial values and numbers of iterations. Some iterations settle down into -cycles that you can see by setting "iterations to display" to a smaller value than the number of iterations computed.