Iterating Rational Functions

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

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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.

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Contributed by: Philip Lee (April 2009)
Open content licensed under CC BY-NC-SA


Snapshots


Details

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.



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