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Iterating Rational Functions

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.

Contributed by: Philip Lee

Show Initialization Code

(23 lines omitted)

This Demonstration was inspired by part of the Open University course MS221.

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.

Fixed Point (Wolfram MathWorld)

"Iterating Rational Functions" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/IteratingRationalFunctions/

Contributed by: Philip Lee

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