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.


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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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Related Curriculum Standards

US Common Core State Standards, Mathematics