Orbit Diagram of the Logistic Map

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Plot the points , where
and the
are the iterates of the quadratic map
. Each
leads to a distinct orbit; for example, for
, the orbit is 0, -1.5, 0.75, -0.9375, …. For constant λ, the set of
is infinite, but in this picture only a finite sample is shown. The whole plot is called the orbit diagram for the map. The set of points on the right that looks like a curve consists of stable points. In the middle the points orbit between two values. Both of these cases are examples of attractors.
Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA
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"Orbit Diagram of the Logistic Map"
http://demonstrations.wolfram.com/OrbitDiagramOfTheLogisticMap/
Wolfram Demonstrations Project
Published: March 7 2011