File:Cml2e.gif

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Cml2e.gif (463 × 344 pixels, file size: 1.15 MB, MIME type: image/gif, looped, 41 frames)

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Description	The animated gif demonstrates chaotic behavior in an uncoupled 2 dimensional lattice. Each site is updated by the logistic map $x_{n+1}=rx_{n}(1-x_{n})$ . The range of the logistic map (randomly seeded between 0.1 and 0.5) is bounded from 0 to 1. The resulting animated contour map smooths the distinction between the sites with respect to the value they hold. Each frame is taken at an iterative time step where the parameter r is increased $r=3.5,3.51,...,3.9$ . Notably not until $3.58$ does the map truly demonstrate chaotic behavior.
Source	Own work
Date	21 May 2009
Author	Travdog8 (talk) (Uploads)
Permission (Reusing this file)	See below.

Summary

The animated gif demonstrates chaotic behavior in an uncoupled 2 dimensional lattice. Each site is updated by the logistic map $x_{n+1}=rx_{n}(1-x_{n})$ . The range of the logistic map (randomly seeded between 0.1 and 0.5) is bounded from 0 to 1. The resulting animated contour map smooths the distinction between the sites with respect to the value they hold.

Each frame is taken at an iterative time step where the parameter r is increased $r=3.5,3.51,...,3.9$ . Notably not until $3.58$ does the map truly demonstrate chaotic behavior.