Friday, November 1, 2013

Chaos Lurks in the Equation y = Rx(1 – x)

   The image shown above is often used to illustrate what deterministic chaos  looks like. The image is the iterated map of the equation y = Rx(1­ – x) with x =0.1 as the seed and R-settings from R = 2.95 to R = 3.95.
   I have uploaded a Scratch project, Chaos Lurks in y=Rx(1–x), to the Scratch website.
The image above has the value of R decreasing from the top down. This is the popular orientation of the image. In my Scratch project, I used the normal convention of R increasing up the y-axis.

   You can view and interact with this project by clicking on this link.
   The Notes and Credits section of the project gives you R settings for computing an approximation of Feigenbaum’s constant.
   A discussion of Feigenbaim’s constant can be viewed at the Sixty Symbols web site.
   If you would like a three-part tutorial in PDF format on the origin of Feigenbaum’s constant just send an email request to http://www.grandadscience.com.


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