# LogisticMap BifurcationDiagram.png

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## Summary Edit

A bifurcation diagram for the Logistic map:

$x_{n+1}=rx_n(1-x_n)\,$

The horizontal axis is the r parameter, the vertical axis is the x variable. The image was created by forming a 1601 x 1001 array representing increments of 0.001 in r and x. A starting value of x=0.25 was used, and the map was iterated 1000 times in order to stabilize the values of x. 100,000 x -values were then calculated for each value of r and for each x value, the corresponding (x,r) pixel in the image was incremented by one. All values in a column (corresponding to a particular value of r) were then multiplied by the number of non-zero pixels in that column, in order to even out the intensities. Values above 250,000 were set to 250,000, and then the entire image was normalized to 0-255. Finally, pixels for values of r below 3.57 were darkened to increase visibility.

## Licensing Edit

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 This page uses content from the Wikimedia Commons. The original content was at File:LogisticMap BifurcationDiagram.png. The list of authors can be seen in the page history. As with this Psychology Wiki wiki, that portion of the content of Wikimedia Commons is available under the GNU Free Documentation License.

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## File history

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Date/Time Thumbnail Dimensions User Comment current 23:41, November 4, 2007 1,838 × 1,300 (229 KB) PhloxBot (Talk | contribs) == Summary == A bifurcation diagram for the Logistic map: :[itex]x_{n+1}=rx_n(1-x_n)\,[/itex] The horizontal axis is the ''r'' parameter, the vertical axis is the ''x'' variable. The image was created by forming a 1601 x 1001 array representing increme