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This image was selected as picture of the month on the Mathematics Portal for December 2011 
Summary
Description 
English: A bifurcation diagram for the Logistic map:
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 nonzero 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 0255. Finally, pixels for values of r below 3.57 were darkened to increase visibility.

Date 
14 September 2005 
Source 
Own work 
Author 
PAR 
Licensing
Public domainPublic domainfalsefalse 

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.Public domainPublic domainfalsefalse

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