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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:
![x_{n+1}=rx_n(1-x_n)\,](../../images/125/12597.png)
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.
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Date |
14 September 2005 |
Source |
Own work |
Author |
PAR |
Licensing
Public domainPublic domainfalsefalse |
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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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File usage
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