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 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.