A bifurcation diagram for the Hénon map for b=0.3. The horizontal axis is the <i>a</i> parameter, the vertical axis is the <i>x</i> variable, the <i>b</i> parameter is fixed at 0.3. The image was created by forming a 1000 x 1000 array representing increments of 0.001 in <i>a</i> and <i>x</i>. A starting value of <i>x</i>=<i>y</i>=0.25 was used, and the map was iterated 1000 times in order to stabilize the values of <i>x</i>. 100,000 <i>x</i> -values were then calculated for each value of a and for each <i>x</i> value, the corresponding <i>(x,a)</i> pixel in the image was incremented by one. All values in a column (corresponding to a particular value of <i>a</i>) were then multiplied by the number of non-zero pixels in that column, in order to even out the intensities. Finally, values above  were set to 300,000, and then the entire image was normalized to 0-255.
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13 September 2005 (original upload date)
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