Henon bifurcation diagram with <i>b</i> = 0.3.  The image was created using Mathematica by determining the value of <i>a</i> for each pixel (i.e., the width in <i>a</i> space for each pixel).  This width was subdivided into 7 parts where each of the seven parts corresponded to the same pixel column but had slightly different values for <i>a</i>.  For <i>x</i> the starting value depended on which of the 7 values for <i>a</i> was used in that pixel column.  The <i>x</i> range (-1.5 to 1.5) was divided into 7 equidistant values,  For each value of <i>x</i>, 7 distinct values for <i>y</i> were selected to obtain a broad range of starting values.  The process of subdividing each pixel column into 7 parts was repeated for each pixel column in the map (2400 times).  After throwing away the first 2000 iterations, the next 1,000,000 were used to create the plot.  Each time a value fell into an [<i>x</i>,<i>a</i>] pixel, that pixel was incremented by 1.  The max value allowed for each pixel was 350,000.  After each pixel column was calculated, the column was divided by the maximum value in that column (could be less than 350,000) to get a scale from 0 to 1.  Axis were then added to the final map.  Altogether 112,000,000,000 iterations were used to generate this map.  Calculation time was approximately 2.5 hours.
<a href="//commons.wikimedia.org/wiki/User:Efecretion" title="User:Efecretion">Jordan Pierce</a>
2011-09-09
<span class="int-own-work" lang="en">Own work</span>  Created with Mathematica