This DOS based program was written by Will Frangos, Dept. of Geology and Envir. Science, James Madison University. This program is copyrighted, but may be downloaded and used by anyone for personal or education purposes as long as the source is acknowledged. Commercial distribution of the program is prohibited.
The X-next program allows us to calculate the output for any value of r, but does not allow us to easily compare the output among r values. This program generates a data file of r values that is then loaded into a graphing program to generate a bifurcation diagram (see below). We use Grapher for this, but any good graphing program will work. What does not work well are spread sheet graphing programs like Excel or QuattroPro.
An advantage of generating bifurcation diagrams this way is that there is great flexibility in the data to be graphed. We have zoomed in on parts of the bifurcation diagram to see the 8th bifurcation. It is possible to go even deeper. For example, see these two pdf files.
BifWindowZoom is a series of three zooms moving deeper and deeper into the bifurcation diagram. There is distortion at each zoom because the length-width axes are not the same each time. Notice the self-similarity; each zoom resembles the last, even though magnification increases. Also, there is always more detail. This zooming can go on indefinitely.
BifZoomZoom zooms in on one of the bifurcations, looking deeper and deeper for the 2nd, 3rd, 4th, 5th, 6th, etc. bifurcations.
Experiment With and Explore XnextBIF - a laboratory guide used in the course; it will help someone run the data generating program, and then graph the data.
