Prof.Chip Ross Bifurcation and Orbit Diagrams Superimposed

Bifurcation and Orbit Diagrams Superimposed
In the following two images, the bifurcation and orbit diagrams appear together on the same plot. Repelling eriodic points on the bifurcation diagram were colored in fuschia and blue, whereas yellow and orange show attracting points. The bifurcation diagram was plotted using thick dots. It shows points whose periods are from 1 to 6.

The orbit diagram was plotted in green. At attracting periodic points, it "agrees" with the bifurcation diagram. This agreement is seen as the thin green lines centered in the yellow and orange curves.

We've used our program's automatic period labeling feature to indicate the periods of the points on the bifurcation diagram. Labels are created when curves of periodic points cross the "gridlines". Curves are not labeled whenever a new label would partially cover one of the same number below it. Other curves are labeled more than they need to be.
Bifurcation and Orbit diagrams Superimposed

In the above image, things are pretty crowded in the lower left. Below is a zoom, with points of period 7 added. Adding points of period 8 again crowds the picture too much. Note you can't see a lot of attracting periodic points. There is a good sized interval of them at the 3 to 6 period doubling, lower right.
Bifurcation and Orbit diagrams Superimposed

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