Zooming in a Bifurcation Diagram

Notice that the attracting fixed points appear to fill out the area near = 4. However, if you zoom in on a portion of a bifurcation diagram (by clicking the "Zoom In" buttom, then clicking and dragging in the diagram), you'll see that this isn't the case. Periods of all orders can be found. For instance, you can find orbits of period 3 in the region 3.825 <= <= 3.86.

Again, recall what the bifurcation diagram is: it is a plot of all the points obtained by iterating F for a particular value of and discarding the first 30 iterations. So, if there are 3 points being plotted for a given value of , then for that value of , F has a period 3 point.

Try some zoom in's yourself in some regions that look interesting to you.

Next: Follow the "Diagram of x2 + " link.