### Explanation of the Applet Period Doubling

It is a well known fact that the scalar logistic map f(x)=a*x*(1-x)
undergoes a period doubling bifurcation if parameter **a** crosses a0=3.
After having started the applet, a visualization of the fixed point
iteration is shown which is called "Spinnwebeniteration" with
**nIt** iterations, initiated in **(x,x)**.

[xMin,xMax] x [yMin,yMax] represents the window in the (x,y)-plane. It
can be interactively changed.

The user can either change the parameter **a** directly in the
textfield or by using the scrollbar. A click on the button **draw
again** initiates an iteration. A repeated click on the button
**PD-scenario** gnerates different parameters **a** before and after
the period doubling bifurcation at a0=3. Alternatively, you may also
use the scrollbar.

In any situation one can choose the starting point x just by a
mouse click in the plane immediately followed by a simulation.

Additionally the fixed point and the slope of the function at
this point are shown. For **a<3** the fixed point is attractive due to
the contraction of f nearby. But for **a>3** f is expansive, the
fixed point is repulsive, and a period 2 orbit is borne.

The user may try to coose **a=3.9** with chaotic behavior. Can you
find **a** such that 3-periodic orbits show up?