Function of a FunctionFunction of a function of a ...
When iterating the recursive equation you apply the function on the function on the ...
At a fixpoint all the functions of a function of a ... intersect.
You can apply the same function on itself over and over again in GeoGebra by using the spread sheet.
Enter the function in terms of x into A1. The cell
A1 becomes the function A1(x).
Now enter the function in terms of A1(x) into the cell A2.
Click on the blue rectangle in the lower right corner of A2 and drag down in
order to do a relative copy.
Exercise
Enter a slider a into GeoGebra. Draw graphs of a function of a
function of a function...using sin(ax). Do not copy more than 6 or
7 functions (otherwise it will lag too much).
Note that for some values of a there are points of intersection that are not fixpoints. It is hence possible to have points of attraction to a recursive equation that are not fixpoints. Such points can give rise to chaos.
