C.a.R. > Applications > Functions > Feigenbaum Interation

This is the famous Feigenbaum iteration. The function is f(x)=a*x*(1-x), and the start point of the iteration x(n+1)=f(x(nn) can be set with the mouse. The parameter a can be changed with a slider. For large a the behavior is chaotic. Otherwise there finitely many fixed points the iterations cycles through.

Technical Information

The iteration is performed with a macro, of course. Do not make the mistake to evaluate the function by intersecting a line and the graph. This is much slower.