Movie of the graphs of the second and forth iterates of the logistic maps with the renormalisation windows
The movie shows the second and fourth iterates of the map μx(1-x) with μ varying from 2.8 to 3.7. Observe that the second iterate restricted to the bigger red window is conjugate to the first iterate of μx(1-x) for a different value of μ. In turn, the fourth iterate restricted to the smaller red window is conjugate to the first and second iterates of μx(1-x) for different parameter values.