Chapter 7.6, Problem 30MS

Periodic attraction (S). Again consider the transformation that takes any point x in the interval $[0,1]$ to $(1+\sqrt{5})x(1-x).$ As you saw in the previous Mindscape, the number 1t2 is a periodic point of period 2, meaning that it returns to itself after the process has been repeated twice. Compute 10 future values of the point 0.48 under repeated applications of this process. Do these points get closer to the repeated values of 112, or do they get farther away?