ABSTRACT
In this chapter the authors make a series of observations based on computer images. They deal with the orbit diagram. This image is one of the most instructive and intricate images in all of dynamical systems. The orbit diagram is an attempt to capture the dynamics of Qc for many different c-values in one picture. In the orbit diagram the authors plot the parameter c on the horizontal axis versus the asymptotic orbit of 0 under Qc on the vertical axis. They gave a geometric reason for seeing an initial sequence of period doublings in the orbit diagram. At each stage of the process, the authors consider the second iterate of the map at the previous stage and then zoom in on a small subinterval on which the map resembles a quadratic function.
