ABSTRACT
This chapter deals with the orbit diagram. This image is one of the most instructive and intricate images in all of dynamical systems. The orbit diagram appears to be self-similar: when certain portions of the picture are magnified, the resulting image bears a striking resemblance to the original figure. Of course, the words “striking resemblance” in this observation are not very precise in a mathematical sense. The curves connecting what appear to be periodic orbits are continuous as c varies—these curves never suddenly jump indicating the co-existence of another attracting cycle. That is, for each c-value, it appears that there is at most one attracting cycle. There is a large proportion of c-values for which the orbit of 0 does not seem to settle down on an attracting cycle.
