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Automated iteration of x = f(x) For the convenience of readers, the graphical iteration procedures of figure 2 have been coded into Prog#9, which also tabulates the result of successive iterations as in table 2. To run Prog#9, you need to only specify r as the required input. It sets the initial population at x0 = 0.3 and automatically figures out a maximum number of iterations required for the input value of r. However, you can override the default initial population and maximum iteration number. The Prog#9 reports up to 160 successive iterates. Should there be more than 160 iterates, it presents the first 32 and last 80 iterates to fit in one screen frame. It then displays the graphical iteration plot of figure 2 carried out to the maximum iteration limit. As expected under r = 2 and x0 = 0.3, Prog#9 actually reproduces the successive iterates of table 2 and graphical iteration plot of figure 2, both of which indicate the stable population of x = 0.5. Here, by stable we mean that the final state x = 0.5 is obtained from any initial x0, except x0 = 0 and 1. To check this out, you can fill in the last column entries of table 3 by Prog#9. Table 3. Input data set for r = 2
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