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This applet demonstrates graphical iteration. In this example, we use
the quadratic iterator xn+1 = fa(xn) , fa(x) = ax(1-x), 0<=a<=4 and iterate for twenty steps. Try different values of x0 and a. Enter a value for x0 (between 0 and 1) in the left box, a value for a (between 0 and 4) in the right box, then hit the "Go" button. Note that some values will produce a stable state and others result in instability. See Peitgen, Jürgens, and Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, New York, 1992, for more information. |
For questions or comments, contact Mark Scheuern