28U we hnd & llly gub bin then stage and a quadratic function. At the nth stage,

Question

28U we hnd & llly gub bin then stage and a quadratic function. At the nth stage, 0" resembles the original function. In particular, as c dw of the 0a" make the transition from a saddle-node bifurcati is a period-doubling bifurcation viewed from one si doubling, and on into the chaotic regime. This accounts for the fta Perid orbit diagram features regions that are apparently self-similar. on which the graph (actually, this side), through a perio th 8.3 Experiment: Windows in the Orbit Diagram Goal: The goal of this experiment is twofold. The first object is for see the remarkable structures and patterns that occur in the orbit di to The second aim is to investigate the similarities and differences between t typical orbit diagrams, for the quadratic function Qc(z) = z'te logistic function FA(z)-Ar(1 -z). Recall that a period k window +c and the in orbit diagram consists of an interval of parameter values for which we fnd of its period-doubling an initial attracting period k cycle together with all "descendants." For example, in the big picture of the quadratic family's orbit diagram, we clearly see a period 1 window and a period 3 windosw. Remember, "period" here means the period of the attracting orbit before it begins to period double. See Figure 8.10 Procedure: The object of this experiment is to catalog a number of smaller windows in the orbit diagrams of both Qe()2+c and F()Az(1-) Clearly, the period-1 and -3 windows are the most visible for each of the two families. Now magnify the region between these two windows for the quadratic family. What do you see? The two largest windows are clearly of period 5 and 6. This is the "second generation" of windows. There are other smaller windows visible, but we record only the two widest windows at this time. We will record this as follows: Quadratic function: Generation 1: 3 Generation 2: 3 Note that we put these windows in the right order. Now go next generation. Find the periods of the two "largest" windows to the between the

Explanation / Answer

The darker curves represent the diffraction pattern. Fraunhofer diffraction by a rectangular aperture provides information about the absolute value of the TC but none about its sign. However, for large values of the TC, it becomes difficult to define an appropriate intensity threshold in the diffraction pattern of a rectangular aperture that yields the absolute value.

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