19.

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		2.1.2— The Difference between Randomness and Chaos

		The pattern of x(n) in both data sets appears to have been generated by a random mechanism. However, not everything that looks random really is random.

		One of these data sets was generated by a random mechanism. However, the other data set was not generated by a random mechanism at all. It was generated by a deterministic mechanism.

		1— Left: Data Set #1 Was Generated by a Random Mechanism

		This data set was generated by a random mechanism. Each new value of the data x(n) was chosen at random.

		2— Right: Data Set #2 Was Generated by a Non-Random, Deterministic Mechanism

		This data set was generated by a deterministic mechanism. Deterministic means that the next value of the data was computed from the previous values.

		The next value of x(n+l) was computed from the previous value x(n) by using the simple rule that x(n+1) = 3.95 x(n) [1-x(n)].

		The phenomenon that a deterministic mechanism can generate data that looks as if it were generated by a random mechanism is called ''chaos."

		The word chaos was chosen to describe the complex output of these deterministic mechanisms. Chaos is a poor choice of a word for this phenomenon because here it means just the opposite of its common usage of "disordered." Here, chaos means that the output of a deterministic system is so complex that it mimics the output generated by a random mechanism. It does NOT mean that a system is driven by disorder, randomness, or chance.

 

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