| | | | | | 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. | | | | |