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		2.1.3— A Simple Equation Can Produce Complicated Output

		The phenomenon of chaos is surprising.

		Let's follow the deterministic equation, step by step, to see how it produces a set of data that looks random:

		The first value of x at n=1 was chosen to be x(1) = .892.

		The value x(n+l) at the (n+l)-th step is computed from the previous value x(n) at the n-th step by using the equation that x(n+1) = 3.95 x(n) [1 - x(n)].

		Thus, to compute the next value of x at n=2, multiply 3.95 by .892 and then multiply that result by (1-.892). This yields x(2) = .380.

		To compute the next value of x at n=3, multiply 3.95 by .380 and then multiply that result by (1-.380). This yields x(3) = .931.

		Continue the same process.

		This deterministic mechanism alone produces a seemingly random sequence of values x(n). That is why the discoverers of this phenomenon called it chaos.

 

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