Absolutely Unpredictable Chaotic Sequences

We study chaotic functions that are exact solutions to nonlinear maps. A generalization of these functions cannot be expressed as a map of type Xn+1 = g(Xn, Xn-1, …, Xn-r+1). The generalized functions can produce truly random sequences. Even if the initial conditions are known exactly, the next values are in principle unpredictable from the previous values. Although the generating law for these random sequences exists, this law cannot be learned from observations.

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