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Fractional Gaussian noises are a family of random processes such that the interdependence between values of the process at instants of time very distant from each other is small but nonnegligible. It has been shown by mathematical analysis that such interdependence has precisely the intensity required for a good mathematical model of long run hydrological and geophysical records. This analysis will now be illustrated, extended, and made practically usable, with the help of computer simulations. In this Part, we shall stress the shape of the sample functions and the relations between past and future averages.