We present a simple statistical model that has no fractal nature, but certain set of measurements of such model might lead to the conclusion, that it is a fratal. We regard plain model and show how usual fractal dimension D of measured trajectory might take any value 1<EQD<EQ2. We regard the system which statistical behavior is described by a set of Hamiltonians (by two Hamiltonians in the simplest case). Similar multi-Hamiltonian models are known, for example. If one uses the simplest assumption on probability P of realization for different Hamiltonians, for example PequalsN-(alpha ) where N is a number of measurements during fixed time interval T, then it can be shown, that the measured trajectory might be treated as a fractal with dimensions Dequals2-(alpha ), 0<EQ(alpha) <EQ1 Dequals1, (alpha) >1. Such results permit us to suggest multi-Hamiltonians models to describe the effects of random media (rain, clouds and turbulence) in the Wave Propagation problems.