The chaotic, but nondeterministic, structure of the ionosphere and radio wave amplitude and phase scintillation measured on the ground have been simulated using the phase screen model with the power law spectrum of random Gaussian phase fluctuations. Comparison of the information dimension calculated for phase fluctuations on a screen with that for amplitude scintillation at the receiver shows that the original chaotic structure in the ionosphere is completely masked by the propagation effects. Hence the ionospheric turbulence attractor (if it exists) cannot be reconstructed from amplitude scintillation data. On the other hand, measured phase scintillation data adequately reproduce the assumed chaotic structure in the ionosphere. Results of the attractor reconstruction for amplitude scintillation observed at high latitudes show an excellent agreement with our simulation.