  High-temperature superconductor $Bi_{2}Sr_{2}CaCu_{2}O_{8}+x$ has been
investigated by the high-resolution electron microscope (HREM) and the
photodensitometric technique in order to resolve the sub-atomic shifts in the
modulated structure. This investigation has shown that the background noise is
pronounced, indicating some kind of ordering in certain crystallographic
directions. We have found that the "mapping" of the charge densities by the
inverse Fourier transform of the diffracted electron image and the connections
to the crystal structure can be easily established in the case of elastically,
as well as the inelastically scattered electrons. The order of the details in
so obtained "inelastic" electron "micrographs", as well as the dependence of
the structure of the EM image on the initial conditions of the inverse Fourier
transform, leads to the conclusion that there is an order emerging from the
diffuse scattered electron diffraction patterns. Data sets from digitalized
densitograms are analysed by the Rescaled range (R/S) method in order to study
fractal and long-range correlation properties of the inelastic scattered
electrons in the "noise" region between Bragg reflections. The results of the
R/S analysis showed that the value of the Hurst exponent was H$\neq$ 0.5,
indicating that the "ordering" of the noise in the Inverse (Fourier) space was
much more pronounced at longer distances (about 440 atom spacings), then for
shorter distances of about 55 atom spacings.

Chaotic Dynamics