We present a study of the scanning electron microscopy images of the TiO2 nanotube array. The initial and modified samples were examined before and after annealing. It has been found that the annealing of the modified and unmodified samples results in different degrees of the local ordering. The nanotubular coverings were modified by Pt nanoparticles formed by the H2PtCl6 solutions infiltration for change of their electro- and photo catalytic properties estimated by measuring the photoelectric currents. The influence of the morphology and ordering degree of the nanotubular coverings on the manifestation of their functional properties has been studied. A two-dimensional Fourier transform was applied for obtaining information on the occurrence of periodicities in the ordering of nanotubes. Correlation analysis was performed to find out the invisible regularities and periodicities in the structure of the nanotube arrays. The analysis of the photoactivity of the samples was also carried out.