  We analyze evolution of the basic properties of simulated large scale
structure elements formed by dark matter (DM LSS) and confront it with the
observed evolution of the Lyman-$\alpha$ forest. In three high resolution
simulations we selected samples of compact DM clouds of moderate overdensity.
Clouds are selected at redshifts $0\leq z\leq 3$ with the Minimal Spanning Tree
(MST) technique. The main properties of so selected clouds are analyzed in 3D
space and with the core sampling approach, what allows us to compare estimates
of the DM LSS evolution obtained with two different techniques and to clarify
some important aspects of the LSS evolution. In both cases we find that regular
redshift variations of the mean characteristics of the DM LSS are accompanied
only by small variations of their PDFs, what indicates the self similar
character of the DM LSS evolution. The high degree of relaxation of DM
particles compressed within the LSS is found along the shortest principal axis
of clouds. We see that the internal structure of selected clouds depends upon
the mass resolution and scale of perturbations achieved in simulations. It is
found that the low mass tail of the PDFs of the LSS characteristics depends
upon the procedure of clouds selection.
