  Recently, the observed cellular nature of the large-scale structure of the
Universe with its quasi-regular pattern of superclusters and voids has been
pointed out by several authors. In this paper, we investigate properties of the
initial power spectrum which lead to prediction of structure consistent with
these observations.For this purpose, we analyze the evolution of structure
within four sets of 2- and 3-dimensional cosmological models, which differ in
their initial power spectrum. The models include HDM and CDM models as well as
double power-law models. We discuss in detail the impact of model parameters
such as the large scale and small scale power and the position and height of
the maxima of the power spectra on the predicted structure. The best agreement
with observations was observed in the model with the Harrison-Zeldovich
spectrum on large scales, a power index $n\approx -1.5$ on small scales, and a
maximum of the power spectrum at $\approx 130$~\Mpc. In this model the
distribution of masses of clusters and superclusters, the correlation function
of clusters, and the void distribution reproduce well the respective observed
distributions. We also investigated the dynamical evolution of the
supercluster-void structure. The results show that the basic supercluster-void
network is formed very early and is essentially given by initial conditions.
