Abstract.  Complexity is ubiquitous behavior in the nature. In cosmology, especially due to the initial conditions mainly and mostly because of other relevant phenomena such as foreground effects, stochasticity in contrast to deterministic behavior are emerged.  Mentioned property is widely experienced in cosmological fields in 1, 2 and 3 dimensions.  In principle the probabilistic frame work according to statistical points of view, enables to introduce the robust method not only in data analysis but also in preparing reliable strategies to predict the evolution and for characterization of underlying processes.  In this talk, I will rely on stochasticity nature of cosmological fields in various dimensions, and attempt to set up cross-correlation of some geometrical features like local extrema and up-crossing.  I will show that mentioned statistics are able to find exotic features hidden in the underlying field and to discriminate between them.  As an example I will focus on 2+1D CMB field and look for non-Gaussianity and cosmic strings networks.