How to disentangle the Cosmic Web?

The Cosmic Web is a complicated highly-entangled geometrical object formed from remarkably simple -- Gaussian -- initial conditions. The full complexity of the Web can be fully appreciated in the six-dimensional phase space only, which study is, however, impractical due to numerous reasons. Instead, we suggest to use Lagrangian submanifold, i.e., the mapping $x = x(q)$, where $x$ and $q$ are three dimensional vectors representing Eulerian and Lagrangian coordinates. Being fully equivalent in dynamical sense to the phase space, it has the advantage of being a single valued and also metric space. In addition, we propose a new computational paradigm for the analysis of substructure of the Cosmic Web in cosmological cold dark matter (CDM) simulations. We introduce a new data-field -- the flip-flop field -- which carries wealth of information about the history and dynamics of the structure formation in the universe. The flip-flop (FF) field is an ordered data set in Lagrangian space representing the number of sign reversals of an elementary volume of each collisionless fluid element represented by a computational particle in a $N$-body simulation. This FF-field is effectively a multi-stream counter of each substructure element of the Cosmic Web. We demonstrate that the very rich subst