Cosmic Web — Zel'dovich Approximation
Gravitational collapse of initial density perturbations into filaments, walls (pancakes), and voids — the large-scale structure of the Universe
Zel'dovich approximation (1970): x(q,D) = q − D·∇Φ(q), where q is the Lagrangian (initial) position, x is Eulerian (final) position, and Φ is the initial gravitational potential. Particles move in straight lines until "shell crossing" (collapse). First collapses happen along the shortest axis → pancakes (2D sheets). Then collapse along second axis → filaments. Finally collapse to nodes (galaxy clusters). The voids between grow, giving the observed foam-like structure of the Universe. This linear approximation breaks down at shell-crossing; N-body simulations are needed after.