How are galaxy filaments formed? And do they have any analogues in stellar formation? 
In physical cosmology, galaxy filaments, also called supercluster
  complexes or great walls, are, so far, the largest known cosmic
  structures in the universe. They are massive, thread-like structures
  with a typical length of 50 to 80 megaparsecs h-1 that form the
  boundaries between large voids in the universe.[3] Filaments consist
  of gravitationally-bound galaxies; parts where a large number of
  galaxies are very close to each other are called superclusters.

So I've always wondered: how are these structures formed? 
One would (naively) expect that gravitationally bound structures would form as either spheres or discs.
 A: My PhD thesis was on the numerical simulation of the formation of clusters of galaxies, but it's not easy to give a concise answer. A useful first approximation is the so-called Zel'dovich Pancake, where on very large scales corresponding to the size of clusters of galaxies or larger, such that pressure is negligible and the gas dynamics is (to a reasonable approximation) entirely gravitational, an ellipsoidal overdensity will collapse most rapidly along its shortest axis, to form a 'pancake'. This will then collapse further to form a filament which then itself fragments to clumps that form galaxies. So the distribution of galaxies will follow the pancake/filamentary structure of the initial collapse. 
However, in reality the density field is a composite of random Gaussian fluctuations at many scales and not the simple overdensity considered in the Zel'dovich Pancake, so collapse is complex and is observed at a variety of stages on different scales. Also, as an overdense region collapses the gas shock-heats to millions of Kelvin and pressure ceases to be negligible (as an aside, strong thermal X-ray emission from this gas is observed by X-ray telescopes, and as it is in hydrostatic equilibrium in the cluster gravitational potential it can be used to derive the distribution of mass). The coupled gravitational/hydrodynamic collapse is highly non-linear, and needs to be followed numerically rather than analytically - my thesis was on N-body (i.e. gravity) + Smoothed-Particle Hydrodynamics (gas dynamics) simulations of this process.
Regarding star formation, this is another extremely complex process and there are both similarities (fundamentally they are both processes governed by a balance of gravitational and gas-dynamic forces) and profound differences. However, star formation tends to be triggered - i.e supernovae in one generation of stars triggers the collapse of molecular clouds and the formation of a new generation - and so is not directly analogous. 
