There have been indications that clusters within superclusters are preferentially aligned, which if true would suggest dynamical processes that can leave a very long-lasting imprint. At turnaround, our ideal grouping approaches constant redshift as all the objects momentarily have zero radial velocity with respect to the core. Turnaround and collapse may well happen on different size scales at different times. This is a useful context to introduce comoving coordinates , a set of coordinates which follows the expansion of the cosmic scale factor so that processes due only to the Hubble expansion disappear. In this way, a cluster will show only collapse toward a relaxed state, since the initial expansion in physical space results purely from the Hubble flow.
Voids pose particular challenges to theories of galaxy formation.
Starting with the uniformity shown by the microwave background, it is not all obvious that there was enough density structure to do this. The following cartoon depicts a density slice through a complicated density field with power on a wide range of scales, and the idea of a bias threshold producing clusters, groups, and voids out of proportion to the local density. It is customary to define a biasing parameter b which relates fluctuations in the overall mass and light distributions. 0.6 b in studies trying to solve derived density fields and galaxy distributions for b . This division in two dimensions gives the set of line segments with minimum total length that separates the generating points into their own regions bounded by polygonal tesselations, with the obvious generalization to three dimensions.