Naturally, peculiar velocities must grow consistently with increased spatial clustering. Again, N-body simulations provide valuable insight, especially into the non-linear regime. Since velocity distributions depend strongly on the amount of clustering it is important to separate galaxies according to the density contrast in their local neighborhood.

For the 4000-body experiments, for example, it is possible to use the integration scheme itself to determine the number density inside the nearest neighbor sphere surrounding any galaxy. This sphere is essentially where the fluctuating component dominates the gravitational force. The result is a measure of the local density contrast, which varies from about 104 or 105 in the centers of rich clusters to less than 0.5 in the field galaxies. A subset of field galaxies may be selected by also requiring them to be separated from their nearest neighbor by at least twice the average separation that a uniform random distribution would have. These most isolated galaxies are called extreme field galaxies. They are almost always well outside the haloes of clusters.

As an indication of the relative degree of isolation these criteria imply, at R = 32 (the present time) in the Ω = 0.1, n = -1 model, about 23% of all the galaxies are in clusters (density contrast > 100), about 62% are intermediate (100 > contrast > 0.5), 15% are field galaxies and 5% are extreme field galaxies.