6.4 Beyond linear approximation 287density, which is a higher-dimensional analog of a mountain peak,α∼β∼γ.
Hence the surrounding region collapses in a nearly spherical way resulting in a
spherical or somewhat ellipticalobject. Usually neighbouring peaks are connected
by a saddleback, which is lower in height than the peaks. Along the saddleback
one curvature scale is significantly smaller than the other. Similarly, density peaks
are connected by higher-dimensional saddlebacks, whereα∼βandγα, β.The
collapse in these regions is two-dimensional and producesfilaments. The filaments
connect the spherical objects formed earlier, resulting in a web-like structure (see
Figure 6.1). There are also regions that have no analog in the lower-dimensional
landscape, where only one of the eigenvaluesα, say, has a local maximum and
β,γα.In these regions the collapse is one-dimensional andwalls(pancakes)
Fig. 6.1.