A feature of the dark matter density field, that becomes visible when looking at thin slices, are extremely sharp edges within the density field. These are called caustics. Now the most pronounced caustics are these, which mark the transition from a single stream to a multi stream region.
A single stream region is - as the name suggests - a region where only a single dark matter stream is present. That means all particles in a small volume element of a single stream region come from a single small volume element in the early homogeneous universe. On the other hand, in multi stream regions particles from multiple different origins have come together. This is illustrated in the phasespace diagram on the right.
Now to distinguish between single stream and multi stream regions in this 1d example, we could do the following: we follow along the dark matter sheet in one direction (indicated by arrows) starting from left to right and, wherever we have to go from right to left to go on, we can be sure to be in a multi stream region. The formal and higher dimensional equivalent of this is: all regions which contain particles whose distortion tensor dx/dq has a negative determinant, are classified as multi stream regions. The remaining volume is single stream region.
In the picture at the top of the page you can see the result of such a classification (single stream regions in white). Further you can find a slice movie below which shows on the left side the density field, and on the right sight the single stream field. Multi stream regions are shown in black and single stream regions are assigned random colors. Each different color indicates a different connected single stream region component. (More about this in the next section).