##### Figure 1. A 3-D Voronoi tessellation of 1000 cells

##### Figure 2. Wire diagram view of Voronoi cells,

edges indicated by solid lines, vertices by red dots

##### Figure 3. Slices through 3-D Voronoi tessellation:

top: geometric view

bottom: slice through Voronoi kinematic model particle distribution

##### Figure 4. Evolution Voronoi kinematic model

particle distribution in Voronoi kinematic model at 6 successive timesteps

##### Figure 5. Voronoi vertex distribution

top: spatial distribution

bottom left: slice through 3-D distribution

bottom right: Aitoff projection of vertex sky distribution

##### Figure 6. Voronoi vertex distribution bias:

spatial Voronoi vertex distribution for vertex samples,

selected at 5 successively richer "vertex mass" limits

(top left --> bottom right: complete sample, 25%, 12.5%, 5%, 1% richest

##### Figure 7. Voronoi vertex distribution bias:

Voronoi vertex distribution in central slice. Red dots: complete sample of Voronoi vertices

In three successive frames (top right, bottom left, bottom right) blue dots indicate

samples of 25%, 12.5% and 5% richest vertices

##### Figure 8. Voronoi vertex distribution bias:

6 samples of Voronoi vertices for 6 successive richnesses

(top left --> bottom right: full sample to 1% richest), scaled to equal number density.

Clear demonstration that differences in distribution not only due to number density but

also to differences in clustering properties

##### Figure 9. Voronoi vertex clustering

Two-point correlation function full Voronoi sample

top: spatial Voronoi vertex sample

bottom left: log-log plot xi(r); bottom right: lin-lin plot xi(r)

##### Figure 10. Voronoi vertex clustering

Two-point correlation function for samples of Voronoi vertices, a sequence of 10 samples of successively richer (more massive) vertices:

top: log-log and lin-lin plots two-point correlation function, as function of true distance

bottom: same, but distance scaled to inter-vertex distance in samples

##### Figure 11. Voronoi vertex clustering: Geometric selfsimilarity ?

left: scaling of clustering length r_0 (xi(r_0)=1) and

correlation length r_a (spatial coherence length at which xi(r_a)=0),

as function of inter-vertex distance lambda_v (lambda_c is basic distance unit,

here equal to distance between tessellation nuclei)

centre: scaling ratio correlation length r_a/clustering length r_0 as

function inter-vertex distance lambda_v:

constant ratio indicates self-similarity Voronoi vertex scaling

right: scaling power-law index gamma of power-law regime correlation function xi(r)

as function of inter-vertex distance lambda_v

##### Figure 12. Significance geometric selfsimilarity:

Top left: slice through full sample Voronoi vertices (red dots)

Top right: selected 25% richest vertices from full sample,

green box: central box of 1/8 volume complete box

Bottom left: select 3.125% richest vertices from full sample,

Bottom right: vertex distribution green box inflated to same size, this scaling

yields spatial point distribution similar to that of 3.125% richest vertices