  We investigate the local- and long-range structure of four different
space-filling cellular patterns: bubbles in a quasi-2d foam plus Voronoi
constructions made around points that are uncorrelated (Poisson patterns), low
discrepancy (Halton patterns), and displaced from a lattice by Gaussian noise
(Einstein patterns). We study distributions of local quantities including cell
areas and topological features; the former is the widest for bubbles in a foam
making them locally the most disordered but the latter show no significant
differences between the cellular patterns. Long-range structure is probed by
the spectral density and also by converting the real-space spectrum of number
density or volume fraction fluctuations for windows of diameter $D$ to the
effective distance $h(D)$ from the window boundary where these fluctuations
occur. This real-space hyperuniformity disorder length spectroscopy is
performed on various point patterns which are determined by the centroids of
the bubbles in the foam, by the points patterns around which the Voronoi cells
are created and by the centroids of the Voronoi cells. These patterns are
either unweighted or weighted by the area of the cells they occupy. The
unweighted bubble centroids have $h(D)$ that collapses for the different ages
of of the foam with random Poissonian fluctuations at long distances. All
patterns of area-weighted points have constant $h(D)=h_e$ for large $D$;
$h_e=0.084 \sqrt{\left< a\right>}$ for the bubble centroids is the smallest
value, meaning they are most uniform. All the weighted centroids collapse to
the same constant $h_e=0.084 \sqrt{\left< a\right>}$ as for the foams. A
similar analysis is performed on the edges of the cells where the spectra of
$h(D)$ for the foam edges show $h(D) \sim D^{1-\epsilon}$ where $\epsilon=0.3$
