  Although random cell complexes occur throughout the physical sciences, there
does not appear to be a standard way to quantify their statistical similarities
and differences. The various proposals in the literature are usually motivated
by the analysis of particular physical systems and do not necessarily apply to
general situations. The central concepts in this paper---the swatch and the
cloth---provide a description of the local topology of a cell complex that is
general (any physical system that may be represented as a cell complex is
admissible) and complete (any statistical question about the local topology may
be answered from the cloth). Furthermore, this approach allows a distance to be
defined that measures the similarity of the local topology of two cell
complexes. The distance is used to identify a steady state of a model
dislocation network evolving by energy minimization, and then to rigorously
quantify the approach of the simulation to this steady state.
