  Identifying and quantifying spatial correlation are important aspects of
studying the collective behaviour of multi-agent systems. Pair correlation
functions (PCFs) are powerful statistical tools which can provide qualitative
and quantitative information about correlation between pairs of agents. Despite
the numerous PCFs defined for off-lattice domains, only a few recent studies
have considered a PCF for discrete domains. Our work extends the study of
spatial correlation in discrete domains by defining a new set of PCFs using two
natural and intuitive definitions of distance for a square lattice: the taxicab
and uniform metric. We show how these PCFs improve upon previous attempts and
compare between the quantitative data acquired. We also extend our definitions
of the PCF to other types of regular tessellation which have not been studied
before, including hexagonal, triangular and cuboidal. Finally, we provide a
comprehensive PCF for any tessellation and metric allowing investigation of
spatial correlation in irregular lattices for which recognising correlation is
less intuitive.
