  The properties of two-state nearest-neighbour cellular automata (CA) that are
capable of density classification are discussed. It is shown that these CA
actually conserve the total density, rather than merely classifying it. This is
also the criterion for any CA simulation of DFT. The effect of boundary and
periodicity conditions upon the evolution of such CA are elaborated by
considering linear and cyclic lattices and boundary conditions consistent with
the conservation criterion. In a bounded linear lattice, it is possible to
achieve a configuration with a single 01 and no 10 domain wall, or vice versa,
but this is not possible in a cyclic lattice, where these two domain walls have
to appear in pairs. This determines the final stable state of the automaton.
