  We present numerical results obtained using a lattice-gas model with
dynamical geometry defined by Hasslacher and Meyer (Int. J. Mod. Phys. C. 9
1597 (1998)). The (irreversible) macroscopic behaviour of the geometry (size)
of the lattice is discussed in terms of a simple scaling theory and obtained
numerically. The emergence of irreversible behaviour from the reversible
microscopic lattice-gas rules is discussed in terms of the constraint that the
macroscopic evolution be reproducible. The average size of the lattice exhibits
power law growth with exponent 1/2 at late times. The deviation of the
macroscopic behaviour from reproducibility for particular initial conditions
(``rogue states'') is investigated as a function of system size. The number of
such ``rogue states'' is observed to decrease with increasing system size. Two
mean-field analyses of the macroscopic behaviour are also presented.
