  A cellular automaton model is used to describe the dynamics of the catalytic
oxidation of $CO$ on a $Pt(100)$ surface. The cellular automaton rules account
for the structural phase transformations of the $Pt$ substrate, the reaction
kinetics of the adsorbed phase and diffusion of adsorbed species. The model is
used to explore the spatial structure that underlies the global oscillations
observed in some parameter regimes. The spatiotemporal dynamics varies
significantly within the oscillatory regime and depends on the harmonic or
relaxational character of the global oscillations. Diffusion of adsorbed $CO$
plays an important role in the synchronization of the patterns on the substrate
and this effect is also studied.
