Thermodynamic limit from small lattices of coupled maps

We compare the behavior of a small truncated coupled:map lattice with rando m inputs at the boundaries with that of a large deterministic lattice essen tially, at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correla tion with increasing truncated lattice size. This suggests that spatiotempo ral embedding techniques using local observations cannot detect the presenc e of spatial extent in such systems and hence they may equally well be mode led by a local low:dimensional stochastically driven system.