A solvable coupled map lattice model exhibiting spatio-temporal chaos
is studied. Exact expressions are obtained for the spectra of Lyapunov
exponents as a function of the model parameters. Although the model h
as spatio-temporal structure, the time series measured at a single lat
tice site are shown to consist of independent, identically distributed
samples for several values of the model parameters. For these paramet
er values, the spatial series measured at a fixed time also consist of
independent, identically distributed samples. In these cases, the inf
ormation dimension density is 1, but the information entropy density d
epends on the model parameters. Thus, the model is an example where th
e information entropy density can be obtained neither from a time seri
es measured at a single lattice site nor from a spatial series measure
d at a fixed time, We conclude that in studying only a time series or
a spatial series without any knowledge of the system, one could be eas
ily led into thinking that there is no spatio-temporal structure. For
a full characterization of the system, structure in time and space wil
l have to be considered simultaneously.