  We consider spatiotemporal chaotic systems for which spatial correlation
functions decay substantially over a length scale xi (the spatial correlation
length) that is small compared to the system size L. Numerical simulations
suggest that such systems generally will be extensive, with the fractal
dimension D growing in proportion to the system volume for sufficiently large
systems (L >> xi). Intuitively, extensive chaos arises because of spatial
disorder. Subsystems that are sufficiently separated in space should be
uncorrelated and so contribute to the fractal dimension in proportion to their
number. We report here the first numerical calculation that examines
quantitatively how one important characterization of extensive chaos---the
Lyapunov dimension density---depends on spatial disorder, as measured by the
spatial correlation length xi. Surprisingly, we find that a representative
extensively chaotic system does not act dynamically as many weakly interacting
regions of size xi.
