  The dynamics of an extended, spatiotemporally chaotic system might appear
extremely complex. Nevertheless, the local dynamics, observed through a finite
spatiotemporal window, can often be thought of as a visitation sequence of a
finite repertoire of finite patterns. To make statistical predictions about the
system, one needs to know how often a given pattern occurs. Here we address
this fundamental question within a spatiotemporal cat, a 1-dimensional spatial
lattice of coupled cat maps evolving in time. In spatiotemporal cat, any
spatiotemporal state is labeled by a unique 2-dimensional lattice of symbols
from a finite alphabet, with the lattice states and their symbolic
representation related linearly (hence "linear encoding"). We show that the
state of the system over a finite spatiotemporal domain can be described with
exponentially increasing precision by a finite pattern of symbols, and we
provide a systematic, lattice Green's function methodology to calculate the
frequency (i.e., the measure) of such states.
