  Cellular automata (CA) can be viewed as maps in the space of probability
measures. Such maps are normally infinitely-dimensional, and in order to
facilitate investigations of their properties, especially in the context of
applications, finite-dimensional approximations have been proposed. The most
commonly used one is known as the local structure theory, developed by H.
Gutowitz et al. in 1987. In spite of the popularity of this approximation in CA
research, examples of rigorous evaluations of its accuracy are lacking. In an
attempt to fill this gap, we construct a local structure approximation for rule
14, and study its dynamics in a rigorous fashion, without relying on numerical
experiments. We then compare the outcome with known exact results.
