  In bricklayers' model, which is a generalization of the misanthrope
processes, we show that a nontrivial class of product distributions is closed
under the time-evolution of the process. This class also includes measures
fitting to shock data of the limiting PDE. In particular, we show that shocks
of this type with discontinuity of size one perform ordinary nearest neighbor
random walks only interacting, in an attractive way, via their jump rates. Our
results are related to those of Belitsky and Schuetz on the simple exclusion
process, although we do not use quantum formalism as they do. The structures we
find are described from a fixed position. Similar ones were found in a paper by
Balazs, as seen from the random position of the second class particle.
