  We focus on a family of one-dimensional probabilistic cellular automata with
memory two: the dynamics is such that the value of a given cell at time $t+1$
is drawn according to a distribution which is a function of the states of its
two nearest neighbours at time $t$, and of its own state at time $t-1$. Such
PCA naturally arise in the study of some models coming from statistical physics
($8$-vertex model, directed animals and gaz models, TASEP, etc.). We give
conditions for which the invariant measure has a product form or a Markovian
form, and we prove an ergodicity result holding in that context. The stationary
space-time diagrams of these PCA present different forms of reversibility. We
describe and study extensively this phenomenon, which provides families of
Gibbs random fields on the square lattice having nice geometric and
combinatorial properties.
