  We investigate one-dimensional Probabilistic Cellular Automata, called
Diploid Elementary Cellular Automata (DECA), obtained as random mixture of two
different Elementary Cellular Automata rules. All the cells are updated
synchronously and the probability for one cell to be $0$ or $1$ at time $t$
depends only on the value of the same cell and that of its neighbors at time
$t-1$. These very simple models show a very rich behavior strongly depending on
the choice of the two Elementary Cellular Automata that are randomly mixed
together and on the parameter which governs probabilistically the mixture. In
particular, we study the existence of phase transition for the whole set of
possible DECA obtained by mixing the null rule which associates $0$ to any
possible local configuration, with any of the other $255$ elementary rule. We
approach the problem analytically via a Mean Field approximation and via the
use of a rigorous approach based on the application of the Dobrushin Criterion.
The distinguishing trait of our result is the possibility to describe the
behavior of the whole set of considered DECA without exploiting the local
properties of the individual models. The results that we find are coherent with
numerical studies already published in the scientific literature and also with
some rigorous results proven for some specific models.
