  Consider a graph $G=(V,E)$ and a random initial vertex-coloring, where each
vertex is blue independently with probability $p_{b}$, and red with probability
$p_r=1-p_b$. In each step, all vertices change their current color
synchronously to the most frequent color in their neighborhood and in case of a
tie, a vertex conserves its current color; this model is called majority model.
If in case of a tie a vertex always chooses blue color, it is called biased
majority model. We are interested in the behavior of these deterministic
processes, especially in a two-dimensional torus (i.e., cellular automaton with
(biased) majority rule). In the present paper, as a main result we prove both
majority and biased majority cellular automata exhibit a threshold behavior
with two phase transitions. More precisely, it is shown that for a
two-dimensional torus $T_{n,n}$, there are two thresholds $0\leq p_1, p_2\leq
1$ such that $p_b \ll p_1$, $p_1 \ll p_b \ll p_2$, and $p_2 \ll p_b$ result in
monochromatic configuration by red, stable coexistence of both colors, and
monochromatic configuration by blue, respectively in $\mathcal{O}(n^2)$ number
of steps
