  Consider a graph $G=(V,E)$ and an initial random coloring where each vertex
$v \in V$ is blue with probability $P_b$ and red otherwise, independently from
all other vertices. In each round, all vertices simultaneously switch their
color to the most frequent color in their neighborhood and in case of a tie, a
vertex keeps its current color. The main goal of the present paper is to
analyze the behavior of this basic and natural process on the random
$d$-regular graph $\mathbb{G}_{n,d}$. It is shown that for all $\epsilon>0$,
$P_b \le 1/2-\epsilon$ results in final complete occupancy by red in
$\mathcal{O}(\log_d\log n)$ rounds with high probability, provided that $d\geq
c/\epsilon^2$ for a suitable constant $c$. Furthermore, we show that with high
probability, $\mathbb{G}_{n,d}$ is immune; i.e., the smallest dynamic monopoly
is of linear size. A dynamic monopoly is a subset of vertices that can take
over in the sense that a commonly chosen initial color eventually spreads
throughout the whole graph, irrespective of the colors of other vertices. This
answers an open question of Peleg.
