  Consider a cellular automaton with state space $\{0,1 \}^{{\mathbb Z}^2}$
where the initial configuration $\omega_0$ is chosen according to a Bernoulli
product measure, 1's are stable, and 0's become 1's if they are surrounded by
at least three neighboring 1's. In this paper we show that the configuration
$\omega_n$ at time n converges exponentially fast to a final configuration
$\bar\omega$, and that the limiting measure corresponding to $\bar\omega$ is in
the universality class of Bernoulli (independent) percolation.
  More precisely, assuming the existence of the critical exponents $\beta$,
$\eta$, $\nu$ and $\gamma$, and of the continuum scaling limit of crossing
probabilities for independent site percolation on the close-packed version of
${\mathbb Z}^2$ (i.e., for independent $*$-percolation on ${\mathbb Z}^2$), we
prove that the bootstrapped percolation model has the same scaling limit and
critical exponents.
  This type of bootstrap percolation can be seen as a paradigm for a class of
cellular automata whose evolution is given, at each time step, by a monotonic
and nonessential enhancement.
