  We study qualitative properties of two-dimensional freezing cellular automata
with a binary state set initialized on a random configuration. If the automaton
is also monotone, the setting is equivalent to bootstrap percolation. We
explore the extent to which monotonicity constrains the possible asymptotic
dynamics by proving two results that do not hold in the subclass of monotone
automata. First, it is undecidable whether the automaton almost surely fills
the space when initialized on a Bernoulli random configuration with density
$p$, for some/all $0 < p < 1$. Second, there exists an automaton whose
space-filling property depends on $p$ in a non-monotone way.
