  On the square lattice raindrops fall on an edge with midpoint $x$ at rate
$\|x\|_\infty^{-\alpha}$. The edge becomes open when the first drop falls on
it. Let $\rho(x,t)$ be the probability that the edge with midpoint
$x=(x_1,x_2)$ is open at time $t$ and let $n(p,t)$ be the distance at which
edges are open with probability $p$ at time $t$. We show that with probability
tending to 1 as $t \to \infty$: (i) the cluster containing the origin $\mathbb
C_0(t)$ is contained in the square of radius $n(p_c-\epsilon,t)$, and (ii) the
cluster fills the square of radius $n(p_c+\epsilon,t)$ with the density of
points near $x$ being close to $\theta(\rho(x,t))$ where $\theta(p)$ is the
percolation probability when bonds are open with probability $p$ on $\mathbb
Z^2$. Results of Nolin suggest that if $N=n(p_c,t)$ then the boundary
fluctuations of $\mathbb C_0(t)$ are of size $N^{4/7}$.
