  We study invasion percolation in two dimensions. We compare connectivity
properties of the origin's invaded region to those of (a) the critical
percolation cluster of the origin and (b) the incipient infinite cluster. To
exhibit similarities, we show that for any $k\geq1$, the $k$-point function of
the first so-called pond has the same asymptotic behavior as the probability
that $k$ points are in the critical cluster of the origin. More prominent,
though, are the differences. We show that there are infinitely many ponds that
contain many large disjoint $p_c$-open clusters. Further, for $k>1$, we compute
the exact decay rate of the distribution of the radius of the $k$th pond and
see that it differs from that of the radius of the critical cluster of the
origin. We finish by showing that the invasion percolation measure and the
incipient infinite cluster measure are mutually singular.
