  Using numerical results from density matrix renormalization group (DMRG)
calculations for the t-J model, on systems as large as 10x7, we examine the
structure of the one and two hole ground states in ladder systems and in two
dimensional clusters. A simple theoretical framework is used to explain why
holes bind in pairs in two-dimensional antiferromagnets. For the case J/t=0.5,
which we have studied, the hole pairs reside predominantly on a 2x2 core
plaquette with the probability that the holes are on diagonal sites greater
than nearest-neighbor sites. There is a strong singlet bond connecting the
spins on the two remaining sites of the plaquette. We find that a general
characteristic of dynamic holes in an antiferromagnet is the presence of
frustrating antiferromagnetic bonds connecting next-nearest-neighbor sites
across the holes. Pairs of holes bind in order to share the frustrating bonds.
  At low doping, in addition to hole pairs, there are two additional low-energy
structures which spontaneously form on certain finite systems. The first is an
undoped Lx2 spin-liquid region, or ladder. The second is a hole moving along a
one dimensional chain of sites. At higher doping we expect that hole pairing is
always favored.
