  Using the density matrix renormalization group, we study the possibility of
real space checkerboard patterns arising as the ground states of the t-J model.
We find that checkerboards with a commensurate (pi,pi) background are not low
energy states and can only be stabilized with large external potentials.
However, we find that striped states with charge density waves along the
stripes can form approximate checkerboard patterns. These states can be
stabilized with a very weak external field aligning and pinning the CDWs on
different stripes.
