  Monte Carlo simulation, experiment and continuum theory are used to examine
the anchoring exhibited by a nematic liquid crystal at a patterned substrate
comprising a periodic array of rectangles that, respectively, promote vertical
and planar alignment. It is shown that the easy axis and effective anchoring
energy promoted by such surfaces can be readily controlled by adjusting the
design of the pattern. The calculations reveal rich behavior: for strong
anchoring, as exhibited by the simulated system, for rectangle ratios $\geq 2$
the nematic aligns in the direction of the long edge of the rectangles, the
azimuthal anchoring coefficient changing with pattern shape. In weak anchoring
scenarios, however, including our experimental systems, preferential anchoring
is degenerate between the two rectangle diagonals. Bistability between
diagonally-aligned and edge-aligned arrangement is predicted for intermediate
combinations of anchoring coefficient and system length-scale.
