A programmable nematic liquid crystal phase plate is formed by sandwiching a layer of liquid crystal material between two glass substrates, each coated with a transparent electrode. Regions of the liquid crystal layer are independently controlled by patterning the electrode into an array of pixels and addressing each pixel with a separate voltage source. The voltage-controlled reorientation (deformation) of the liquid crystal layer far from the pixel edges is well understood; however, very few investigations of the deformation near a pixel edge have been published. We show that near the pixel edges the deformation decreases monotonically, but a transition region located in the center of the pixel results. The transition region, called a liquid crystal inversion wall, is undesirable for most applications but can be forced to form near the edge of the pixel by adding a pretilt to the surface alignment. We present computer simulation results of the voltage-dependent pixel edge deformations and relate the deformations to the phase profile experienced by a wavefront propagating through the programmable phase plate.