Hi, Mike.
I absolutely
love square compositions! I have done quite a few in this format; there is something about the square that I find settling. I do agree, though, that there are different challenges involved in balancing its static shape.
The two things I think are most important are to find and use strong diagonals in the way the space is divided, be it by shape, value, or line; and to place the focal point sufficiently above the midline to counteract the eye's tendency to visually drop the image. (Although this visual drop occurs regardless of shape, I think it can be extra dangerous in the square.) I'll post a few example here of portraits in the "square".
First, this little oil (The Artist's Child; 12" x 12"), which is on my home page, tends, I think, to work in the square because the values read in a strong upper left to lower right pattern; this directional is reinforced by the line of vision created by the direction of the gaze. The angle of the head provides a counterbalancing diagonal.
Administrator's note: See Peggy Baumgaertner's excellent post on compositional sighrtlines at http://forum.portraitartist.com/show...=&threadid=726