I highly recommend 7 Keys to Great Paintings by Jane R. Hofstetter. This variation of The Extended Game is based on her definitions and references to six different compositional arrangements.
Throw either one six-sided die or a twelve-sided die to determine which of the compositional arrangements you will use in your drawing. Use your imagination. Any object or scene may be adapted to all of the arrangements.
#1 and #7 = Horizontal Composition … Link to Samples
#4 and #10 = Axial Hold Composition … Link to Samples
#5 and #11 = Radial Composition … Link to Samples
#6 and #12 = Cantilever Composition … Link to Samples
Definitions of Compositional Arrangements (adapted from 7 Keys to Great Paintings, North Light Books, 2005)
Horizontal – a strong horizontal subject interrupted by a lesser vertical to break up the side-to-side eye movement.
Vertical – a strong vertical subject interrupted by lesser horizontals to break up the up and down eye movement.
Cruciform – a combination of strong horizontal and vertical subject with each corner a different shape and size.
Axial Hold – a horizontal shape connected at top and side of composition with middle or dark values. This horizontal strip holds the subject of contrasting value in place as it hangs below the strip.
Radial – The eye is led to the off-center focal area by the diagonal shapes radiating toward it.
Cantilever – The focal area hangs out into space, balanced and anchored by a strong and heavy mass shape connected to one of the sides.