Merely knowing what symmetry means in a formal sense doesn’t help much in art. It may even get you in trouble, from an aesthetic standpoint.
A perfect mirror reflection doesn’t seem to be terribly interesting to our cortical processing machinery. This observation seems to fall into the same general category of misunderstanding that the so-called Rule of Thirds causes so very often.
It doesn’t help to have a grid of thirds overlay included with every new camera without an associated warning that plainly representing such a simple fraction visually is boring (as the photographer Axel Bruck documented very effectively in Practical Composition in Photography, with a bit of data to back up his statements).
However, this doesn’t seem to exist. So, viewing as many good examples as possible and learning from them is our only option.
Then again, as these paintings demonstrate when viewed more closely, visual artwork isn’t purely geometric.
Spatial arrays or time series of images imply much more to people viewing them. Juxtaposition of iconic source materials to imply a tertium quid (or third thing) is exemplified in the cinematic movement often represented by Eisenstein.
The Odessa stairway sequence, which coincidentally is not exactly 2/3 of the way through Battleship Potemkin, has been used as a classic example.
The following short excerpt from an equally famous contemporary film clarified the whole point of juxtaposing pictures for me.
Extending the use of metaphors from literature to the visual arts seems like another useful process. I can’t get as much mileage as the great English Bard did from staccato similes, and the like.
…King. So sweete a kisse the golden Sunne giues not,
To those fresh morning drops vpon the Rose,
As thy eye beames, when their fresh rayse haue smot.
However, a bit of referential humor a la Falstaff may be possible.
Heere comes leane Iacke, heere comes bare-bone. How
now my sweet Creature of Bombast, how long is’t agoe,
Iacke, since thou saw’st thine owne Knee?
Thanks to a kid with a lot of character, here is a short series of photos that potentially implies more than its constituent parts – although the exact effect encountered depends highly upon the perspective of the viewer.