The Rule of Thirds, in my humble opinion, is what teaches you that asymmetry is beautiful, and then puts it in a grid and makes it symmetrical, although still beautiful. It explains the beauty of most of the images.
It took me a while to find a good picture that I made myself, and I finally got to my old DeviantArt account where I found this:
This photograph with a reaching hand is mostly played on the contrast and we can see the most contrast, and the main character, lets say, on the left side, in the exact position of two crossovers. These are the highlights. But the interesting part is a third object in the picture - a shadow, which looks so thick you can assume it can grab you. Its pinnacle, its brightest point merges perfectly with the top-right crossover, thus making this image even more beautiful. The final, bottom-right crossover points out the blue of the ceiling making more than just a background. It seems that you mind should insert something of its own into that seemingly empty space for the hand to grab.
I think it is a great example of the composition that features only two real objects, but lets you add many of your own.
Thank you and good night,
Ed.
P.S. a websit I found - http://www.shutterfreaks.com/Actions/RuleOfThirds.php#Download