Most photographers become aware of the 'Rule of Thirds' at some time or other. It is a rule that can be broken, and one that I believe some people understand instinctively. There is another, older, 'rule' that the ancient Greeks developed to give harmony to images, sculpture and architecture and which I learned a little about (and subsequently forgot the detail of ) as a student. The Golden Section, also known as the Golden Mean or Golden Ratio. It is similar to The Rule of Thirds in that it encourages image makers to place the focal point off-centre - which in my opinion is all you need to know, the degree of 'off-centredness' can be varied (otherwise all your images will look a bit samey).
I was reminded of all this when I stumbled across a nifty little web-gadget for placing the Golden Section over a photo of your choice. Give it a try here.
When I uploaded a recent shot of mine I was quite surprised how it fitted the Golden Spiral. So much so I made a composite of the shot with the Golden Section and Spiral crudely superimposed on it for a bit of fun. I can assure you none of this was in my mind when I framed the shot, but it seems to fit quite nicely. Or am I seeing what I want to see?