This is one of my favorite topics with students. What are the best rules, wathever is the subject, painting, architecture, photography, literature, etc, etc...
I generaly sell them the rule of thirds, just as a starter. To make them realise that the centered composition (the one that comes from childhood) is not an universal one. This makes them think about it, which is a good thing for a human ;-)
After that, I start playing with the rules, making them think about the relation between form and content. Yes, I agree with Mitchall, there must be a relation, if not, it might became an empty piece of work. But, even so, there might be something more (or less) in this equation. Intencionality.
This one is empty, of anything. The rule of thirds has a role here, to help creating empty spaces, which wouldn't be possible with a centered composition:
Quite uninteresting, hein? But I wanted it that way, it's all flat, quiet, (boring?)... but, somehow, I can feel the moment and the balance that it made me feel with all that "silence".
The same rule makes this composition more dinamic. Or I made a composition more dinamic and found the rule after? I don't care about that, neither if someone finds the rule to justify themself to like or dislike the image.
But I can assure you that it was the "interaction" with the object that made me compose in that way, not the respect for the rules. So what, am I going to compose differentely just to be "in" or "out"?
This one is the "golden" one, when I found myself, a kind of enlightment. You're free to find rules and connections in there. But there's no emotional content. It's a graphical object, only:
So it's only form, and I'm very confortable with that. It's my intention, and my style, mainly.
Someone refered the golden mean, there's always this reference. But this is an endless topic. Here's a very dull composition, based on the most basic golden rectangle where the longest side has the lenght of the square diagonal:
Here I'm sorry to have lost the moment when the couple would be in the first third instead of centered. It wouldn't be less "dull", but it would be more balanced because of the triangulation...
I could spend the night showing examples but, the conclusion, for me, is:
We can find whatever rule we want in any "object". It's a human thing, to find lines, strong points (golden one's), and start decoding the organizative underlines. The rule of thirds is just one of the most popular (maybe that's why we have this "wonderful" feature in camera's lcds), as well as the golden mean.
BTW, which "golden mean" do you mean? There are many golden sequences and geometries, from the Fibonacci sequence (or geometrical one's), the divine triangle (inside the pentagon), to the spiral (triangular, square, pentagonal, etc), to so many variations in rectangle proportions, that it's so easy to find one anywhere.
It's all over in Nature. Terefore I've had to ask myself the question about our genetic code. There must be something there that makes us organize things the same way over and over...
Believe it or not, take two similar objects with some differences in proportions. The one you'll choose will have some rule waiting to be find ;-)
Sorry by the lecture, but I've come back from school and it's very difficult to stop :-(
edit: Man, I took so long writing this that I lost lot's of good post in this thread. Yes, a very interesting one!
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Cheers.............. Rui
http://www.flickr.com/photos/ruinog/collections/
(sorry, it set my entire stream as private and I'm slowly reorganizing my page)