Composition is one of the first lessons most photographers take seriously and its power over the quality of your images is undeniable. However, the "one composition to rule them all" mindset that is prevalent in photography is both limiting and boring.
The rule of thirds is a good composition, I'm not denying that. I still use it and most landscape photographers who are top of their game will use it too. It's easy to remember, easy to compose, and easy to spot scenes that fit the grid. What it isn't, however, is the only composition. One alternative is, as Mark Denney points out, more in keeping with our minds: the Golden Spiral.
Not only is the Golden Spiral more pleasing to the eye in many cases, but it's also the more natural shape I believe. There are few straight lines in nature, but spirals are observable from galaxies down to sinkholes. In this video, Mark Denney — a fantastic landscape photographer — shows just how beautiful the Golden Spiral composition it can be.
My only real question, as somebody who doesn't take many landscapes, is how many times images actually fit the Golden Spiral composition. I agree, it's better and more interesting that the rule of thirds, but I think there are fewer true examples of it. Many of the examples I see (though not necessarily in this video) are more like wishful thinking when they overlay the spiral onto their image. What do you think?