The Mathematics of Composition

Moderns Film could be considered one of the most advanced forms of media we have today. When done well, films effectively combine the elements of sound, composition, story, talent and more to create one fluid cinematic piece. It takes years of hard work and sheer talent to master all of these elements. Until then, it’s a good idea to focus in on one area of film that interests you more then the others.

Chris Knight, writer of fstoppers.com, has created an ultimate guide that makes learning one such element much easier. Specifically, composition – a defining element of film, and pretty much the defining element of photography.

Wait, You mean that rule of thirds thingy?

Ah yes, but as Knight proves in his article, it goes far beyond that nine-box rule.

With pictures and examples guiding his definitions all the way though, Knight provides a clear guide to the mathematics behind beautiful composition.

After reading his article, and in an effort to beat Arturo to the punch, I’ve decided to review some of my own work to see if it stands up to the test.

Center Composition

The first and most basic type of composition Knight mentions is center composition. For this I used a picture I took while in the middle of nowhere. The road stretched on for miles and the lighting was fantastic. With flat land on both sides of the road, this was a perfect time to use symmetry to my advantage.

It's not mathematically perfect, but still an effective example.

Rule of Thirds

The classic. The 101 of photography. When unsure how to compose a photo it's best to stick with the good 'ol threes. I found this photo of a prairie dog which falls right on the sweet spot. 

Golden Triangles 

When playing with angles, golden triangles are a great way to check composition. Knight uses a picture of the eiffel tower as a great example. 

I found one picture from Santa Monica that again, is not mathematically perfect, but shows how this type of composition can have a compelling effect. 

Frame Within a Frame

Another type of composition he mentions is the frame within a frame effect. 

It's a great way to give an extra layer of depth to the photo while at the same time putting extra focus on the subject. I managed to achieve this once this summer as Erin walked through the main gate at Mount Rushmore. I was lucky enough to capture the moment by chance, but usually you need to plan out shots like this. 

In this picture her figure does not fall right on the rule of thirds line. In fact, she's quite a bit under it. But it slightly dwarfs her and makes Mount Rushmore seem even larger. The point is that in the end, art is art, and mathematics can't always determine its effectiveness. But it's a great starting point for discovering what might look cool.