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. 

A Knight in Golden Armor

Get it? Chris KNIGHT? GOLDEN ratio? I digress.

I'm a big fan of this article, mainly because our man Chris Knight found an unpretentious, non-patronizing way to tell us not-so-savvy-with-a-camera people how to make small adjustments to better our poorly composed scenes. He understands what a film/television student really needs: big pictures with not a lot of words underneath.

This is a circle.

I've had a slew of high school teachers attempt to explain the golden ratio, and all I really got out of it was that I would never pursue a career in math and George Clooney was scientifically gorgeous (duh).

Symmetry is sexy.

But along came Mr. Knight with his diagrams and BAM! I am now a member of the club known as "Basic Understanding of Rectangles". Shot a little too crowded? Take ten paces to your left and try again. Subject look a little boring in the center of the frame? Shimmy over to your right and the interesting shot is yours.

The most adorable Rule of Thirds.

I was most affected by one of the smaller points of the article. Knight explained the basic technique of using a frame within the frame (a tunnel, a tree, a window, etc...). But, you can also use darkness as a frame. If you want to highlight a subject in the distance, keep your foreground dark. I always found lighting tricky, but this quick little tip really helped keep the basics of lighting in perspective.

Obviously these concepts are only the basics of composition, but it's a great start to the more complex aspects of setting up a shot. So put down your "Composition for Dummies" book, check out Chris Knight's "The Ultimate Guide to Composition", and explore the depths (of field... ha...) of framework. 

Composition & Bokeh

The part of these articles that I was drawn to was bokeh. I personally love the aesthetic of bokeh. Knight says “Obsession with bokeh is bad for your photography.” I somewhat agree with this statement. Too much can become repetitive and boring, however, I think if you use it in the right way and for the right photograph it can be amazing. Sometimes it’s better to see all the details and textures throughout the frame and other times those details don’t add anything. It really comes down to personal preference and judgement.

For example, in this photograph I think the bokeh works very well because it would be too busy with every detail in focus. You would get lost in all of the details and wouldn’t be drawn to the intended subject.

Chris Knight did a great job explaining some complicated concepts. Talking about composition rules such as the Baroque Diagonals, the Golden Ratio, the Rule of Thirds can become overwhelming. I like how he stated these are rules but are not rules at the same time. If you follow these rules it will not always lead to a provoking photograph. However, it is obviously important to read about and understand the rules for reference. I loved how well Knight explained what each rule was and how to apply most of them. After reading these articles I am more confident in what they are and how to integrate them. I’m looking forward to incorporating this new information into my future class, personal, and professional projects.

Chris Knight's Photography Stuff Article

First, hats off to Chris Knight for writing in two fairly easy to read articles about a bunch of concepts I've been struggling to grasp for something like three years of college in an easy to digest way. Takes skill to right about all this in an articulate way that isn't dizzying to read.

He started off strong by making it clear that these are NOT rules. I mean, yes, they are, but they don't determine what makes an image resonate. Photos have to have a core to them that is worth building upon for any of these guides and tricks to mean anything. I can compose a perfectly lit pile of dog poop that abides by every single one of these rules, even some fancy use of negative space, and it would still just be dog poop. That is the most important thing to take away from this article. We're all in an institution of learning. Going in, we assume that whatever we're taking away from all this is what we'll live by day in day out. These rules MUST be binding and exact, telling, if we're paying $50,000 a year for them. This is what leads a young 20 something coming out of film school to hate Spider-Man 2 because "they didn't like the lighting." It's a real corrosive and limiting mindset and I'm glad that Chris immediately did away with it before diving deep into the article.

On the actual principles themselves? Man this was fantastic. Aside from a few instances (He just defined the golden ratio and then gave no explanation at all of how to use it, what it means or how not using it could be powerful and that was infuuuuriating. He was similarly withholding on Sinister and Baroque lines.), Chris both teaches what and how. WHAT Chiaroscuro is and why it's evocative, HOW to use complementary colors and why it can be meaningful, WHY symmetrical compositions can be both empowering and damaging to a shot. If he went a bit deeper on a few of these I would have been happy but overall he handled all these very well.

Perhaps the principle that interests me most of the lot is negative space. Just the way the mind works in that regard, where the focus of the shot isn't really the point of the shot and yet at the same time without it it would not be nearly as powerful, is really interesting. I just want to figure out the variety of ways I could use this to find some differing understandings of a scene. The idea of symmetry also interests me. What makes a good shot of symmetry stand out and what makes a bad one bore you to your iPhone. These subtle little nuances are the kind of tool I want ready at disposal in my brain to bring life to whatever I'm working on. Not the sort of thing I remember I can use but that I know on instinct to do. I suppose that'll only come from constantly employing them but reading stuff like this is the first step.

"The Ultimate Guide to Composition"

Chris Knight's "Ultimate Guide to Composition" covers the five types of compositions: center, the rule of thirds, golden triangles, diagonals, and the golden ratio/golden rectangles/golden spiral.

Center composition puts the subject in the center of the frame. If it's done well, the symmetry and intricate detail makes it aesthetically pleasing. I really enjoy this composition, but it is very hard to create a center composition that is very visually appealing and memorable. For inspiration, here are some of my favorite Wes Anderson's shots that use the center composition:

The rule of thirds divides the image into nine equal parts. Using the rule of thirds makes it easier to create an interesting image, as the off-center subject creates more tension in the shot.

The golden triangles divide the image into three or four triangles with a strong diagonal line, called the "major line," and another diagonal line that goes from one corner to the major line, connecting perpendicularly. That line is called the "reciprocal line." This creates a more dynamic photograph, as seen below. Just look at that bridge and its diagonal line. Powerful stuff.

The two types of diagonals are Baroque and Sinister. Baroque are read from left to right and Sinister are read from right to left.

Baroque:

Sinister:

The golden ratio is all about geometry and proportions. The largest shape is divided by a perfect square, and the remaining portion is the same proportions as the first shape. Then that shape is divided by a perfect square, and so on and so forth. It creates somewhat of a spiral on the frame:

This ratio also works on other shapes and is seen in the Great Pyramids, Stonehenge, the Parthenon, on the human body, seashells, and hurricanes.

Knight also focuses on other important concepts and theories that help make photographs more dynamic, such as a frame within a frame and the Gestalt Principles.

A frame within a frame is an extremely important theory that uses objects to frame the main subject. It's good to have a foreground frame that is darker than the background because our eyes go to the brightest parts of the image. 

Some of the Gestalt Principles are figure/ground, proximity and grouping, symmetry and balance, similarity, continuity, and closure.

Figure/ground means the subject and everything surrounding it is very contrasting. Using either chiaroscuro, strong contrasts between light and dark, and/or negative space, it enhances the illusion of depth.

When elements are placed together, they become a group. When similar objects are placed together, it becomes a whole. And elements with similar characteristics can be viewed as a group or pattern and can be very nice to look at.

Symmetry creates an equilibrium. As long as you make the center composition purposeful and dynamic, the symmetry is strong and appealing. Also, balance does not always mean perfect symmetry.

Continuity deals with leading lines. They can be straight or curved, but they're not alway obvious. They guide the viewer's eye to continue through the object.

Last, but not least, is closure. The subject is not fully seen, but the image gives your brain enough to form the rest. It "leaves a little to the imagination."

For me, learning the five main compositions was very helpful. I've learned the rule of thirds before, but learning and seeing the other compositions in use will help me frame my own shots and understand why certain photographs are more aesthetically pleasing than others.