Here are few of them:
Simplicity
When you look at a scene with your naked eye, your brain quickly picks out subjects of interest. But the camera doesn’t discriminate – it captures everything in front of it, which can lead to a cluttered, messy picture with no clear focal point. What you need to do is choose your subject, then select a focal length or camera viewpoint that makes it the centre of attention in the frame. You can’t always keep other objects out of the picture, so try to keep them in the background or make them part of the story. Silhouettes, textures and patterns are all devices that work quite well in simple compositions.
Balancing Elements
Placing your main subject off-centre, as with the rule of thirds, creates a more interesting photo, but it can leave a void in the scene which can make it feel empty. You should balance the "weight" of your subject by including another object of lesser importance to fill the space.
Negative Space
Negative space is the area which surrounds the main subject in your photo (the main subject is known as the "positive space"). Negative space defines and emphasises the main subject of a photo, drawing your eye to it. It provides "breathing room", giving your eyes somewhere to rest and preventing your image from appearing too cluttered with "stuff". All of this adds up to a more engaging composition. Negative space provides breathing room and draws your eye to the main subject. Image by Ruben Alexander. When used properly, negative space provides a natural balance against the positive space in a scene. Getting this balance right is tricky and rather subjective, but it's something you'll get better at with time and practice.
Leading Lines
When we look at a photo our eye is naturally drawn along lines. By thinking about how you place lines in your composition, you can affect the way we view the image, pulling us into the picture, towards the subject, or on a journey "through" the scene. There are many different types of line - straight, diagonal, curvy, zigzag, radial etc - and each can be used to enhance our photo's composition.
Symmetry and Patterns
We are surrounded by symmetry and patterns, both natural and man-made., They can make for very eye-catching compositions, particularly in situations where they are not expected. Another great way to use them is to break the symmetry or pattern in some way, introducing tension and a focal point to the scene.
Viewpoint
Before photographing your subject, take time to think about where you will shoot it from. Our viewpoint has a massive impact on the composition of our photo, and as a result it can greatly affect the message that the shot conveys. Rather than just shooting from eye level, consider photographing from high above, down at ground level, from the side, from the back, from a long way away, from very close up, and so on.
Background
How many times have you taken what you thought would be a great shot, only to find that the final image lacks impact because the subject blends into a busy background? The human eye is excellent at distinguishing between different elements in a scene, whereas a camera has a tendency to flatten the foreground and background, and this can often ruin an otherwise great photo. Thankfully this problem is usually easy to overcome at the time of shooting - look around for a plain and unobtrusive background and compose your shot so that it doesn't distract or detract from the subject.
Depth
Because photography is a two-dimensional medium, we have to choose our composition carefully to conveys the sense of depth that was present in the actual scene. You can create depth in a photo by including objects in the foreground, middle ground and background. Another useful composition technique is overlapping, where you deliberately partially obscure one object with another. The human eye naturally recognises these layers and mentally separates them out, creating an image with more depth.
Framing
The world is full of objects which make perfect natural frames, such as trees, archways and holes. By placing these around the edge of the composition you help to isolate the main subject from the outside world. The result is a more focused image which draws your eye naturally to the main point of interest.
Cropping
Often a photo will lack impact because the main subject is so small it becomes lost among the clutter of its surroundings. By cropping tight around the subject you eliminate the background "noise", ensuring the subject gets the viewer's undivided attention.
There are also these rules:
Rule of Thirds (Avoid the Middle)
Imagine that your image is divided into 9 equal segments by 2 vertical and 2 horizontal lines. The rule of thirds says that you should position the most important elements in your scene along these lines, or at the points where they intersect. Doing so will add balance and interest to your photo.
Golden Ratio and Golden Rectangle
The golden ratio, also known as the divine proportion, is an irrational mathematical constant with a value of approximately 1.618033987. If the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one, then the quantities are said to have a golden ratio. [ a+b/a = a/b = 1.618033987 ]
Golden triangles
Divide your image diagonally from corner to corner, then draw a line from one of the other corners until it meets the first line at a 90 degree angle. Now place your photograph’s elements so that they fall within the resulting triangles.
Here are few examples:
References:
http://www.smashingmagazine.com/2010/02/09/applying-mathematics-to-web-design/
http://cios233.community.uaf.edu/design-theory-lectures/layout_lecture/
http://www.photographymad.com/pages/view/10-top-photography-composition-rules
http://www.digitalcameraworld.com/2012/04/12/10-rules-of-photo-composition-and-why-they-work/
http://www.digital-photo-secrets.com/tip/3372/18-composition-rules-for-photos-that-shine/
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