Mathematics in Image Composition”

The Law of Thirds

Image used from The image at first appears to break the law of thirds spoken of in the article, but you will notice that the clear lines in the image, at the edge of the statue and the edge of the table lie nearly on the thirds. The image also shows the power of symmetry placing the gavel in the center draws our attention to the objects in the background.

By Scott Hamilton

Last week I wrote about the use of mathematics in photography and promised to talk about an additional aspect that applies not only to photography, but to other two-dimensional works of art. There are mathematical rules that can be applied to the composition of artworks such as photographs, paintings, sketches, and even film-making. Most of us do not realize that when we view a piece of art, the way our brain interprets the image has a lot to do with mathematics and symmetry.

If you take any introductory photography course, one of the first things you are taught on image composition is called the rule of thirds. The rule of thirds basically means to split the image into thirds, both horizontally and vertically. This will create four points of intersection in the image. These points of intersection help to draw the eye away from the center of the image to the subject of interest.

The art of image creation, in my opinion, is nearly the opposite of music composition. Two weeks ago I wrote about how our brain interprets sound as pleasant (music) or unpleasant (noise) based on several rules around the composition of music. We find music pleasing when it follows the mathematical order. Imagery is quite the opposite; our minds find art more pleasing when it breaks the rules of symmetry and seems less organized.

The law of thirds breaks the natural tendency to focus on the center of the page. This is true not only for artwork, but if you take the time to look, the advertisements in this paper that draw the most attention are the ones that lack symmetry. Our minds are drawn to the misalignment and we tend to focus our attention on the thing that is out of center. The rule of thirds is a great way to remember to try and avoid symmetry in artwork. That being said, there are times where symmetry is an excellent tool in artwork. For example an artist may create a work of art that is perfectly symmetrical except for one small difference in a part of the image. Our eyes will be drawn to the small difference.

The second rule one learns on image composition is very similar to the law of thirds and also deals with symmetry. You should always try to balance elements in your imagery. For example, you would not want to take a photo of a person on a plain background, following the law of thirds, leaving two-thirds of the image completely empty. The blank space looks too unnatural and draws our attention away from the subject. Empty space with no imagery looks unnatural in most cases, but as with all “rules” related to art there are always exceptions. The one exception I can think of is images of the objects in the sky; an image of a rainbow or the moon off-centered with nothing but sky on the rest of the page is pleasing because it is expected.

The third rule is related to linear objects in the image. Imagery with only straight horizontal and vertical lines does not allow our brains to see any depth in the imagery. Since a majority of imagery based artwork is two-dimensional, we have to create the appearance of depth in the image to make it interesting. We live in a three-dimensional world and expect to see depth in the world. Making sure to include diagonal lines in imagery gives us that perception of depth. These lines are not always clearly visible lines, but can be created by things in the image. A great example is a picture of a herd of cattle; there are no visible diagonal lines in the image, but since there are cattle that overlap and cattle standing nearer and farther away from the camera, it creates the diagonal lines of depth in the image.

These are just three of the first rules in image composition, but you must never forget that in any form of art, the first rule is that there are no rules, so make what you find beautiful. Just don’t be too surprised if you find that your most beautiful creations follow at least some of the rules. Until next week, stay safe, learn something new and create something beautiful.

Scott Hamilton is an Expert in Emerging Technologies at ATOS and can be reached with questions and comments via email to or through his website at

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