Some people are apt to assert that the rule of thirds is the same as the golden mean. The proportions are close, but not the same. In addition, most of the various golden mean methods emphasize a primary, off-center subject; the rule of thirds does not suggest an order of precedence among subjects. The rule of thirds involves only straight lines, while some golden mean offers the Fibonacci spiral for placement. The rule of thirds offers four points of interest and four division lines for the main elements; the golden mean can be used to proportion elements more deeply embedded in the composition.

In the following image, a 2:3 image, divided in vertical thirds and horizontal thirds, is shown in pink. A frame conforming to the golden ratio is shown in green.

Thirds vs. Golden Mean

You do not have to use either of these methods to construct your compositions. In four years of art school, not a single instructor or textbook mentioned either of these methods. They are relatively quick and easy ways to begin thinking about composition and the placement of elements. For this reason, many photographers benefit from trying them.

Also see: The Golden Mean

Also see: The Rule of Thirds

To see how the Fibonacci sequence relates to visual space, consider the following representation. We stack squares based on the numbers in the sequence. The first two numbers are one, so the first two squares have sides equal to one unit. The next number is two, so this square lines up nicely with the first two. As the arrangement becomes larger, it begins to fall into a recognizable, repeating pattern.

Creating an arc that traces the edges of each block leads us toward the center in what is called the Fibonacci spiral. Starting with just a few blocks, the spiral is not yet very accurate, but we can extrapolate what the spiral should look like given an infinite number of iterations. Artists call the center of the spiral the cradle and mathematicians call it the pole.

Fibonacci spiral

Consider how Phi applies within a composition. The ratio between lines and masses will correspond to the golden ratio. In the previous illustration, the ratio of line B to line A is Phi, 1.618. For example if line B is 16.18 inches long, line A is 10 inches, 16.18/10 = 1.618. The borders of the outside rectangle follow the same proportion. The area in pink is a square. The remaining rectangle is divided in the same way, by creating a square whose proportion to the overall rectangle is Phi. Each subsequent rectangle can be subdivided, and so on, to infinity.

Golden ratio, Fibonacci Spiral, and Cradles

The preceding diagrams are a form of armature, or a framework on which a photograph can be composed. The armature can be flipped horizontally, vertically, or rotated 180 degrees and it would still be in accordance with the golden mean. Additional golden mean armatures can be applied to subsections of the image. One way to use the golden mean in a composition is to place the design elements along the lines indicating the golden rectangles and Fibonacci spiral. Also, the golden mean should appear in the subjects. This means showing body proportions and other compositional elements that correspond to the golden ratio when compared to one another. For example, if you photograph a model laying on a rock, you might choose a rock that is 1.6 times her length rather than one that is twice her length. A group of rocks with a visual mass totaling this ratio would also suffice, especially if the subdivisions of the rocks also conform to the golden ratio.

Some photographers follow the golden mean religiously and sometimes sacrifice everything else in their photos in the process. Others reject the golden ratio outright, deeming it an over-practiced fad and actively avoid it. I prefer to produce images that I find interesting and innovative, rather than photograph according to a formula-but I also apply lessons learned from the classic methods of composition.

Also see: Rule of Thirds

Also see: Comparing Golden Mean and Thirds (soon to be published)

The rule of thirds states that you should place your subjects and other important compositional elements along the division lines between the nine squares formed by dividing both vertical and horizontal edges into thirds.

An application of the rule of thirds

A standing subject would be placed on one of the two vertical lines, and the horizon would be placed on one of the two longitudinal lines. A subject can be aligned either through its center or along one of its edges. The most important compositional elements would be placed on the four points created by the intersection of these lines. Bear in mind that placing subjects along all four lines runs the risk of a static composition with symmetry from top to bottom and left to right.

Of course, there are many great photographs and other visual compositions throughout history that do not conform to this. Nonetheless, the rule of thirds is a good start for anyone who is learning composition, and this knowledge can help you produce satisfying images at any stage in your career.

Also see: Golden Mean (soon to be published)

Also see: Comparing Thirds to Golden Mean (soon to be published)

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