Composition Talk: The Golden Ratio, The Fibonacci Sequence & The Rule of Thirds

Understanding composition fundamentals is so very important, but how many of us really do understand it and/or how to use it effectively? We all know when something doesn't look 'right', but how do we figure out why and how do we fix it? The following is an excerpt from a talk on composition that I give to all of my workshops. It's a bit technical, a bit boring maybe, but knowing these simple rules may be helpful to you when something not 'right' befalls you in the studio. Read on...this is going to be fun!

There is a reason why some compositions look better than others and that is because the relationships between the colors and forms in the work are proportionate and likely somehow follow one of the following rules: The Golden Ratio and/or The Rule of Thirds.

The Golden Rectangle

First, let's take a look at the Golden Ratio, also known as the Golden Mean and Golden Rectangle. The idea was started by the ancient Greeks, who believed that all things, both tangible and intangible, have a perfect state of being that define them and felt that one should always strive toward achieving this ideal state. Greek mathematicians, after repeatedly seeing similar proportions in nature and geometry, developed a mathematical formula for what they considered an ideal rectangle: a rectangle whose sides are at a 1:1.62 ratio. -Nelson. Ever wonder why the Mona Lisa is so pleasing to the eye when she's actually not conventionally beautiful? It's because she's perfectly proportionate from the tip of her nose to her knees..see how she fits perfectly into the Golden Rectangle in the image below.

This same idea goes for buildings and rooms, furniture and other forms of design. The closer to the Golden Mean they are, the more comfortable they will feel and the better they will look to us as humans.

This is because our bodies are also proportionate and also fit the Golden Ratio, we are all familiar with the image on the left which illustrates these proportions.

If you're really bored and want to test this theory out, consider your comfort level in the room you're in right now and rate it on a scale of 1-10. Now measure the room and see how close it comes to the Golden Mean. Interesting, huh? Now try this same exercise with one of your paintings that just isn't working and see what happens.

The Rule of Thirds

Next up is the Rule of Thirds, which states that if you divide any composition into thirds, vertically and horizontally, then place the essential elements of your image either along these lines or at the intersections of them, you'll achieve a more pleasing arrangement. Edmund Dulac was a stickler for this Rule and it's perfectly illustrated in his painting below of the Little Mermaid. Here Dulac has placed the column, figures and the horizon line perfectly along a line of thirds. The empty space leads the eye to the action in the composition, therefore creating a more interesting composition. These images were borrowed from the informative Art With Nelson.

Now, watch what happens when the rule is ignored and the action is centralized...kinda boring... and why is that? The column now dominates the image, which takes away from the figures, the source of the action in the image. The viewer's eye goes directly to the strong column shape and there is no empty space calmly leading the eye into the image.  In any painting, one design element must be more dominant than the others, which creates an imbalance, thus creating tension and attracting the viewer's eye. When the canvas is segmented in half, there is no imbalance or tension, which makes for a not so interesting composition.

Imbalance and tension can also be applied to many compositional elements of your painting including value, color and contrast.

The Fibonacci Sequence

Composition is a complicated, multi-faceted spooky mystery that baffles even the best of us, but knowing a few simple guidelines like The Golden Ratio and the Rule of Thirds can make all the difference. The Fibonacci Sequence is another tool for you to add to your composition toolbox and is the one I use most often in my own work.

The Fibonacci Sequence is named after Italian mathematician Leonardo of Pisa, also known as Fibonacci. The Sequence, illustrated below, begins at 0, 1 then those two numbers added make up the next number in the sequence, which is 1, then those last two numbers added make up 2 and so on into infinity. In addition to being used extensively in other mathematical formulas, these versatile numbers are also proportionately related to the Golden Ratio, have been used in poetry and are seen in the growth rate of biological forms nature such as trees, sunflowers, pinecones and pineapples, even human skeletal growth. When these numbers are utilized in any kind of art or design, that design is said to be more pleasing to the eye-it just feels right.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144....

I first learned about this Sequence as an undergrad in a class called Math for Design and I was fascinated. Later, when I was working as a textile designer, we applied these numbers to our stripe patterns, tile designs and anything else that required repetition. Last, I return to the Sequence again and again in my personal work whenever I have a question about repetitive elements or where an element should be placed within the painting.

To utilize the Sequence in stripe patterns, we applied the numbers to inches, mixed up the sequence and naturally applied color. Illustrated below is a stripe pattern (created in candy corn colors for Halloween : ) that is first shown in the sequence as it stands (1), then the numbers in the sequence are mixed up (2), then another stripe pattern in a random number of inches (3). Which is more pleasing?

Design 1

Design 1A

Design 2

Design 2A

Design 3

Design 3A

See the images below for examples of how you can apply this Sequence in your own work. I used this Sequence in grad school and beyond by applying inches to the spacing between repetitive elements as well as in the measurements of squares, circles and ovals themselves. See if you can find the Sequence in the images below. For me, the Fibonacci Sequence is just numbers to aid in measurement, but the idea also contributes to my content in that it represents growth in nature, time, intervals and gradual change. When you begin to apply this sequence to your own work, please let me know how it's working for you and if/how it's made your composition life easier.

It is important to keep in mind that all three of these composition tools are just tools and not necessarily rules that should impede your creativity. They should be kept in a drawer within your mental toolbox to use when you need them. As Francis Bacon is attributed to saying, "Knowledge is Power", so learn what you can and use it wisely.

Addendum: In response to Tess Stieben's comment regarding which stripe pattern is more pleasing, I added repeat patterns below to illustrate my response. Thank you, Tess!

Tess: Interestingly I prefer #3, it is dramatic, #1 is boring, #2 ok but #3 has a bold punch in the way the colors are divided making the dark contrast with the lighter colors.

My Response: Thanks for your comment, Tess. I see what you mean. Looking at it as is, without repeating, as if we were looking at a painting is quite lovely and I see what you’re saying. Now, think of the stripe as a repeat pattern, floor to ceiling running across a wall or even on a large sofa. Still think the same? The Fibonacci Sequence and the other ratios are used in design because they make the design more pleasing, more comfortable. The dynamic quality of pattern #3 may be more exciting as a painting, but not necessarily if it was covering the four walls of a room. While making paintings, this is also something to consider.

According to the theory, stripe pattern 1 and 2 would be most pleasing. You certainly could have chosen 3, which is totally arbitrary and follows no compositional rules. Feel free to comment, I would be interested to know which stripe pattern is most interesting to you and why.