The Golden Ratio
Scientists and mathematicians marvel over its geometrical virtuosity, architects and musicians wonder at its proportions and harmony and conspiracy nuts are convinced that its numbers hide secrets that the Illuminati will kill to protect. Many artists have been captivated by the idea that a simple ratio can have such a universal aesthetic appeal. A ratio derived through maths and reflected endlessly in nature.
So what exactly is the Golden Ratio and what makes it cognitively so pleasing and yet so shrouded in mystery?
The Golden Ratio is a ratio of 1:1.618, with the Greek letter Phi usually used to represent the number 1.618. Within art and architecture the ratio is most easily understood and utilised in the form of a rectangle, the so called Golden Rectangle. It has been argued that this golden rectangle turns up everywhere, from the design of the Great Pyramids and the Parthenon, to supermodels faces and insect mating habits… and I do mean argued. For every person extolling the virtues of the ratio there is another one waiting in the wings to tear them down.
Why is it considered beautiful? One of the latest theories is that it represents the best proportions for getting information to the brain. The assimilation of visual information often being imperative for a human or an animals survival. It is easier to scan side to side than up and down and consequently the shape often manifests itself in human made objects, giving the appearance of design. By extension, we as animals respond to things that make life easier for us, they give us pleasure. We respond to this pleasure and call it beauty.
As for the mystery, anything that has been around for two and a half thousand years is going to generate a fair bit of mystique. Natures fondness for the ratio and Dan Brown also help.
In 1509 a Franciscan Friar by the name of Luca Pacioli produced a three volume work called ‘De Divina Proportione’. Illustrated by his mate Leonardo da Vinci the work expounded on the the golden ratio and divine proportions with much Catholic religious significance (as Friars were wont to do)… enter Tom Hanks some 500 years later and much conspiracy and nonsense abounds.
To add to the opaqueness of it all, a group of numbers called the Fibonacci sequence is often added to the discussion. Even though they are not really part of the genesis of the golden ratio, by some intriguing mathematical gymnastics they end up being aligned to, and often confused with, the golden ratio. Again, along comes Tom Hanks to clear it all up…
Below is a golden rectangle and we can immediately see its relevance to cinematography.
It looks very similar to that enormous flat screen telly that sits pride of place in your man cave. The aspect ratio it is closest to is super 16 with a ratio of 1:1.66 but HDTV comes a close second at 1:1.77. And aspect ratio is really the starting point in creating a compelling photographic composition. While a painter starts in the middle of their canvas the cinematographer starts with the frame. Their first important decision is what to include within it and what to reject.
There is much more to this humble rectangle than just its outer dimensions. One of the things about the Golden Rectangle that sends mathematicians scrambling for their slide-rules is that if one were to remove a square from it, the remaining rectangle would also be a golden rectangle.
Not only is this mathematically curious, it also divides the frame (approximately) into a one-third / two-third split which can be used for placing key elements in a composition. If we then split the square in half we get a pattern that is very close to the ‘rule of thirds’ framing convention.
But wait, there’s more… if we go back to the image with the square and second rectangle and repeat the ‘cutting of the square’ in each resulting rectangle, we end up with the following pattern.
While it starts to look a bit like a Mondrian canvas before he coloured it in, there are a couple of ways that this sequence of squares and rectangles can be exploited compositionally. Using the blocks as areas to group or place elements within a frame for instance. Many websites use layouts similar to this.
Another way is to use it to create what is referred to as the Golden Spiral. Produced by joining the corners of the squares, it is a logarithmic spiral whose growth factor is again the golden ratio and whose shape remains unaltered despite the fact that the size of the spiral increases with each successive curve. Sometimes called the ‘miraculous spiral’ (after a chap called Jacob Bernoulli), this logarithmic spiral form has evolved in nature, appearing in forms such as shells, sunflowers, spiral galaxies, tree branches, tropical cyclones, certain types of broccoli…
How do you apply the golden spiral to your composition?
It builds on the aforementioned blocks within the frame, and acts as a lead, allowing the spiral to draw the eye to its centre, along with compositional items often aligning with the spiral itself. It is a guide at best. Some times it seems to work brilliantly...
If you browse the internet, most of the photographic examples demonstrating the spirals prowess are, to say the least, stretching the concept.
I mentioned earlier that you can’t talk about the golden ratio without referencing the Fibonacci sequence. A lot of people seem to think that the Fibonacci sequence is the golden spiral and visa versa. The Fibonacci sequence is a series of numbers that starts with a 0 and a 1 and whose each successive number is the sum of the previous two.
Ie 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,…
Together they create an array of squares whose side lengths are successive Fibonacci numbers and that approximates the grid from which a Spiral can be generated. They are also represented in nature, appearing in such things as branching in trees, the arrangement of leaves on a tree and in pine cones.
Not the same as the Logarithmic spiral but near as damn it…
So the Golden Spiral is not the Fibonacci Spiral… but it is… if you know what I mean.
Because it has been around for such along time and is so much apart of our visual language, (even if subconsciously), compositions based on the golden ratio can be a little predictable, a little conventional, even a little dull. Anticipated by the audience and holding little visual surprise, if we framed using only these conventions our work would be more akin to graphic design, more two dimensional than the three dimensions we are always trying to create with our photography.
We should understand it and make use of it, exploit it as part of our visual repertoire and combine it with the many other elements that make up our approach to composition.