Pleasing to the Eye

What do the human body, architectural structures, and galactic spirals have in common? Some scientists may claim that the answer is found in the Fibonacci sequence. We put the theory to a small (non-scientific) test.

Fibonacci

The man who first published a book about this irrational sequence was Leonardo Pisano also called Fibonacci. He published this beautiful sequence in his cookbook ‘Liber Abaci’ that explained food calculations for cooking. The Fibonacci sequence is known as the most beautiful mathematical equation. It is made up by a mathematical pattern that starts with zero and then evolves exponentially by finding the sum of the two previous numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 and so on…

These numbers can be visualized as geometrical constructions where the exponential factor is calculated by taking each number divided with the one before, which estimates what is popularly known as Phi [fi] :

a/b = (a+b)/a = 1.618 = φ = Phi

This number also referred to as the Golden Ratio, has been scientifically related to findings that prove a direct relationship between the Golden Ratio and beauty. Not so surprisingly, has the Golden Ratio been of interest to many people over the years including scientist Leonardo da Vinci and architect Le Corbusier.

Leonardo da Vinci

Da Vinci in relation to the book ‘The Divine Proportion‘ (Luca Pacioli, 1509), which he illustrated with geometric drawings and calligraphic letter templates using the Golden Ratio, illustrating what Pacioli described as “the secret of harmonic shapes“.
Some of da Vinci’s artistic works, such as Mona Lisa and the Vitruvian Man, also contain the Golden Ratio. The Mona Lisa has multiple golden rectangles – which dimensions reflect the Golden Ratio = 1:1.618 – for example the width of her face through her eyes to her mouth is a golden rectangle. And the rectangles that appear if you divide this rectangle around her face by drawing a line down her nose are golden. Coincidental? Maybe, maybe not.

Image: arthipstory.com

The Vitruvian Man illustrates the Golden Ratio throughout the dimensions of his whole body. E.g. the length of his hands, arms, and legs, as well as his height: As the measurement from the top of his head to his navel, as well as from his navel to his feet, is golden.

Image: geogebra.org

Golden Image Composition

The Fibonacci Spiral – as also shown in the images above of the Mona Lisa and the Vitruvian Man – is a spiral drawn from golden rectangles. It is a logarithmic spiral with an exponential growth factor of φ = 1.618.
Applying golden guidelines, such as the Fibonacci Spiral, can help guide appropriate cropping and placement of a subject in an image and it aids the composition of an organic and pleasing image.

Image: source.ggy.bris.ac.uk

Using a spiral as a guideline supposedly allows the spectator’s eye to wander along the curved line of the spiral and around the picture. Providing some kind of guided-tour of the image that ends in a central focus.
However, it can be hard to see how that really works. If you look at the Mona Lisa and the Vitruvian Man this means that the intentional focus respectively is supposed to be on the side of Mona Lisa‘s nose and in the Vitruvian Man‘s armpit.

Image composition can also successfully be guided through other composition principles e.g. the classic Rule of Third or the golden Phi Grid. However, the artist needs to pick one of the three (Fibonacci Spiral, Rule of Third or the Phi Grid), as they do not coexist in the same image.
All three composition principles, in different ways, aims to guide the eye of the viewer towards the important part of the image by framing the motive. Ideally used to balance the image and help storytelling.

Image Composition in Practice

Nevertheless, as image-makers, image composition is absolutely vital and obviously, we do not really use any specific one. Maybe it is because images are just as much about colors, light, motive, etc. And maybe we are just the exception to the rule, proving that great image can be created even without using generic image composition techniques.

Golden image non-golden composition © Nightnurse Images

Leave a Reply

Your email address will not be published. Required fields are marked *