Fibonacci Spiral and Photography

Leonardo Bonacci (Fibonacci) was an Italian mathematician, sometime in the middle ages. He is best known for his sequence of numbers called Fibonacci Sequence. This is a series of numbers where each consecutive number is a sum of the prior two numbers (1,1,2,3,5,8,13,21,34,55….. and so on). Though these numbers had been known to Indian mathematicians many centuries earlier, they were introduced to Europe by Fibonacci and caught the media attention some years back with the publication of Dan Brown’s novel, The Da Vinci Code. Painters have long used this sequence knowingly or unknowingly to create beautiful artworks and now photographers over the past few decades are understanding to use it.

The word is that the Fibonacci Numbers exist in the nature everywhere around us. They also appear in branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple,  the number of flower petals, an uncurling fern, sea-shells and even in pine cones.

The Fibonacci numbers can be plotted in a rectangular frame. A tiling with squares whose side lengths are successive Fibonacci numbers is shown in the image below-

Fibonacci Blocks


A Fibonacci Spiral can be created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling, starting from the inner most squares. The Fibonacci Spiral thus formed looks like the image below-

Fibonacci Spiral

The basic principle in using it in photography is to place the subject on the lines of the Fibonacci Spiral. A lot of other common composition rules like the ‘Rule of Thirds’, de-centering the subject, creating curved leading lines  and many of their derivatives are based around the Fibonacci Spiral (Composition Clichés – Part I).

Our minds interpret these images as pleasing. The Fibonacci Spiral aligns our mind with forces which we are still not aware of. This is also known as the Golden Mean, Phi, or Divine Proportion.

In common photography, the images can be composed using it in various orientations. It can be flipped and/or turned clockwise or anti-clock wise. The mirror image of the spiral works as well as the spiral itself. The mirror image can also be further flipped and/or rotated in increments of ninety degrees.


Cows with Fibonacci Spiral

(The head of the second cow falls in the smallest squares of the Fibonacci Spiral with the trees roughly forming the large arc. The partially hidden head of the second cow creates drama and the head of the first cow falls in the consecutive larger squares.)


Stairs with Spiral

(This photograph of the stairs also approximately follows the Fibonacci Spiral. The spherical head of the post falls just outside of the smallest squares.)

Placing the various objects of interest as per the Fibonacci Spiral is an easy way to get a powerful composition. Try placing the main element of the composition near the beginning of the spiral (beginning is where the spiral curves a lot or where the squares corresponding to the first numbers were located). Next compose in a manner that all the secondary elements and helping elements fall near the spiral as it moves out towards the edge of the frame. (More about these elements in composition and telling a story – Story in a Photograph)

Sometimes I wish that the cameras had an option to overlay a Fibonacci Spiral on the viewfinder or liveview and flip and/or rotate it around. It could have been more useful than the rule of thirds grid that is commonly available. Adobe used to permit overlaying the spiral on images for assistance (I have not used their softwares for quite sometime now so can’t comment on the recent offerings).

Among the photographers who commonly used this composition technique (knowingly or unknowingly), Henri Cartier Bresson takes the top slot. Do check out his compositions to get an insight into his work. On the other hand, there are a small group of photographers who consider this as just a coincidence and a figment of imagination when it comes to photography. Choice is yours.


Image of Fibonacci Boxes – 克勞棣 / Wikimedia Commons / CC BY-SA 4.0


Further reading-

Composition Clichés – Part I
Composition Clichés – Part II
Composition Clichés – Interpreting Images

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