Fibonacci’s Golden Ratio

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Most photographers may think immediately of the rule of thirds as their primary tool when composing their images. Some may suggest, however, that there is a more masterful tool for composing ones works, the Fibonacci Ratio, which is steeped in history and mathematical research.

Those who graduate from tutoring in photography will see a clear change in their work, from the snapshot scenario with subject slap, bang in the middles of their images to more aesthetic works which allow the subject to drift around the intersection of thirds or a power point. Enter Leonardo Fibonacci.

Fibonacci discovered that there was a ratio which was commonly found in nature, which was later referred to as the divine proportion or Phi. Apparently an attractive human face follows these proportions, and we see it subconsciously, recognising the perfection of the ratio in those we perceives as good looking.

Phi is considered so powerful that in today’s modern world large corporate organisations assume this ratio in much of their design work. Artists and architects have been using it for centuries. Some say much of Leonardo Da Vinci’s works were based on the Fibonacci ratio painstakingly applied, but let us not forget though Vitruvian Man based on squares and circles.

There is a concept called rabatment (also called rebatement) which states that in every rectangle there are two imaginary squares. The square is such a primal geometric, that the human brain apparently seeks these out in any image. Placing the subject on the inside edge of the square within the rectangle provide some comfort, provided, of course the rectangle ratio is not 2 : 1 (which would result in the two square intersections being in the middle. In a 3 : 2 sided rectangle (the size of old 35mm film) the rabatment lines are exactly on the intersection of thirds.


The power point determined on the left and a Phi matrix on the right

Its application in photography may be relevant. The golden ratio, as it is otherwise known, is based on a formula which will arrive at the factor 1 : 1.618 and will suggest that images should be sized about this ratio; and then, secondly, the subject should be oriented towards a golden spot or power point derived from ratio of rebatment intersections (both horizontal and vertical).

There is more. The diagonals, horizontals and verticals should fall on ratio intersections or at least be parallel to the intersection lines of the ratio. A few of the more popular photographic software programs incorporate these grids based on the golden ratio. So rather than using the intersection of thirds where your image is broken down into three equal areas horizontally and vertically, on a 1 : 1 : 1 (or 1 : 2) ratio that is, try a grid of 1 : 0.618 : 1 (or 1 : 1.618).

Applying the principle to an image… golden ratio power point determined and the resultant image

Confused? Do not be. To suggest that you might get a more pleasing picture from the more exacting Phi ratio, rather than the rule of thirds would be folly. Some suggest the rule of thirds was actually derived from this, being an easier approximation rather than the more finite ratio. Principally both ratios are doing one thing which does count, off center composition of the subject. Irrespective of the ratio used, both are more aesthetically pleasing than simply plopping the subject square in the middle.