Leonardo Fibonacci was an Italian mathematician that lived c.1200. He was responsible for introducing the Fibonacci sequence - lots of maths behind this. (If you really want to look at the maths try this - Maths re Fibonacci and nature ) This looked at sequences and patterns that occur in nature. When developed as a ratio it can be shown graphically as a pattern of squares or a spiral.
Naturally occurring pattern
It has been recognised that images that conform to this pattern are pleasing to the eye. This may also contribute to other names that are given to it; "The Golden Ratio" and "Divine Proportion". It does not mean that everything has to have a spiral within it just that an image is more likely to be pleasing if elements sit within the pattern of boxes or spiral. As well as paintings it is also found in architecture such as the Parthenon.
It has been developed into a ratio - 1:1.618 that is commonly used by artists etc. This ratio maked it easier to use for compostion as it can itself be represened as a grid.
It is similar to the "Rule of Thirds" but the grid is not evenly spaced across the area. As with the previous rule the composition will appear pleasing if the lines and intersections are used as focal points. The "Rule of Thirds" probably derives from this as a quick and easy method for composition.
The Olympus Pen that I use can be set up to overlay this grid over the screen to aid composition while preparing to take a photograph. Lightroom 3 also has the option to use this as an overlay to aid post-production cropping of images.
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