Rule of Thirds
The Rule of Thirds can be applied to create balanced and interesting photographs. This is achieved by splitting the what we can see through the viewfinder into 9 equal squares using two vertical lines and two horizontal lines as shown above. This creates four points of interest where the lines intersect. This allows the photographer to compose the elements of the image around these, using the lines as guides to create balance.
Further research suggests that we viewers of photographs are more inclined to view these points of interests naturally, rather than simply just view the centre of the image on first sight. From this, it seems clear why photographers would apply this rule when creating their photographs.
The Golden Ratio is hailed as 'the perfect number', a design principle design principle based on the ratio 1 to 1.618. The application of this principle provides a strong composition to the photograph, attracting viewers to it as it is perfectly balanced from their perspective.
It is said that the Golden Ratio appears throughout nature, which is why it is pleasing to the human eye. Due to the organic nature of the Golden Ratio, viewers of the photograph will be naturally inclined to view all the particular points of interest of the photograph. This could be beneficial, as we could say viewers of our photographs do not want to work hard to see the beauty of it.
The above diagram shows the Fibonacci Spiral. Created by splitting the frame up into squares in the manner of numeric sequences (discovered by the 12th Century Mathematician, Leonardo Fibonacci). A series of diagonal points are then visible, which allows for a spiral to be formed over the frame. This spiral is then used to compose a photograph, placing points of interest around the spiral. The viewer will be led around the image naturally, so the viewer inherently sees the balance and beauty of the photograph.
Phi Grid
Here, the black lines show the the Rule of Thirds Grid and the blue lines show the Phi Grid. The reason why this method of composition follows that of the Golden Ratio is because the frame is not divided into equal thirds (1:1:1), instead the Golden ratio has been applied resulting in a grid that is divided in to sections 1:0.618:1, showing a grid where the intersections or points of reference are displayed more centrally in the frame.
The Fibonacci Spiral and Phi Grid may be implemented depending on what we are taking a photograph of. I find that the Fibonacci Spiral is most easily shown in the works of portraits; take the Mona Lisa, below, as a classic example, whilst the Phi Grid is more evident when viewing landscapes.

This is my own personal opinion, however, both the
spiral and the grid can be applied interchangeably,
depending on the preference of the photographer.
I personally find it difficult to visualise the spiral when looking through the viewfinder. You can see the use of the Fibonacci Spiral being applied on a landscape below:
I have researched how it to more easily visualise the Fibonacci Spiral when out taking photographs for my photo essay. I found the example below to be the most clear and concise:
If we strip the spiral down so we can visualise the smaller rectangle in the top-left hand corner of image above, we can more easily visualise the below diagram when taking a photograph.
We would want to be able to see several key focus points within this smaller rectangle in order for the image to be composed implementing the golden ratio. If we take a look back to to the image that compares the Rule of Thirds Grid to the Phi Grid, we can see that this smaller rectangle can be applied in many places across the frame, allowing a level of flexibility in creating an image that follows the Golden Ratio.
We could say that the Rule of Thirds grid can be quite restricting, and does not occur as naturally the Golden Ratio.

I also think the Rule of Thirds Grid is also difficult to apply when we consider the image of the dancers on the left. We can see that this image has been composed to canted. This would be difficult to achieve when trying to apply this rule as the horizon (where the floor and wall meet) are not horizontal, unlike the other images we have looked at so far.
Dynamic Symmetry
A diagonal line, when compared with the horizontal or vertical
line, is the most dynamic of all three. Take for example, in our seminar this week, when Micheal asked us how we felt when he turned the speaker to an angle and asked us how we felt. We said it made us feel 'uneasy' or 'uncomfortable'.
When we look around in nature we could say anything diagonal is unstable - full of a dynamic energy or tension, which is why we answered his question the why we did that day.
In Jay Hambidge's book The Elements of Dynamic Symmetry, Lesson 5 explains what is known as 'The Diagonal'. If we were to view a diagonal line across the frame, we can also visualise a line which is perpendicular too it. The angle of where these lines are to intersect creates a 90 degree angle. We can see these 90 degree intersections in the image above. In the example below by Henri Cartier-Bresson (1932), we can see that the perpendicular lines intersect on the knee where the man lying down. Other points of interest have been places along these lines, resulting in an aesthetically pleasing photo.
Diagonals can also provide a photograph with a sense of direction and movement.
We can see the use of diagonals here used to create a sense of direction. The edge of the platform and the lines that run through the roof, along the tracks and along the train carriage itself direct the viewer to view outside of the train station in the distance. We can follow these lines naturally to view all the points of interest.
The image above shows how diagonals create a sense of movement. Here, the train tracks are running one way, while the man appears to be walking across an invisible perpendicular line in a different direction (parallel with the line created by the shadow). This emphasises the mans movements.
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