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I learned about rule of thirds only recently, and it excited me a lot, and it seems to apply to a lot of situations.

But my question is why does it make pictures look more appealing? Does it have something to do with how our brain portrays images?

Is there any scientific explanation behind this?

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Did you look at the questions photo.stackexchange.com/questions/521/… or photo.stackexchange.com/questions/8965/… ? I'm not sure it's quite what you're after. –  Håkon K. Olafsen Feb 25 '13 at 20:27
    
For more information regarding the goldon ratio, read the wikipedia article en.wikipedia.org/wiki/Golden_ratio –  Michael Clark Feb 26 '13 at 0:14
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mattdm's answer to photo.stackexchange.com/questions/8965/… is one of the best explanations I have seen. –  Michael Clark Feb 26 '13 at 0:17
    
See also cogsci.stackexchange.com/questions/1627/… is-golden-ratios-association-with-perceived-beauty-a-myth –  Michael Clark Feb 26 '13 at 0:21
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6 Answers

The rule of thirds is a simplification of the golden ratio. Basically if you put something on 3rd's line like a person's eye or something on a horizon, the composition of the image will often conform to the golden ratio.

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The golden ratio occurs often in nature such as conch or snail shells, flower petals, and so on. Since it's identification (or definition) by the Greek's it's been used frequently in art and architecture ever since.

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The golden ratio really wasn't used much in art until Luca Pacioli wrote De Devina Proportione in 1509 A.D. (Leonardo da Vinci illustrated the book), but it was later pointed out what he advocates is the Vitruvian system of proportions. There has been a lot of controversy over whether elements of the Parthenon incorporate it or not. It depends on how many of the steps that surround it you include and how many you don't. If you include all of them it doesn't work. –  Michael Clark Feb 26 '13 at 0:27
    
Please see this answer. The probably inventor of the Rule of Thirds was almost certainly unaware of the Golden Ratio, or at least of the Golden Ratio as an aesthetic idea, since that wasn't invented until about 20 years after his death. That means that the idea that the Rule of Thirds is a simplification is a non-starter, particularly if we are looking for scientific proof. It would be much more accurate to say that they are both competing attempts at claiming that a specific magic number has a special aesthetic appeal. –  mattdm Feb 26 '13 at 19:14
    
Could you outline how you see the golden ratio in the flower pattern you've given as an example? The curve is not a characteristic Fibonacci curve. –  mattdm Feb 26 '13 at 19:21
    
Perhaps, but the Rule of Thirds it still often produces golden ratio compliant images. Intended or not, it can be argued that it is still a less complicated method of employing the golden ratio. Also, the golden ratio (as an aesthetic) is just a name for a compositional layout that was commonly found in art and nature. It just might not have been a formal concept before a certain period, but it was still there. –  cadmium Feb 26 '13 at 19:29
    
If you mean "golden ratio" to be shorthand for "centered composition tends to be static", then sure. But if that's the case, I think you have it backwards — that's more like a relaxed reading of the rule of thirds, whereas the golden ratio usually tends to be about the specific division and its derivatives (like the specific spiral). Your answer seems to tend more toward that, and (despite repetition in books and on the Internet) there's very little evidence for it. –  mattdm Mar 1 '13 at 18:21
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A design teacher from a Danish design school lectured us at a phd course about composition of our scientific powerpoint presentations. He also mentioned that we should never place two figures side by side, but one or three. He used an example of 2 vs 3 candle lights as well. He argued that it had to do with how our eyes move around when inspecting the scene.

If there are two halves the eyes will ping-pong back and forth, never finding rest. One principal point will let the eyes rest on that, and three will make the eyes inspect one by one and rest on the most prominent. Which means that not only should you make a division of three, but also compose the scene such that there is a dominant part to catch the attention, and make sure the other parts are complementary.

Nowadays people like this do eyetracking to research how we inspect images, but Mr Smith mentioned in What is the "Rule of Thirds"? doubtfully had such research available in the 18th century. Maybe they found the reason later for what he intuitively found.

Smith's other guideline about not having two equally prominent lights in teh scene falls in line with the designer's theory.

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The Rule of Thirds isn't anything like a scientific 'law': it is just a guideline, a rule of thumb. Whether or not a photo taken using it is 'better' than another without is subjective.

It is also only one of a number of similar guidelines such as the golden ratio and splitting the scene into triangles. It is up to you as the photographer to decide what looks the best.

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There is much science behind the Golden Ratio (Golden Section), of which the Rule of Thirds is a simple approximation. The ratio (known as phi) of approximately 1.618 occurs time and time again in nature and mathematics.

The question is if there is any science behind the aesthetics of that ratio. Sure it occurs in nature, the Greeks thought the ratio was beautiful, etc., but is there any actual proof behind it? It would seem very difficult to scientifically prove something that is subjective, and research would seem to be inconclusive.

A study of famous paintings concludes:

A statistical study on 565 works of art of different great painters was done and it was calculated the ratio of the 2 sides of a paintings. Assuming that all the painters under discussion enter in a statistics with equal weights it is shown that the average value obtained for the ratio of the sides is 1.34. This value, determined experimentally is significantly different from the value of the Golden Section F=1.618, which is a theoretical ratio, obtained from an abstract, mathematical theory, which supposedly ought to impress on a painting a supreme harmony

Fechner, Godkewitsch, and Benjafield conducted studies where subjects were asked to rank various rectangles on attractiveness. These studies have contradicted each other, but overall there seems to be a preference towards rectangles that have sides whose lengths are near the golden ratio.

Dr Mario Livio, a scientist and art fanatic, has written an article on the subject, and concludes:

The history of art has nevertheless shown that artists who have produced works of truly lasting value are precisely those who have departed from any formal canon for aesthetics

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It really doesn't show up in nature all that much either, outside of idealization. –  mattdm Feb 26 '13 at 1:13
    
Golden ratio seems to be related to Fibonacci numbers, which can describe things as diverse as spiral nautilus shells, breeding of rabbits, arrangement of flower petals and seed heads. But as I think you're saying, if you measure enough things, you can find any ratio you want –  MikeW Feb 26 '13 at 1:18
    
Yes, that's pretty much what I'm saying. :) Read some more on this here: lhup.edu/~dsimanek/pseudo/fibonacc.htm –  mattdm Feb 26 '13 at 19:16
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It's possible that we're conditioned to find images composed with the rule of thirds pleasing or "correct". It's very prominent in historical works of art & architecture, modern photography, design, etcetera. I've even observed people being criticized for not following it in photo competitions. It could be considered sacred simply because of conditioning and use, and not because of any inherent property of its own. I don't know if I'm starting a whole chicken-and-egg thing here, though.

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There is no need for scientific explanation for rule of thirds, because it is a fact.
Probably you saw image of Vitruvian Man drawn by Leonardo da Vinchi. This drawing is sometimes called Cannon of proportions. Why this picture is so interesting to us? Actually it is based on ideal human proportions, and that is a very good source for understanding proportions and implementing it not only in drawing, but architecture, design, picture, statuary and so on.
For example: the maximum width of the shoulders is a quarter of the height of a man. Better you achieve this in your picture composition, your pictures are going to be better. And this is not only connected with human proportions, it's connected with nature, humans, things etc...

Vitruvian man

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What does the shoulders being one quarter of the width of a man have to do with a rule of thirds?!! –  MikeW Feb 26 '13 at 0:15
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No need of scientific explanation because it is a fact? I think that is a tautology. If it is a fact, it should be explainable surely? –  MikeW Feb 26 '13 at 0:25
    
The Vitruvian Man is called that because it's an illustration of Vitruvius's system of proportions, which has little to do with either the rule of thirds or the golden ratio. –  mattdm Feb 26 '13 at 1:16
    
OK, my bad sorry –  D4Am Feb 26 '13 at 11:12
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