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The Golden Ratio in Photography and Nature
The mathematics of the golden ratio are trivial compared to trying to figure out the psychology as to why that ratio is particularly beautiful to the human eye. The ratio can be expressed in many ways. Some of which are below. Take a calculator and work out each for fun and enlightenment. The ratio is correctly called Phi.
Phi is most simply understood by:
1 = Phi * (Phi -1)
[think of 0.xxx * 1.xxxx =1 where xxx is the same infinite decimal]
((5^.5)*.5)+.5) then do ((5^.5)*.5)-.5) and compare the numbers
In photography try taking the rule of thirds and making it a rule of golden ratios. Starting from the left make the 1st line at .309 ( 1/2 of Phi-1 ) and the second at .618 do the same from the bottom up. Now try to place objects on the intesections. You can do the same from the top down and from the right to the left. How you orient depends on the flow of the image. IE left -> right, right -> left, etc. This is much more complex than the rule of thirds but the results will be more pleasing to the mind's eye.
If you draw all 8 lines on a rectangle and then draw the lines for the rule of thirds, you will see how the rule of thirds is just an approximation of a golden rule but without the direction of flow being considered.
For Phi in nature read the following
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat2.html
Of course the primary url is: http://goldennumber.net/
Phi is most simply understood by:
1 = Phi * (Phi -1)
[think of 0.xxx * 1.xxxx =1 where xxx is the same infinite decimal]
((5^.5)*.5)+.5) then do ((5^.5)*.5)-.5) and compare the numbers
In photography try taking the rule of thirds and making it a rule of golden ratios. Starting from the left make the 1st line at .309 ( 1/2 of Phi-1 ) and the second at .618 do the same from the bottom up. Now try to place objects on the intesections. You can do the same from the top down and from the right to the left. How you orient depends on the flow of the image. IE left -> right, right -> left, etc. This is much more complex than the rule of thirds but the results will be more pleasing to the mind's eye.
If you draw all 8 lines on a rectangle and then draw the lines for the rule of thirds, you will see how the rule of thirds is just an approximation of a golden rule but without the direction of flow being considered.
For Phi in nature read the following
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat2.html
Of course the primary url is: http://goldennumber.net/
Charles Richmond IT & Security Consultant
Operating System Design, Drivers, Software
Villa Del Rio II, Talamban, Pit-os, Cebu, Ph
Operating System Design, Drivers, Software
Villa Del Rio II, Talamban, Pit-os, Cebu, Ph
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Operating System Design, Drivers, Software
Villa Del Rio II, Talamban, Pit-os, Cebu, Ph
Lynn
cmr, I take a calculator and beat it with a hammer for fun and enlightenment. I'm a lover, not a math major.
Catapultam habeo. Nisi pecuniam omnem mihi dabis, ad caput tuum saxum immane mittam
http://www.mcneel.com/users/jb/foghorn/ill_shut_up.au
To keep it at my level, which is below the FAA required minimum flying altitude: in nature lots of things grow to the ratio found in the Golden Mean; they do so because it's an efficient structure; therefore the Golden Mean is pleasing to our eye because it reflects what we see in nature.
So to get into the psychology of it, if things in nature for some reason grew in square blocks (1:1?), we'd find that ratio pleasing when replicated in photographs.
As Fish said, I may be full of c**p, but I do it with such authority!
Great discussion, 164, very enlightening.
Catapultam habeo. Nisi pecuniam omnem mihi dabis, ad caput tuum saxum immane mittam
http://www.mcneel.com/users/jb/foghorn/ill_shut_up.au
Lynn