The Golden Ratio in Photography and Nature

cmr164cmr164 Focus! I need Focus!Registered Users Posts: 1,542 Major grins
edited August 27, 2008 in Technique
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/
Charles Richmond IT & Security Consultant
Operating System Design, Drivers, Software
Villa Del Rio II, Talamban, Pit-os, Cebu, Ph

Comments

  • cmr164cmr164 Focus! I need Focus! Registered Users Posts: 1,542 Major grins
    edited February 18, 2004
    Molsondog wrote:
    I keep tossing this up against the wall, but it won't stick. What does this mean in engrish?
    My post was only up for 7 minutes before you replied. You can not possibly have done the math or drawn the lines on a rectangle let alone read the followup URLs I provided. Put in some effort baldy.gif and the results will be worth it. thumb.gif
    Charles Richmond IT & Security Consultant
    Operating System Design, Drivers, Software
    Villa Del Rio II, Talamban, Pit-os, Cebu, Ph
  • ShakeyShakey Rule of Thirds?Phhhhhthh! Registered Users Posts: 1,004 Major grins
    edited February 18, 2004
    Nobody said anything about math when I signed up!:D
  • lynnmalynnma Moddess Emeritus Homosassa, Florida (Paradise)Registered Users, Retired Mod Posts: 5,163
    edited February 18, 2004
    cmr164 wrote:
    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/
    Charles.... I understand the concept but I'm so tied up in the math I'm ending up guessing where to draw the lines!! I'm LOUSY at math. I've printed it all out to study, and I did visit the links re Fibonacci bunnies etc. I think it's basically rule of thirds shoved over a bit (I hope).
    Lynn
  • wxwaxwxwax Immoderator Registered Users Posts: 15,471 Major grins
    edited February 18, 2004
    cmr164 wrote:
    Take a calculator and work out each for fun and enlightenment.

    cmr, I take a calculator and beat it with a hammer for fun and enlightenment. I'm a lover, not a math major. rolleyes1.gif
    Sid.
    Catapultam habeo. Nisi pecuniam omnem mihi dabis, ad caput tuum saxum immane mittam
    http://www.mcneel.com/users/jb/foghorn/ill_shut_up.au
  • wxwaxwxwax Immoderator Registered Users Posts: 15,471 Major grins
    edited February 18, 2004
    Fascinating links. Thanks for posting them, cmr.

    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! rolleyes1.gif

    Great discussion, 164, very enlightening.
    Sid.
    Catapultam habeo. Nisi pecuniam omnem mihi dabis, ad caput tuum saxum immane mittam
    http://www.mcneel.com/users/jb/foghorn/ill_shut_up.au
  • lynnmalynnma Moddess Emeritus Homosassa, Florida (Paradise)Registered Users, Retired Mod Posts: 5,163
    edited February 19, 2004
    wxwax wrote:
    Fascinating links. Thanks for posting them, cmr.

    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! rolleyes1.gif

    Great discussion, 164, very enlightening.
    so true Sid, attractive people are only that because of the Golden Mean, most efficient breeding structure with best demensions for reproducing the species... now if only I could fine my calculator... I have graph paper ready, I'm going to prove out the Golden Mean for compostion.
    Lynnnod.gif
  • lynnmalynnma Moddess Emeritus Homosassa, Florida (Paradise)Registered Users, Retired Mod Posts: 5,163
    edited February 19, 2004
    the golden mean...ish? rule of thirds? ish?headscratch.gif
  • lynnmalynnma Moddess Emeritus Homosassa, Florida (Paradise)Registered Users, Retired Mod Posts: 5,163
    edited February 19, 2004
    lynnma wrote:
    the golden mean...ish? rule of thirds? ish?headscratch.gif
    No.. this more rule of thirds I think... or maybe not.. I'm thirds challenged!!
  • GREAPERGREAPER Major grins Registered Users Posts: 3,113 Major grins
    edited February 19, 2004
    I always hated fractions.
  • kometkomet Major grins Registered Users Posts: 117 Major grins
    edited February 24, 2004
    wxwax wrote:
    cmr, I take a calculator and beat it with a hammer for fun and enlightenment. I'm a lover, not a math major. rolleyes1.gif
    Wow!:ha
    komet gives light so that you may find the way.
  • Bob HughesBob Hughes Big grins Registered Users Posts: 18 Big grins
    edited July 15, 2008

    Another good resource for the Fibonacci sequence is this radio show, aired on BBC radio 4 last November:

    http://www.bbc.co.uk/radio4/history/inourtime/inourtime_20071129.shtml
  • geospatial_junkiegeospatial_junkie Livin' In 3/4 Time Registered Users Posts: 707 Major grins
    edited July 15, 2008
    Excellent post! I really learned something today. Often you see images in photography books that do not quite fit the rule of thirds (intentionally or not), but seem to be oddly pleasing.

    I really like your explanation too. Thanks for sharing, and I'll definitely give this a try.thumb.gif
    "They've done studies you know. Sixty-percent of the time, it works every time."

    My Website
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  • OffTopicOffTopic Searching for the light Registered Users Posts: 521 Major grins
    edited July 15, 2008
    geospatial junkie, you might enjoy playing around with this composition adjuster tool. It allows you to overlay the golden mean, golden triangles or golden spiral and analyze your photo (or a crop to your photo) accordingly.

    Also a wealth of additional info on the golden ratio and composition in this collection of articles.
  • geospatial_junkiegeospatial_junkie Livin' In 3/4 Time Registered Users Posts: 707 Major grins
    edited July 15, 2008
    AWESOME! Thanks. I'll definitely take a look at this.:D
    "They've done studies you know. Sixty-percent of the time, it works every time."

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  • geospatial_junkiegeospatial_junkie Livin' In 3/4 Time Registered Users Posts: 707 Major grins
    edited July 15, 2008
    Lori,

    Do not take this this wrong way but.... I LUV U!!!!!!iloveyou.gif The calculator is such a great tool to give an initial preview of each theory. I am in your debt.
    "They've done studies you know. Sixty-percent of the time, it works every time."

    My Website
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  • OffTopicOffTopic Searching for the light Registered Users Posts: 521 Major grins
    edited July 15, 2008
    :D Glad you like it! I stumbled on that tool a few years ago. I think it really makes things click to actually see it in action rather than just read about it... how many people are actually going to take out a ruler and measure (as you can see from the earlier responses to this thread)? rolleyes1.gif
    Mention math and most people's eyes glaze over. Since photographers are visual people, having a tool that allows you to overlay the golden ratio on your own photos and then see the difference that different crops make to the image makes it easier to understand.
  • geospatial_junkiegeospatial_junkie Livin' In 3/4 Time Registered Users Posts: 707 Major grins
    edited July 15, 2008
    I am fortunate with the respect that I do not fear math. I have a photo in my gallery with farm fields, a barn, and hay bales that follows this rule. I was composing for the rule of thirds, but I think now, it fits the golden mean rule perfectly (as well as the golden triangle) for the hay bales.

    332003691_hJVXn-X2.jpg

    The rectangles line up almost perfectly in the calculator you've shown me.
    "They've done studies you know. Sixty-percent of the time, it works every time."

    My Website
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  • OffTopicOffTopic Searching for the light Registered Users Posts: 521 Major grins
    edited July 15, 2008
    I'm a bit of a math geek myself. Love that photo, very peaceful. You have some beautiful images in your gallery.
  • geospatial_junkiegeospatial_junkie Livin' In 3/4 Time Registered Users Posts: 707 Major grins
    edited July 15, 2008
    As do you Offtopic. I like your landscapes!
    "They've done studies you know. Sixty-percent of the time, it works every time."

    My Website
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  • achambersachambers mudtographer Registered Users Posts: 255 Major grins
    edited July 15, 2008
    Kind of funny, I entered this photo in the recent challenge. For some reason it really spoke to me, wasn't sure why. Just ran it through the little tool up above and viola, I can see why. Kind of scary how our minds work.

    332434340_LYrpE-X2.jpg
    Alan Chambers

    www.achambersphoto.com

    "The point in life isn't to arrive at our final destination well preserved and in pristine condition, but rather to slide in sideways yelling.....Holy cow, what a ride."
  • geospatial_junkiegeospatial_junkie Livin' In 3/4 Time Registered Users Posts: 707 Major grins
    edited July 15, 2008
    Laughing.gif... great stuff!rolleyes1.gif
    "They've done studies you know. Sixty-percent of the time, it works every time."

    My Website
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  • achambersachambers mudtographer Registered Users Posts: 255 Major grins
    edited July 15, 2008
    If you flip the spiral over the it follows the back of the guy bending over. Really weird huh?
    Alan Chambers

    www.achambersphoto.com

    "The point in life isn't to arrive at our final destination well preserved and in pristine condition, but rather to slide in sideways yelling.....Holy cow, what a ride."
  • geospatial_junkiegeospatial_junkie Livin' In 3/4 Time Registered Users Posts: 707 Major grins
    edited July 15, 2008
    That is strange. I can't wait to actively start looking for these patterns. It should be fun!
    "They've done studies you know. Sixty-percent of the time, it works every time."

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  • achambersachambers mudtographer Registered Users Posts: 255 Major grins
    edited July 15, 2008
    Still playing, the triangle is spooky too.

    332448372_b4v5y-M.jpg
    Alan Chambers

    www.achambersphoto.com

    "The point in life isn't to arrive at our final destination well preserved and in pristine condition, but rather to slide in sideways yelling.....Holy cow, what a ride."
  • cmorganphotographycmorganphotography I can haz fotergrafs? Registered Users Posts: 980 Major grins
    edited July 17, 2008
    achambers wrote:
    Still playing, the triangle is spooky too.
    Both of those tools centered on his crotch. rolleyes1.gif
  • achambersachambers mudtographer Registered Users Posts: 255 Major grins
    edited July 17, 2008
    Both of those tools centered on his crotch. rolleyes1.gif

    And look where your eyes wentrolleyes1.gifrolleyes1.gifrolleyes1.gif it works.
    Alan Chambers

    www.achambersphoto.com

    "The point in life isn't to arrive at our final destination well preserved and in pristine condition, but rather to slide in sideways yelling.....Holy cow, what a ride."
  • cmorganphotographycmorganphotography I can haz fotergrafs? Registered Users Posts: 980 Major grins
    edited July 17, 2008
    achambers wrote:
    And look where your eyes wentrolleyes1.gifrolleyes1.gifrolleyes1.gif it works.
    clap.gifclap.gif Um... but you posted the picture and you really liked it and you didn't know why.... turn that pointing finger right back on yourself mister!!
  • achambersachambers mudtographer Registered Users Posts: 255 Major grins
    edited July 17, 2008
    clap.gifclap.gif Um... but you posted the picture and you really liked it and you didn't know why.... turn that pointing finger right back on yourself mister!!

    But, but, but ... I was looking at his arms, yeah, his arms.
    Alan Chambers

    www.achambersphoto.com

    "The point in life isn't to arrive at our final destination well preserved and in pristine condition, but rather to slide in sideways yelling.....Holy cow, what a ride."
  • geospatial_junkiegeospatial_junkie Livin' In 3/4 Time Registered Users Posts: 707 Major grins
    edited July 17, 2008
    Definitely... the arms....
    "They've done studies you know. Sixty-percent of the time, it works every time."

    My Website
    My Photo Blog
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  • cmr164cmr164 Focus! I need Focus! Registered Users Posts: 1,542 Major grins
    edited August 27, 2008
    Definitely... the arms....

    Laughing.gif!!!

    Glad to see my blast from the past is collecting junkies. And what a great tool. I'm glad i swung by today.
    Charles Richmond IT & Security Consultant
    Operating System Design, Drivers, Software
    Villa Del Rio II, Talamban, Pit-os, Cebu, Ph
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