The Golden Ratio in Photography and Nature

[cmr164]

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/

[cmr164]

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 http://www.dgrin.com./images/smilies/baldy.gif and the results will be worth it. http://www.dgrin.com./images/smilies/thumb.gif

[Shakey]

Nobody said anything about math when I signed up!:D

[lynnma]

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

[wxwax]

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. :rofl

[wxwax]

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! :rofl

Great discussion, 164, very enlightening.

[lynnma]

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! :rofl

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.
Lynn:nod

[lynnma]

the golden mean...ish? rule of thirds? ish?:scratch

[lynnma]

the golden mean...ish? rule of thirds? ish?:scratchNo.. this more rule of thirds I think... or maybe not.. I'm thirds challenged!!

[GREAPER]

I always hated fractions.

[komet]

cmr, I take a calculator and beat it with a hammer for fun and enlightenment. I'm a lover, not a math major. :rofl
Wow!:ha

[Bob Hughes]

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/

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_junkie]

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

[OffTopic]

geospatial junkie, you might enjoy playing around with this (http://photoinf.com/Golden_Mean/photo-adjuster.html) 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 (http://photoinf.com/Golden_Mean/) of articles.

[geospatial_junkie]

AWESOME! Thanks. I'll definitely take a look at this.:D

[geospatial_junkie]

Lori,

Do not take this this wrong way but.... I LUV U!!!!!!:lust The calculator is such a great tool to give an initial preview of each theory. I am in your debt.

[OffTopic]

: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)? :rofl
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_junkie]

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.

http://Cartographica.smugmug.com/photos/332003691_hJVXn-X2.jpg

The rectangles line up almost perfectly in the calculator you've shown me.

[OffTopic]

I'm a bit of a math geek myself. Love that photo, very peaceful. You have some beautiful images in your gallery.

[geospatial_junkie]

As do you Offtopic. I like your landscapes!

[achambers]

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.

http://achambers.smugmug.com/photos/332434340_LYrpE-X2.jpg

[geospatial_junkie]

LOL... great stuff!:rofl

[achambers]

If you flip the spiral over the it follows the back of the guy bending over. Really weird huh?

[geospatial_junkie]

That is strange. I can't wait to actively start looking for these patterns. It should be fun!

[achambers]

Still playing, the triangle is spooky too.

http://achambers.smugmug.com/photos/332448372_b4v5y-M.jpg

[cmorganphotography]

Still playing, the triangle is spooky too.
Both of those tools centered on his crotch. :rofl

[achambers]

Both of those tools centered on his crotch. :rofl

And look where your eyes went:rofl :rofl :rofl it works.

[cmorganphotography]

And look where your eyes went:rofl :rofl :rofl it works.
:clap :clap 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!!

[achambers]

:clap :clap 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.

[geospatial_junkie]

Definitely... the arms....

[cmr164]

Definitely... the arms....

LOL!!!

Glad to see my blast from the past is collecting junkies. And what a great tool. I'm glad i swung by today.