Divine Proportion

Discussion in 'Photography' started by seank, 9 Sep 2012.

  1. seank

    seank

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    I have been doing research over the last couple of months to see if I can get my photographs to look better. In doing so, I also decided to share this with others as to help them improve their photographs too.
    Hope this helps:


    @Helga this is what I mentioned to you some months ago


    A Mathematical Guide to Aesthetics
    Have you ever observed a really profound piece of art (or maybe even a movie poster) and wondered why it was so compositionally pleasing? The most likely reason is that the artist intentionally (or unintentionally) employed the use of the Divine Proportion (also known as the golden ratio, the golden section, and part of the Fibonacci series). The Divine Proportion is a little-known phenomenon that suggests that there’s a mathematical equation that’s consistent with the aesthetics of good composition.



    Composition

    [​IMG]

    A technically perfect photograph can turn out to be a boring, uninteresting image. That is not to say the image should be flawed to be great. But, even flawed images can be intriguing and cause the observer to stop and think.
    A truly great photo will invoke several different emotions and tell a story as the eyes wander in and out of each level in the photograph.
    Every single photo I have ever taken is flawed in some aspect. The key to improving is learning from those flaws and making changes in future situations that will hopefully result in a better photo. I will often return to a site a dozen times or more to try and capture an image I am happy with, and still not succeed. Sometimes, the session produces images I think are better than the previous session, and other times, it seems like a wasted trip. In reality, even failed sessions are productive, as I learn some techniques that do not work.

    There are entire studies devoted to composition. It involves every aspect of photography and all the infinitely intertwined interactions that go on between the camera, the photographer, and the scene.
    It is not the purpose of this section to provide a comprehensive review of composition, as that is something slowly acquired through trial and error. This section's purpose is to get us started in thinking about what goes into each photograph. More importantly, the goal is to keep composition in mind each time we press that shutter release.

    Rule of Thirds

    Which photo is more interesting?


    [​IMG] [​IMG]


    Ask this to a group of people, and some will say the left one, but a majority will like the right one better.

    Why is this?

    Both images come from exactly the same photo. One is simply cropped differently than the other.
    In the left photo, the subject is in the dead center. There is a reason it is called the dead center.

    Objects placed in this position tend to appear static and uninteresting.

    The camera is not a rifle, and we are not out for target practice.

    We want to create a photo which is interesting and moves the viewer. Spare the poor hermit and move him to a better location.
    If we divide the frame into thirds and place the subject near one of these lines, the result is a much more pleasing composition. The subject does not necessarily have to be at the intersection, and we do not need to whip out our measuring tape, but approximate placement along these lines will generally improve the overall composition of the photograph.
    This rule is the most commonly taught rule, as it results in the largest improvement in a photo's overall composition.


    The Golden Spiral

    [​IMG]

    Leonard Fibonacci noted that in a sequence of numbers starting with, 1, 1 the sum of the last two numbers approaches the golden ratio:
    1+1=2, 2+1=3....


    The resulting sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
    Move the mouse cursor over the image to the left to see the underlying golden rectangles.


    1, 1, 2, 3, 5, 8, 13, 21, 34, 55... A rectangle with sides in a 1:1 ratio is a perfect square.
    1, 1, 2, 3, 5, 8, 13, 21, 34, 55... The second rectangle in the Fibonacci sequence is in a 1:2 ratio - two squares side-by-side.
    1, 1, 2, 3, 5, 8, 13, 21, 34, 55... The ratio of the next numbers in the series, 2:3, should be familiar. It is the aspect ratio used by 35mm cameras. A print size of 4x6" is simply a multiple of this 2:3 ratio.
    Spira Mirabilis: Arranging these rectangles in a spiral pattern creates an equiangular spiral - the radial angle increases geometrically, but the polar angle increases arithmetically. This pattern is seen commonly throughout nature, not only in its likeness to a nautilus shell, but also in snails, flora, and even the human embryo. It is often seen in man-made structures and works of art as well. Photographers refer to this as the "Golden Spiral."


    The Golden Triangle

    [​IMG]


    The Golden Triangle is a derivative of the Golden Spiral discussed above. Its vertices are the midpoints of the sides of the Golden Rectangle.
    Placing diagonals along these lines can make an otherwise static subject appear more dynamic.


    Some examples of these above mentioned ways in taking photographs:


    [​IMG]

    [​IMG]

    [​IMG]

    Credit must go to Gregory T. Ho from Ximina's Photography, as I have contacted him and ask permission to use his photos and text.

    Please peruse his website at Ximina's Photography

    Hope this will help some of you in getting that extra flair to your images
     
    Last edited: 9 Sep 2012
    Omnitank, butcherman and Mc like this.
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  3. Mc

    Mc

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    Nice guide thanks.
     
  4. seank

    seank Thread Starter

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    Some more info for those who want to learn a bit more:

    Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold, the second we may name a precious jewel.
    --Johannes Kepler
    [​IMG] In a paragraph towards the end of his 1611 essay On the Six Cornered Snowflake Kepler mentions the “Divine Proportion" (Golden section) and the "fibonacci sequence” in practically the same breath as flowers and pentagons.
    "It is in the likeness of this self-developing series that the faculty of propagation is, in my opinion, manifest: and so in a flower the authentic flag of this faculty is shown, the pentagon." (emphasis added)
    What does Kepler mean here?
    [​IMG]
    First, we examine the nature of the logarithmic spiral, for reasons that will become evident below.
    The 17th century mathematician Jakob Bernoulli named the figure at right the Spira mirabilis or "miraculous spiral" and assigned it the following motto: "Eadem mutato resurgo" ("although changed, I rise again the same").
    The logarithmic spiral does not change its shape as its size increases. This feature is known as self-similarity. If we could zoom into the coils of the figure near the origin and enlarge them, they would fit precisely on the larger spiral.
    The spiral has another extraordinary property: turning by equal angles increases the distance from the pole to the spiral by equal ratios.


    What are fibonacci numbers?
    In the "fibonacci sequence," referenced by Kepler, each number is the sum of the two proceeding numbers (1, 2, 3, 5, 8, 13, 21...). Therefore, the sequence can be called a "self-developing" series. ​
    Interestingly, dividing two adjacent fibonacci number (8/5 or 21/13, for example) by each other produces increasingly precise approximation of the "Divine Proportion," which we will explore below, as the numbers grow larger.
    Why does Kepler mention flowers?
    Scientists, beginning with Leonardo da Vinci, observed that the displacement of leaves around a stem occurs in patterns defined by the fibonacci series.
    This phenomenon is known as "philotaxis."
    In the case of roses an angle that is congruent to 360 degrees by the Divine Proportion (137.5 degrees) separates the petals from each other.
    [​IMG][​IMG]
    [​IMG] In other plants the number of leaves measured around a screw-type displacement between one leaf and the leaf directly above it, and the number of rows separating the two are both fibonacci numbers.
    The same phenomenon occurs in pinecones and the hearts of sunflowers.


    Credits and copyright: The Divine Proportion
     
  5. seank

    seank Thread Starter

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    Building of the Golden Spiral
    If you’re ready to take advantage of the Divine Proportion in your designs, here are some easy steps to create your own “approximate” golden spiral in Adobe Illustrator.

    STEP ONE:

    The first step is to draw a square with all equal-length sides (hold the Shift key when using the Rectangle tool to constrain the shape to a square). Let’s begin by drawing the largest square first. Tip: Make sure you Fill is set to None so you can see all the shapes as you draw.
    [​IMG]
    STEP TWO:
    Next, from the bottom center of the square draw a circle out until the edge of the circle touches the top corners of the box. You can use a guide to help locate the center of the square, and then hold Shift-Option (PC: Shift-Alt) to draw a perfect circle from the bottom center of the square outward.
    [​IMG]
    STEP THREE:
    On the right side of the square, draw a rectangle from the top-right corner down to the bottom of the first square and out to the edge of the circle. This shape is now 0.618 the size of the main square.
    [​IMG]
    STEP FOUR:
    You can now delete the circle. From the top-left corner of the rectangle that you just drew in Step Three, draw a square (hold the Shift key) until you reach the right side of the rectangle.
    [​IMG]
    STEP FIVE:
    Continue drawing these squares in a sort of clockwise downward spiral, starting from the bottom right of the last square that you just drew.
    [​IMG]
    STEP SIX:
    To test the proportion accuracy, draw a line from the top-left corner to the bottom-right corner, and then draw a line from the top-right corner to the bottom point of that middle line. These lines should cross at the corner point of each shape that they intersect.
    [​IMG]
    STEP SEVEN:
    Lastly, starting at the lower-right corner of the smallest square (not the small rectangle), begin a line spiraling out, intersecting the outside corners of each square (as shown here) until it reaches the bottom-left corner of the overall shape.
    [​IMG]
    Now we have a group of shapes that are geometrically representative of the golden ratio. Once you’ve created a complete and accurate golden spiral, you can now save it as a custom shape in Illustrator or Photoshop and use it in your design work as a compositional guide. You can also use it to overlay existing art to understand other artists’ use of composition.
    [​IMG]
    Credits and copyright goes to: The Divine Proportion Layers Magazine Layers Magazine

    A Brilliant magazine I often read as well as get tips for those extra effects.....

    Unfortunately the Magazine closed, but there is still a wealth of info for your perusal:
    Here is the letter from Scott Kelby as to why they had to close doors:
    From The Editor by Scott Kelby Layers Magazine Layers Magazine
     
  6. Gerhard DP

    Gerhard DP

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    There are quite a few rules like the rule of thirds that can be used to do scaping too.
    The freshwater scaping guys have been using it for some time.

    You know when you scape and scape and it all just seems wrong for some reason?
    It is because you are breaking the rules and your subconscious mind sees it.
     
  7. seank

    seank Thread Starter

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    Agreed, since me starting this research, I have noticed it in many buildings, even in my garden......
     
  8. Gerhard DP

    Gerhard DP

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    Everything in nature is arranged to 1.618 and you grow up seeing it al the time, flower petals, trees and even peoples faces. The closer your face is to this ratio the prettier you will be to others :)

    Romans used it a lot in their building.

    The rule of thirds is just a quick reference for the golden ratio.
    Basic art classes teach all these techniques and more to new students. Viewing your fotos and tank in the same way will
    make it look a lot better without changing the content.
     
  9. ChrisRaubs

    ChrisRaubs

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    Wow!!! @seank ,,

    Thanks for sharing. This is very nice!:thumbup:
     
    Last edited by a moderator: 26 Nov 2015
  10. seank

    seank Thread Starter

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    Pleasure, hope you benefit from it
     
  11. 459b

    459b Moderator MASA Contributor

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    Thanks for posting, very enjoyable read.
    That pic of the hermit on the monti is brilliant.
     
  12. Evo R

    Evo R

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    Thanks for sharing all this great info! :peroni:
     
  13. Helga

    Helga

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    Wow @seank,

    Brilliant thread. Excellent additional info to the photographic course I did. Should'nt we make this a Sticky??? I'll save it under my favourites anyway :thumbup:
     
    Last edited by a moderator: 26 Nov 2015
  14. seank

    seank Thread Starter

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    Pleasure Helga. How did the course go?
     
  15. butcherman

    butcherman Moderator MASA Contributor

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    Great read! I hope to apply the same technic to my pictures in future
     
  16. Helga

    Helga

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    The course was really good. Was a 6 weeks Intermediate. Would love to do the advanced course as well. Was actually thinking, maybe I should go into photography as a hobby, less stressful than Reefing ;)
     
  17. seank

    seank Thread Starter

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    Lol, agreed, with pics you just delete the bad ones, with reefing there are no room for error, as mistakes cost lives
     
  18. seank

    seank Thread Starter

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    Have any of the members used this technique yet, how about posting some pics
     
  19. Toolboysa

    Toolboysa Moderator

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    I have. Only on holiday photos so far. I dont have any corals to photograph atm

    Photos come out awesome. Thanks for sharing your inside info on the subject
     
  20. seank

    seank Thread Starter

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    post some here. Would be nice to see
     
  21. carlosdeandrade

    carlosdeandrade

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    Plan on using it on how to place my base rock in my tank. Will take a pic of it on my veranda (mock up version).
     
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