Mundo Fractal

While doing some tweaks in old images I noticed that some images don’t really fit that well if just centered, mostly some spirals and images that have a certain detail that is the main “subject” of the image. If they are just moved a few bits to the side, they look more interesting. I’ve figured this by myself I guess since I never had any formal art training, and my older images seem to suffer more from this “problem”. It seems that I just did the fractal image and wherever it started, it stayed, I never tried to make it look better in terms of proportions or positioning. A small rotation the most, and that was it. But why this happens to the images? Why some appear to look better if their subjects are in certain places, mostly off-center? It can be sort of explained by the Rule of Thirds and also by the Golden Ratio.

The Rule of Thirds is well known in the photography world, and it’s not exactly a rule that you must follow all the time, it’s more like a guideline (same applies to the Golden Ratio). It says that your main subject(s) of your pictures/paintings etc. will look better if they are located 1/3 away from the image’s edges (I’d prefer to say though that the images might look better instead of will look better). It’s not a must follow rule, but it helps in some particular images.

And how do I know where is this specific location?

Try to imagine a simple grid over your image, with 2 horizontal and 2 vertical lines. The lines will be at 1/3 from the image edges, so just place the subject(s) of your picture where these lines are and you’ll be fine.

Image: Wikimedia Commons

If you place any of the subjects at any intersections of lines, it’s supposed to be even better. Look at this example above. The tree is in the intersection of 2 lines, and also the horizon is aligned to the bottom horizontal line. Some new digital cameras even have an option to display this grid in the LCD screen to help you align your photo based on this rule.

The Golden Ratio is a bit more complicated for me to describe it here, mostly because i’m not well versed in mathematics so I’ll try to get bits and pieces from some places trying to explain it in a not very formal way as much as possible. In very basic terms the Golden Ratio is a constant based on the Phi number (denoted by the greek letter Phi φ and equals to 1.618033988749895…). The ratio, or proportion, determined by Phi (1.618 …) was known to the Greeks as the “dividing a line in the extreme and mean ratio” and to Renaissance artists as the “Divine Proportion“  It is also called the Golden Section, Golden Ratio and the Golden Mean. Phi, like Pi, is a ratio defined by a geometric construction. Just as pi (Ï€) is the ratio of the circumference of a circle to its diameter, phi (φ) is simply the ratio of the line segments that result when a line is divided in one very special and unique way.

In this link they show you the relation between the Fibonacci numbers and the Golden Ratio – and the spirals! (I guess this is why it works so well when positioning spirals). Basically it says:  in the Fibonacci Sequence (0, 1, 1, 2, 3, 5, 8, 13, …), each term is the sum of the two previous terms (for instance, 2+3=5, 3+5=8, …). As you go farther and farther to the right in this sequence, the ratio of a term to the one before it will get closer and closer to the Golden Ratio. Like this: if we take the ratio of two successive numbers in Fibonacci’s series, (1, 1, 2, 3, 5, 8, 13, ..) and we divide each by the number before it, we will find the following series of numbers:

¹/₁ = 1,   ²/₁ = 2,   ³/₂ = 1·5,   ⁵/₃ = 1·666…,   ⁸/₅ = 1·6,   ¹³/₈ = 1·625,   ²¹/₁₃ = 1·61538… which gets closer and closer to the Golden Ratio.

For more details on the Golden Ratio, check the Wikipedia article about it, and also this very interesting site about the Phi number. There’s a lot of very interesting relations between proportions of artworks, animals, objects like the pyramids and this magic number, found in some links in these sites.

Of course these rules are just guidelines, but they seem to happen everywhere, from trees to churches, so they really seem to make a lot of sense. Start noticing some of these in common objects, known paintings, animals, and you’ll see how they can relate to your own pictures or artwork and how you can apply them in your work. I hope this small text could help you understand at least the basic concepts behind these rules, it’s a bit hard for me to explain these things being a non-mathematician but these are sort of important subjects that most people never paid attention to, simple details that can improve an image or composition. The links might help you with the more detailed explanations, for those that are interested in the math behind it.

Related Images:

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