# Weekly topic: Golden Ratio



## tsunami (Jan 24, 2004)

For this week's weekly topic, I have chosen to write an article on the golden ratio with visual examples. At the end of the article, I invite everyone to participate in a Golden Ratio excercise.

The invention of the golden ratio dates back to the classical era, created by the ancient architect Vitruvius, who states:

"For a space divided into equal parts to be agreeable and aesthetic, between the smallest and largest parts there must be the same relationship as between this larger part and the whole space."

Since the Rennaisance period, painters have used and applied the formula to other subjects as well. The golden ratio has even been applied to human faces!

The ratio can be summarized as the small is to the large as the large is to the whole. Mathematically, the whole is 1, the large is 0.618, and the small is 0.382. When drawn on an aquarium, there should be four intersections which refer to the four possible focal points. These intersections can also denote other key areas of negative or positive space which are not necessarily the focal point of the tank. Also, the horizontal lines can be used in creating a horizon line (the line dividing the water column from the plants or substrate). All these statements will be clarified below with the visuals.










In this concave layout with Rotala sp 'Green' and Glossostigma elatinoides, where is the focal point? The focal point lies on the top left hand intersection on the branch where the two mounds of Rotala meet. More typically, a concave layout will have the golden intersection fall on the negative space (i.e. background) between the two mounds.










In this layout, the upper right hand intersection seems to be the focal point ---and also the vanishing point, where the plants end and the negative space (black background) begins. The top horizontal line also fits perfectly with this aquarium's horizon line.










For my third example, I chose a Dutch aquarium. The focal point seems to fall on the colorful Ammania gracilis on the top, right hand side. Is this the correct focal point?

Keep in mind, that these rules are not hardset and that there are several other guidelines you can follow in creating your aquascape. The golden ratio is just one tool out of many.

How to apply the golden ratio to your tank:

When first setting up your aquarium, I find it useful to take out a ruler or measuring tape and mark the aquarium with a marker. Measure the length of the aquarium and multiply that length by 0.618. For example, a 36 inch long tank x 0.618 = 22.25 inches. Draw a vertical line. Now, measure 22.25 inches from the opposite side. Draw another vertical line. Measure the height of your tank from bottom to top and multiply that by 0.618. Draw a horizontal line. Measure the height from top to bottom this time and repeat. When all is said and done, you should have a square in the dead center of your tank with four intersection points just like the aquariums pictured above. If you want to use the golden ratio, now you know where exactly is the focal point, where the horizon line should be located, etc.

Discussion #1:

What draws the eye the most in the three photos? What do you think is the focal point?

Discussion #2:

Using a photo of your aquarium, apply the golden ratio lines. What do you find? Does your aquascape use the golden ratio? Post here to discuss!

Carlos

(thank you Jay for editing and drawing the lines on the pictures for me!)


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## Sir_BlackhOle (Jan 25, 2004)

Very interesting post! I must not have much artistic talent in me because I am never able to "see" the focal point. I understand that it is supposed to be a spot your eye is drawn to when you look at something, but for me it never works this way. I can sit down and attempt to find a focal point in a picture/painting and unless it really really stands out, I am unable to determine where the focal point is. Looking at the three photos, I am able to see the focal points listed, but I dont understand what makes them the focal point. I find my eye looking all over the tank and not lingering anywhere specific...... :roll:


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## Gomer (Feb 2, 2004)

Call me a skeptic, but I think a lot of the so called focal points are just points we convince ourselves to be toe focal point. I have definately seen plenty of scapes where there were definate focal points and some definately followed the golden ratio.


I do think however, that we are falsely generating the illusion of a focal point just because there "has to be a focal point" ..and that it must lie on a golden ration bound/intersection.

For example, in the first picture, I really don't see a strong focal point at all. I see an "area of interest" in the darkened center, but no focal point. I can see a very weak "after taste" of a focal point that tsunami mentions, but that is it. If I had to find a focal point, his pick probably would be mine....but that is only if I had to find one.

In the second picture, I definately see horizontal banding that fit within golden ratio boundries. The bit of emptiness IMO is not what I'd call a focal point. Sure your eye get drawn there because of its visual interuption, but I see no reason to WANT to focus there. If anything, I'd call the crypt? in the lower left the focal plant, although there are no real visual ques leading you there.

In the last scape, I can see how you may wan tto call the ammania a focal point since it lies on the intersection of golden lines, but my eyes are drawn all over the place in this tank equally well.


..so why do I babble?...well...I think a focal point should be obvious. If you ask yourself "Is this the correct focal point? ", then I think the point of the focal point was l somewhat lost if a focal point was intended. Slapping a few golden ratio lines on an image and calling an interesection the intended focal point of the aquascape IMO is the wrong way to do it.

Focal points IMO are like showcased plants, rocks, wood etc that draw attention to themselves. It could be purely by them selves, or by leading lines. Not all scapes were designed with focal points. Must we HAVE TO FIND a focal point in all scapes?


..well,..those are my 2 cents. ..probably more or less than some want to hear  I mean no offence if anyone takes offence


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## tsunami (Jan 24, 2004)

For those who have trouble locating the a focal point on the images, look at the image. Then close your eyes for 15 seconds. Open them again -- what is the first thing that catches your eye? 

Remember that "focal points" can be subtle. It doesn't have to be a flaming red plant on the intersection. It can even be a dark space in the undergrowth, etc. Many times, there are lines in an aquascape which lead the eye to this point --it can be pieces of wood, a row of orange plants leading up to a red plant, etc.

Nice points, Gomer. However, please do realize that I said the intersections of the golden ratio do not necessarily have to denote a focal point. They can be used as a guideline for locating other aquascaping elements/areas of interest as well. 

I did notice that the two Cryptocoryne bunches in the second picture lie on the two lower intersections. One of my questions: were these Cryptocoryne bunches placed there intentionally or just a random decision or a little bit of both? 

Definitely, the intersections in the above three photos do seem to land on key areas of interest. However, are there other key elements in each aquascape that do not lie on an intersection? 

Keep the discussion rolling.  

Carlos


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## ShaneSmith (Feb 15, 2004)

In the first picture my eye is led to the fish in the dead center of the picture, the contrast between the fish and the dark space is what caught my eye. Bu that is just me, I find putting the red plant in the back right corner is my favourite place for the focal point. Luis navarro does this and some of his tanks rank up there with some of amano's tanks.


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## niko (Jan 28, 2004)

I too often think that all these attempts to capture or describe beauty in geometrical or mathematical terms is pointless. But just as often it's hard to deny the simplicity of the Golden ratio.

To me the first tank's focal point is the "passage". It falls in the top left of the center rectangle.

The second tank has always puzzled me with the long row of plants that somehow "work" and still manage to create a harmonic impression. To me the focal point is the dark area, but it does feel awkward to call it a focal point 

The third tank - I agree, the Ammania is the focal point. If we imagine that the Ammania is not there the tank will look "pontless" - as if the plants are just planted rather randomly there.

Here is a photo of my 6 ft tank as it appears tonight. Still a work in progress: 









And here is a rough Photoshop rendition (with the Golden ratio lines superimposed) of a possible future layout of the same tank. The plants that would fill the left are Ludwigia repens x arcuata, Rotala rotundifolia (red), and green rotala. The plants that woud fill the right are Hygro difformis and Hygro siamensis: 









It seems that the Hygro angustifolia is the focal point. I didn't really mean to make it a focal point but after drawing the red lines it seems like that is the plant that is in the strong point. Again - that may not be the final layout, just a possible one 

--Nikolay


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## Faruk Gençöz (Nov 4, 2005)

All the pictures except Carlos' first one are not seen in this thread. Could it be possible to fix them?


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## Rek (Jul 19, 2005)

i can't see more images


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## Faruk Gençöz (Nov 4, 2005)

I found the original article written by Carlos in the address below. The article includes the pictures he used.

http://www.aquaticplantcentral.com/forumapc/showthread.php?t=12051


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