• Articles about computing
• Articles about graphics and illustration
A load of old ROT — an exploration of the Rule of Thirds
I'm sure everybody who works in the visual arts — whether it's drawing,
illustration, photography, oil painting, or whatever — will have heard
of the Rule of Thirds (ROT). It's a well-established compositional
guideline, which suggests that one or more elements of the main subject
of the picture should be placed at the points of intersection of lines
that divide the frame into thirds. The photograph below is an
Three shall be the number thou shalt count, and the number of the counting
shall be three. Four shalt thou not count, neither count thou two, excepting
that thou then proceed to three. Five is right out. Once the number three,
being the third number, be reached, then lobbest thou thy Holy Hand Grenade of
Antioch towards thy foe, who being naughty in my sight, shall snuff it
— Monty Python
Here the subject's eye, and the tip of the magic wand she is holding, lie
(more or less) at two of the intersection points of the lines that divide
the frame into thirds. Arguably the chimney of the house in the background
lies on one of the other intersection points, but that was just a
You'll notice that the subject is much larger in the frame than
the point of intersection which is, well, a point. There have never
been any compelling arguments to line up any particular feature of
the subject with the intersection points, nor to line anything
up exactly. So the question must naturally arise: is there anything
particularly relevant about the division into three here, or is
it simply a matter of placing the subject somewhere off-center?
Origin of the ROT
The term "Rule of Thirds" appears to originate from a book
Remarks on Rural Scenary (1797) by one John Thomas Smith,
an English engraver and painter.
"Two distinct, equal lights, should never appear in the same picture : One
should be principal, and the rest sub-ordinate, both in dimension and degree:
Unequal parts and gradations lead the attention easily from part to part, while
parts of equal appearance hold it awkwardly suspended, as if unable to
determine which of those parts is to be considered as the subordinate.
Analogous to this "Rule of thirds", (if I may be allowed so to call it) I have
presumed to think that, in connecting or in breaking the various lines of a
picture, it would likewise be a good rule to do it, in general, by a similar
scheme of proportion; for example, in a design of landscape, to determine the
sky at about two-thirds; or else at about one-third, so that the material
objects might occupy the other two : Again, two thirds of one element, (as of
water) to one third of another element (as of land); and then both together to
make but one third of the picture, of which the two other thirds should go for
the sky and aerial perspectives. This rule would likewise apply in breaking a
length of wall, or any other too great continuation of line that it may be
found necessary to break by crossing or hiding it with some other object : In
short, in applying this invention, generally speaking, or to any other case,
whether of light, shade, form, or color, I have found the ratio of about two
thirds to one third, or of one to two, a much better and and more harmonizing
proportion, than the precise formal half, the two-far-extending
four-fifths—and, in short, than any other proportion whatever."
Notice that Smith does not begin by considering proporption, but
the balance of light and shade. His argument is that if two features
in an image are of equal prominence this will confuse the viewer, whose
attention will be drawn back-and-forth between them. Presumably
the same reasoning applies to composition, but Smith gives no particular
reason for chosing thirds, beyond the fact that four-fifths would be
too unbalanced. No reason is given, so far as I can see, for
excluding the use of a quarter however, which lies between a third
and a fifth in size.
So, ultimately, it would appear that the so-called Rule of Thirds
stems from one artist's assertion that two-thirds to one-third is a more
agreeable proportion than some other: not
particularly scientific. I think that we might reasonably rewrite Smith's
guidance like this without changing its meaning very much:
"Try to vary your image in terms of proportion, colour, and light,
but not too evenly, and not too unevenly."
But thirds is what he asked for and, since 1797, the
ROT has been elevated almost to an
undisputed principle of art. My camera has ROT guidelines in its viewfinder,
and many photo-editing applications (for example, Adobe Lightoom) display
ROT lines whilst cropping images. Nobody seems to give a whole lot
of thought to whether the ROT has any empirical basis.
Of course, I don't know many visual artists who comply slavishly with the
ROT — although I've certainly heard tales of some who do. Very often, those
who seek to elevate the importance of the ROT do so by comparing it
to the Golden Ratio, to which we now turn.
The Golden Ratio
The Golden Ratio (GR, or Golden Mean, or Divine Proportion,
is a way of dividing a line into two
such that the resulting division has — or is claimed to have —
a particular aesthetic appeal.
The value of the GR is determined by considering a rectangle being cut
in half along its long edge. If the two rectangles that result from
the cut have the same proportions as the original rectabngle,
then the cut was
at a distance along the long edge defined by the GR.
Anybody familiar with British paper sizes will have seen the GR in
use: the common A1, A2... sizes all have their heights and widths
in proportion to the GR. However, I suspect that this is less
a matter of aesthetics and more one of pragmatism: all the other
paper sizes can be cut from an A1 sheet with no wastage, something
that is not true for other proportions. In addition,
an A3 sheet can always be photo-reduced to A4 with no change in the
aspect ratio, and the same is true for all the other sizes.
Mathematically, the GR is the number φ which solves this equation:
1/φ = φ-1
and is approximately equal to 1.618.
The GR does appear clearly from time to time in the natural world, such as in
the proportions of certain sea shells or, remarkably, some spiral
galaxies. However, claims that this ratio is widespready in nature
need to be considered with a degree of scepticism: there
are many, many measurements that might be made of any natural object,
and it is very easy to find whatever propertions we go looking for.
The GR is mathematically related to the Fibonacci series, which
is something that also appears in nature from time to time.
The Fibonacci series is what we get when start with the number
sequence "1, 1" and extend it by adding the previous two numbers
together. So the first few terms are 1, 1, 2, 3, 5, 8, 13...
13/8 (1.625) is pretty close to the GR (1.618) and as the terms
increase in size, the ratio of two successive terms gets closer
and closer to the GR. This is not a coincidence, of course.
The Fibonacci sequence is a striking feature of certain natural
structures, such as the distribution of petals on the leaves
of some flowers. However, like the GR itself, it is hardly
ubiquitous, and there are enough measurements in nature that it can
be found if we seek it hard enough in enough places.
Similarly, while the mathematics of the GR were known in antiquity,
there aren't a whole lot of historical buildings that are proportioned
according to it. The Parthenon in Athens is an example that is
often cited — the GR appears several times when comparing the lengths
of certain features. However, the Parthenon is prominently symmetrical
(that is, it's primary division is into two) and the GR was
used, if it was used, for less prominent measurements.
If the GR does lead to an aesthetically-pleasing
rectangular shape, it's worth asking why traditional sizes of
photographic paper or painter's canvas are rarely in this ratio. In
practice, these items are usual manufactured to have sides in a ratio
3:2 or 4:3 — a standard 35mm negative has a 3:2 aspect ratio. Computer and television screens are increasingly made with
a 16:9 ratio or even wider — cinematography has usually favoured
wide aspect ratios. This is a bit of a digression, however, because we aren't
really considering the aspect ratio of an image here, but the placement
of objects within it, and there's no particular reason to think that the
same considerations should apply.
The Golden Ratio and the ROT
I've lost count of the number of times I've heard that the ROT is
derived from, or based on, the Golden Ratio. Even if it were, we are
still left with attempting to justify the GR in terms of natural
aesthetics which, as I've explained, might not be as straightforward as
is often claimed.
The reality is that the GR and the ROT are not related to one another in any
non-contrived way. They give very similar proportions, but that
is merely a coincidence.
The diagram below shows a rectangle divided both according to the ROT
and to the GR (shown as φ in the diagram). The vertical
red stripe shows the area of difference between the two approaches.
We just can't write down some simple mathematical formula that will
turn φ into the number 1/3 or 2/3 — that connection simply
What could legitimately be claimed, I think, is that the ROT is a
simplification of the GR. It's much easier to say "divide the
width and height into three equal parts" than to say "divide the
width and height into two unequal parts such that the ratio of their
lengths is given by the solution of this equation..."
If there were some aesthetic significance to the GR, then
simplifying it this way might be a sensible, pragmatic thing to do.
However, looking at the examples that various photographers and photography
tutors use to illustrate their use of the Golden Ratio, it's pretty clear
that it's applied pretty loosely when it is applied (the same is
true of the ROT, in my experience.)
If the GR genuinely were aesthetically compelling, I would think
that artists would tend to gravitate towards following it quite closely
but, in practice, this does not seem to be the case.
Thirds in art
Whatever we might say about the GR, the number three, or ratios involving
the number three, do crop up in the arts, and do so very commonly.
For example, the ratio of musical pitches that we call a fifth in the
Western world is a frequency ratio 3:2. A fourth is 4:3
(sort of; see
this article for a much more
detailed discussion of the significance of integer ratios
in musical scales.) A large-scale musical composition has traditionally
comprised three movements; often individual movements will have three
sections of which the first and third are similar (or even identical)
while the second is in contrast to them.
Many plays are divided into three acts.
In Britain, half-hour radio
shows were traditionally divided in to three, ten-minute 'acts,' although
the need for advertising breaks has somewhat eroded that practice.
In ancient Greek literature and mythology entities tended to be grouped
into threes: three Fates, three Furies, three Graces, etc. Macbeth had
three witches. Threes
turn up also in Christian, Jewish, and Buddhist mysticism, and probably
in other traditions as well.
A common way of presenting paintings, particularly of religious
subjects, was as a triptych — three connected panels, usually
with the central panel larger or differently shaped to the outer panels.
The same layout sometimes features in religious architecture: the
facade of Notre Dame Cathedral resembles a triptych.
It isn't hard to find other threes in architecture, both ancient and
modern. There's a whole bunch of three-arch buildings in Washington, DC,
for example. In fact groups of three in architecture
are so ubiquitous that it's scarely
worth trying to list examples.
Despite all these threes in the arts, there remain plenty of twos and fours.
Three is a common number of movements in a symphony, but four-movement
pieces are far from rare. There are many pieces of music written for
trios of instruments, but the number of string quartets alone probably
outnumbers them all put together. Most buildings have a four-sided
plan, and usually a four-sided elevation. The pyramids at Giza have
four faces, not three (five if you count the base.)
And, of course, three is the number to which we count before throwing
a hand grenade. Modern software engineering favours a three-tier approach
to system architecture. There are three sizes of coffee cup at Starbucks.
And so on.
Perhaps the reality is that three is nothing more than a convenient
Rules, we are often told, are made to be broken. The so called 'Rule'
of Thirds is broken so frequently that it is safe to say explicitly:
There is no Rule of Thirds. Any claimed connection to the
Golden Ratio — itself a concept of dubious aesthetic significance — is bogus.
The reality is that, in the visual arts, we humans tend to prefer our
focus of interest to be somewhat away from the centre, but usually
not right on the edge. And that's really all there is to it.