The Square Format - Example 1

THE SQUARE FORMAT


The Rest by the Stream - 1872
Artist: Alfred Sisley (1839-1899)

In this picture the square format helps achieve a peaceful, stable effect, much like a tondo (which is in the shape of a circle) does and for the same reasons (see Rudolf Arnheim's The Power of the Center, Chapter VI: Tondo and Square). The tondo shape, however, does not give a feeling of being grounded, which a square format is very capable of doing, and does here.

Although once you have seen this picture for the first time you may then look around the scene for details in other areas, your eyes are first and foremost drawn to the middle, where close and distant foliage mingle. For me, at least, that center area seems like a pinwheel that turns slowly and hypnotically, sometimes to the right, sometimes to the left, and it's hard to glance away from it.

The intense focus on the center (in spite of there being nothing there but indistinct leafy branches) has as much to do with the square format as with the large shapes in the composition that lead you there. A horizontal format or a vertical format would suggest something is happening or about to happen, or relationships are being revealed, or etc., causing you to look all around the picture to get some clues as to what's going on. But a square scene seems to just sit there quietly, its outer four edges implying a central point that they're all equally distant from and related to so that you simply can't help but look toward that calm and steady central point when you begin to search for the subject.

The square shape, with four straight edges of equal length and at right angles to each other, imply the balancing center of picture is in the actual "geometric" center of the square. This central focal point makes the picture (or at least whatever is at the very center of it) seem very balanced, solid and stable, as if it's not going anywhere nor is it concerned with anything that is outside of the edges of the picture. (Certainly an artist could make the subject look as if it's concerned with something beyond the edges, but in general the square format is used for a self-contained picture and it is very suitable for it.) The scene is made to look even more stable in this particular picture because of the depth the artist has given the scene, giving it the look of being inside a square "box" (cube) that is solidly resting on the earth's surface.

The role of the Cartesian Grid

The feeling of stability is further reinforced by the tree trunks that repeat the verticals of the sides of the picture, as well as the lower edge of the brightly lit grass behind the tall trunks and the bit of horizontality seen in the distant footbridge and suggested on the roof of the house at left which repeat the horizontals of the top and bottom of the square frame. These large and small bits of vertical and horizontal "lines" that can be seen imply a stable structure beneath the rolling ground and other curving shapes that fill the canvas. They suggest that the Cartesian grid is being utilized in this painting. The Cartesian grid considers the earth to be fundamentally flat (though of course, those who use the Cartesian grid know the earth is spherical; it is just that for many practical purposes it is flat enough within the areas we make use of that it is most practical for us to consider it flat and even to flatten it if it's not, e.g. in the case of floors, roads, sidewalks, and building foundations). The Cartesian grid (or Cartesian Coordinate System) is made up of verticals and horizontals that are perpendicular to each other. These horizontals and verticals are seen to be stable (inactive but solid and secure). When the structure of the Cartesian grid is evident in the composition, you are able to notice when things are not in line with it (i.e., not strictly vertical, or not strictly horizontal), thus enabling you to detect movement, direction, slopes, curves, etc. To find out more about what the Cartesian grid has to do with art, you might want to read an earlier post: Art, Gravity, Life, and the Cartesian Grid.

The Cartesian Grid combined with the Centric System

In this particular picture being discussed here (The Rest by the Stream by Alfred Sisley - see above) the Centric System and the Cartesian grid system are both effectively utilized to bring about the feeling of calm restfulness the painting's title promises.


Combined Centric and Grid Systems

The above diagram, which so perfectly applies to this square painting by Sisley, and more on this subject can be found in an earlier post, entitled Centric Systems. In that post it is noted that the Introduction to The Power of the Center, by Rudolf Arnheim, begins with this sentence: "This book derives from a single idea, namely that our view of the world is based on the interaction of two spatial systems." Those two spatial systems are the Centric System and the Cartesian grid system.

The similarity to a mandala

"Mandala is a Sanskrit word that means 'circle'. In the Hindu and buddhist religious traditions, their sacred art often takes a mandala form. The basic form of most Hindu and Buddhist mandalas is a square with four gates containing a circle with a center point." (This quote is from a Wikipedia Article on the mandala.) The article goes on to say that "mandalas may be employed for focusing attention of aspirants and adepts, as a spiritual teaching tool, for establishing a sacred space, and as an aid to meditation and trance induction."

Note how the mandala seen below combines the Centric System and the Cartesian grid system in the same way they are combined in the Sisley painting.

Tibetan Sand Mandala
Uploaded by Mary Mueller [CC-BY-2.0], to Wikimedia Commons

The cubical "enclosure"

The feeling of a snug cubic "enclosure" surrounding this scene also adds to the serenity and satisfaction we feel when viewing it. It is like viewing a scene in a glass sphere except that in the case of the cube we feel as if we could actually enter the scene, whereas the sphere rejects us -- we can only look at it from the outside. (You can read about the scene within a sphere under the last picture in an earlier post, titled Round Artworks).

There are other factors, also, which contribute to the
"restfulness" of this picture, but they do not have to do with its "squareness."

The Square Format - Example 2

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How to Make a Fat Man Look Even Fatter

(And Like a Fool As Well)

A vertical format can make a subject look more slender and tall than it actually is.

Philip II of Spain - 1551
Artist: Tiziano Vecelli or Tiziano Vecellio (c. 1488/1490-1576), better known as Titian
From Wikimedia, this picture is in the public domain

But a vertical format can also accentuate fatness.

Porträt eines dicken Herrn, des sogen - 17th century

("eines dicken Herrn" seems to translate to "a fat lord")
("des sogen" seems to translate to "so-called")
Artist: Bernardo Strozzi (c. 1581-1644), Italian Baroque painter
From Wikimedia, this picture is in the public domain

This man, the artist seems to be saying, is not just fat - he's too fat (and not just fat but clueless - Strozzi did not like this guy).

A very large person can be made to look comfortable and quite acceptable and even admirable in his or her world -- the "world" of the painting. But Strozzi has made this large man look like he doesn't fit at all into the scene he has painted him into (even though the subject looks quite conceited, apparently completely unaware of how ridiculous he appears).

Other paintings by Strozzi show that those people he cared to flatter or whom he had something else to say about were not painted in the same way at all. For example:


David with the Head of Goliath - c. 1636
Artist: Bernardo Strozzi
From Wikimedia, this picture is in the public domain

David (as well as Goliath's head) blends in with the background (and foreground - let us just say with the "ground"), whereas the "fat lord" stands out as a dark figure against a very light background so that we can very clearly see his entire bulging contour. As we can see from the painting of David and Goliath, Strozzi did not paint all subjects alike - How he painted them had to do with what he wanted to get across about the subject, so obviously the artist made the "fat lord" look as fat as possible quite intentionally.

How the artist made the fat lord look bigger:

- First of all, he chose the shape of the overall picture: a narrow vertical rectangle. A narrow vertical format can help to lengthen and slenderize a bulky vertical subject but other factors have to be manipulated as well or the same vertical rectangle can make the subject look even bulkier than it is - because of the contrast between tall/slim and bulky/wide. This is especially true if the sides come quite close to the subject, indicating that it barely fits or even that it's expanding toward the edges of the composition. This is the case here.

- And of course the rectangular shape (rather than an oval or round shape) of the perimeter of the picture -- along with the straight vertical columns -- strongly suggests the "Cartesian grid" understructure of the painting, making it impossible for us not to notice the bulging shape of the man as contrasted with the straight vertical and horizontal lines of the grid.

- As mentioned above, there is the contrast of the very dark subject against the very light "ground," making his large and bulging profile extremely obvious, and in fact more immediately noticeable than anything else in the picture.

- The dark shadow the man's stomach casts on the column blends in with the adjacent stomach to make it seem even larger than it is. "Where the overlapping units together form a particularly simple shape, they tend to be seen as one and the same thing." (Rudolf Arnheim in Art and Visual Perception, page 121)

- The man is, for some reason, pulling up his hem. Not only does this show us that he has huge legs, but it also plumps up the fabric and adds more bulk to the profile on the side of the picture opposite the stomach.

- The slenderness of the sword, which reaches down to his feet, contrasts with the bulk of the body, making the body look all the larger. The sword is so narrow that it looks like it might snap under the weight.

- The sword also accentuates the protrusion of the stomach since it is directly in line with the stomach's profile beginning at its outermost extension and acts as an arrow that points out the outer edge of the frontal bulk. (Another function of the sword is to "pin down" the lord's balloon-shaped stomach, as it seems to be rising.)

- The "heavily planted" feet seem to be pushed downward by a great weight.

- The artist takes advantage of the fact that we perceive objects that are higher in the picture as being heavier than they would look in a lower position "[I]n a painting the higher an object is in pictorial space, the heavier it looks." (Rudolf Arnheim in The Power of the Center, page 24) Thus the stomach looks particularly heavy.

- The vertical shape (a column) that is closest to the man's body and to the front plane of the picture not only contrasts with the rotund shape of the man's body, making it stand out all the more, it (the column) also helps to "lift" the stomach up, making it seem all the more prominent (and even "active!") - as if it were being shown off. ("Look at my magnificent stomach!")

The reason the column appears to lift up the stomach is that it (the column) is seen to be rising like a rocket just starting to lift off the ground - and in doing so "pulling" the nearby stomach upwards with it. The reason the column appears to be rising is that although there is a very definite base attached to its bottom, essentially "blocking" any perceived downward thrust, in contrast there is no change in shape (like a bulge) or anything else (such as a capital at the top) that appears to slow down the "ascent" of the column at the top the picture, and so the column appears to continue rising upward and out of the scene. -- When something immediately adjacent to something else looks like it is reaching upward, as this column is, there is a tendency to perceive that almost-attached "something else" as being lifted along with it. (See The Power of the Center, by Rudolf Arnheim, pp. 21-23)

- The fat lord's maximum girth is above the horizontal center of the picture, attracting our attention to it more strongly than would be the case if it were lower in the picture where heavier objects, pulled down as they are in real life by gravity, are usually found.

- The man's hands seem to cradle a large globular mass (his stomach), thereby emphasizing its size and shape. And speaking of the cradling hands, notice the difference in their apparent size, with hand in the foreground looking much larger than the one in the background - yes, there is probably more of the hand that we can't see from that position but what is important is what we can see; also the hand in the background is darker by far than the very prominent and brightly lit larger foreground hand...This difference in hand size and brightness emphasizes the distance between the one and the other.


Hold cursor over pictures to read directionsClick on above pictures to see left divided into upper and lower halves, right divided into quarters
- The large pear-shaped face (which we can see clearly as it is lit from the side and is of a light color modeled by dark shadows) is similar to the shape of the main bulk of the man's body. The light/dark modeling makes the face and neck area look 3-dimensionally bulgy, suggesting that the adjacent similar (though much larger) shape is also 3-dimensionally bulgy.

- The fat lord's feet (it looks like only one foot is shown, but we assume the other is there beside it!) are shown sideways and they seem very long - Whether or not it's just that he has very long shoes, or whether part of what we see is the "flag" or whatever it is lying on the floor doesn't make any difference. It is the dark shape we see and where the foot ends and the shoe ends or where the material behind his foot ends makes no difference as it is all one dark mass that we see as "the feet." Even if we saw only a bare foot and knew where it ended, this sideways view of it is the largest image we could have of it; obviously the artist gave us this profile view of the feet to make them seem very large and virtually planted to the floor in order to emphasize the man's great weight pushing downward ... Look at that heavy-looking, downward aimed wedge-shaped calf directing all the weight of the body above into the shoe; the leg seems not to end at the bottom of the shoe, but, rather, the shoe that we see looks like it opens up at the bottom so that the wedge extends into a deep pit.

- Another way he has been made to look large and heavy is by seemingly rubbing up against the column, as if there wasn't room for him to stand without bumping into something.

How the artist made this man look foolish:

It has been implied by the artist that the man, who looks very conceited, and proud of his figure, is delusional and foolish. Here are some of the ways the artist shows that the man is not what he thinks he is:

- His facial expression shows that haughty and satisfied look just mentioned, in spite of the ludicrous figure he presents.

- He is holding a very odd pose in a very odd place, just barely fitting on that pedestal and facing in the direction of the column. Obviously there's nowhere to go in that direction; he has run into a blockade.

- Note the viewpoint, from a little below. The artist has put this man quite truly on a pedestal and has us (ironically) looking "up" to him. Actually it appears as if the fat man had put himself on that pedestal, having had to step up there in order to take that pose.

- The man is (awkwardly) turned to show his profile, as if showing off his huge stomach quite proudly. (I don't think the subject knew anything about this picture, do you?)

- Perhaps what looks like a crumpled flag under his feet and just behind his lower legs might be there to show that he is capable of crushing things easily. Or it could be the remains of a flimsy chair he had been sitting on. With the other "clues" we've been given, we tend to think that the reason that "crumpled fabric" is there probably has to do with this man's weight and/or size.

- Why is the man pulling up his hem and showing his huge leg?
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     The artist must have really enjoyed creating this picture (and probably his other pictures as well).  He knew what he wanted to "say" about this man (i.e., that this delusional fat man is a pompous fool), and in order to get that across he had to do a lot of thinking (or "problem solving") to figure out how to accomplish this goal.  Sounds like fun to me.

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Centric Systems

I have no illusions about someone happening upon this post, seeing the title, and thinking "Oh! This sounds like a fun read!"

However, for someone who is just now trying to understand just what centric (or concentric) systems are, it might be a sight for sore eyes (okay, maybe I'm stretching things a little!). At any rate, it's not very long, there are several examples, and it's something artists need to know about.

The Introduction to The Power of the Center, by Rudolf Arnheim, begins with this sentence: "This book derives from a single idea, namely that our view of the world is based on the interaction of two spatial systems." Those two spatial systems are the centric system and the Cartesian grid system. They are both gravity-based systems, one (the centric system) natural and one (the Cartesian grid) constructed by humans.

Centric System

The Cartesian Grid

Combined Centric and Grid Systems

I've written about the Cartesian grid in a post called Art, Gravity, Life, and the Cartesian Grid. Also, in a post on Round Artworks I showed examples of how the two systems are used together in art. The post you're reading now is a (very) basic introduction to centric systems, but it should be kept in mind that the two systems work together (I will write more about that in the future).

DEFINITIONS In case you wish to refer to them as you read CARTESIAN GRID: A system of straight lines meeting at right angles, either on a two-dimensional surface or in three-dimensonal space. (The Power of the Center) CENTRIC: Having a center. (thefreedictionary.com) CENTRIC SYSTEM: A system organized around a center, either two-dimensionally or three-dimensionally. CONCENTRIC: Having a common center. (thefreedictionary.com) COSMIC: immeasurably extended in time and space; vast. (dictionary.com) GALAXY: A massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. (wikipedia.com) GRAVITY: The fundamental force of attraction that all objects with mass have for each other. (thefreedictionary.com) HIERARCHY: Any group of objects ranked so that every one but the topmost is subordinate to a specified one above it. (dictionary.net) PAROCHIAL: very limited or narrow in scope or outlook; provincial (dictionary.com) SYSTEM: An assemblage or combination of things or parts forming a complex or unitary whole: a mountain system; a railroad system. (dictionary.com)

I include the definitions above because the two systems are called so many different things by Arnheim. Centric systems are also called by Arnheim cosmic systems and concentric systems -- and at least once he refers to a centric system as a cosmic onion. (He also refers to the Cartesian grid as a parochial system.. .not to impress you with his extensive vocabulary, as there is a very good reason for calling it that and also for using the other terms rather than just one for each of the two systems ... but it can be confusing nonetheless to encounter all these names for just two spatial systems, and this is why for the most part I have only used the term "centric" to describe the one system that this post is about.)

TO BEGIN.....

Let's take just the most important definition out of the above table and look at it here. CENTRIC SYSTEM: A system organized around a center, either two-dimensionally or three-dimensionally.

And look at this simple diagram of a centric system again:

Centric (or Concentric) System

Holding that definition and the diagram in mind, read on.

OUR SOLAR SYSTEM - EXAMPLE OF A CENTRIC SYSTEM

Possibly the best example of a natural centric system, held together by gravity, in this case with the sun at the center, is our solar system (aka planetary system): Earth, Mars, Venus, etc., and the sun [star] they travel around).

"Our Solar System...showing the Sun, Inner Planets, Asteroid Belt, Outer Planets, the largest object in the Kuiper Belt - Pluto (originally classifed as a planet), and a comet."

A CENTRIC SYSTEM IS USUALLY (IN NATURE) AND OFTEN (WHEN HUMAN MADE) PART OF OTHER CENTRIC SYSTEMS (and sometimes has centric systems within itself)

Just as in our solar system there is the sun (a star) that is orbited by planets some of which are orbited by moons (all of which together make a centric system), in a galaxy there are an incredibly huge amount of stars, some of which are at the center of their own centric systems that include planets (some of which are orbited by moons). In other words, there are what seems to me at least (not being a scientist) probably a huge amount of solar systems (which are centric systems) within galaxies that are centric systems themselves. Centric systems within centric systems, that is. And so on...this not being a science blog nor I a scientist ... but the point is that centric systems often have smaller centric systems within them and, as well, they are often parts of other, larger, centric systems.

GRAVITY IS WHAT HOLDS A CENTRIC SYSTEM TOGETHER

Gravity (roughly defined as the attraction of a smaller mass by a larger mass) is what holds a natural cosmic (centric) system together. You will already know that moons are held in place by the gravitational pull of the planets they orbit, and the planets are held in orbit by the gravitational pull of a star that we call a sun (the center of a solar system), and so on.

A SOLAR SYSTEM IS PART OF A GALAXY, A LARGER CENTRIC SYSTEM

We call the galaxy that contains our own solar system (the solar system is also called a planetary system) the Milky Way. Galaxies do not all have the same shape, but they are all centric systems, even though the "center" of these systems may not be one object but a cluster of many very dense objects (a black hole, stars, dark matter...) all of which add up to an immense gravitational pull on everything further away in the galaxy.

The Sombrero Galaxy

The Sombrero galaxy is about the size of our Milky Way galaxy. It probably contains hundreds of billions of stars, many of which are probably orbited by planets. Not only is a galaxy a centric system, but any planetary systems it contains are also centric systems.

EFFECTS OF GRAVITY THAT WE CAN SEE HERE ON EARTH

We and everything around and under us is affected by gravity in many ways. One example of how gravity works is the quite observable (though probably seldom thought of) fact that the pull of gravity of our own planet is holding us to its surface thus preventing us from floating off into space (we feel the pull of gravity on our bodies as weight). The pull of gravity from the center of the earth is the reason it takes energy for us to rise from our beds, to lift our arms (especially when carrying something heavy), to walk uphill or even to walk downhill if the incline is steep as we must expend energy to keep from falling ("falling" means being pulled by gravity). It even causes our nose and ears to grow longer as we age (they sag toward the center of the earth).

Another example, which most of us probably do relate to gravity, as it is fairly common knowledge, is the moon's gravitational pull and (to a slightly lesser extent because it is so far away) the sun's gravitational pull which cause the tides here on our planet. "Tides are the rise and fall of sea levels caused by the combined effects of the rotation of the Earth and the gravitational forces exerted by the Moon and the Sun." (Wikipedia article on tides)


Mount Orgueil at low tide

CENTRIC SYSTEMS ARE HIERARCHICAL

A centric system is hierarchical and what's at the center is at the "top" of the hierarchy. As you move away from the center, objects are, generally speaking, less affected by the center, and eventually you get to a point where objects belong to another centric system. However, of course, all objects within a centric system are by definition a part of it and affected to some degree by its center no matter how far away they are.

THE SHAPE OF A CENTRIC SYSTEM IS NOT ALWAYS ROUND

"Centric" systems are not always round (natural centric systems are round, or at least symmetrical, only when there is enough space to achieve their ideal shape and when there is no interference by agents -- chemical, physical, or etc. -- that are able to deform them; and certainly centric systems are not usually round in works of art).

The "Network Tree Diagram," above, is a good example of a centric system that is not round, nor even symmetrical, yet is a hierarchical system like any centric system. It also shows how a centric system can be a part of other centric systems, as there are actually several centric systems within the large one here.

BIG THINGS, SMALL THINGS -- ALL ARE HELD TOGETHER IN THE SAME WAY

The same thing happens in nature even in systems that are much, much smaller than planetary systems, as all matter attracts other matter, the matter with more mass attracting with greater effect and from a greater distance. However, when it comes to very small objects (compared to planets and moons and stars) gravitational attraction is hardly if at all perceptible. Yet it is there. The pictures below show some examples of smaller centric systems in nature.

"Even in the crowded world of our direct experience, inorganic and organic matter occasionally has enough freedom to follow its inclination and form symmetrical structures -- flowers, snowflakes, floating and flying creatures, mammalian bodies -- shaped around a central point, a central axis, or at least a central plane. The human mind also invents centric shapes, and our bodies perform centric dances unless this basic tendency is modified by particular impulses and attractions." -- Rudolf Arnheim in the Introduction to The Power of the Center.

CIRCLE DANCES ALSO CONFORM TO A CENTRIC SYSTEM ARRANGEMENT


American Indian circle dance

"The circle is probably the oldest known dance formation." Wikipedia article on the circle dance

Bird's eye view of Avebury, in Wiltshire, England.
(Image from fromoldbooks.org)

Avebury is about 5,000 years old, even older than Stonehenge. You can easily see the centric systems involved in these man-made structures.

WHY DO WE NEED TO KNOW ABOUT CENTRIC SYSTEMS?

Knowledge of how centric systems work in nature (along with knowledge of how the Cartesian grid system that we have imposed upon centric systems in order to organize and understand what we see works) is essential for artists, and often is understood intuitively, if unconsciously. It is likely that we already "know" much of how these spatial systems work just from what we have observed in the world around us and what we have learned from school and books and so on -- and in the case of the centric system, we may even have been born with a tendency to arrange things hierarchically in circles and possibly even to find round or spherical patterns and places comforting (especially when we are at the center) and "complete" (thus satisfying) -- but we may easily mistrust and/or ignore, or even have no conscious awareness at all of this "knowledge" nor any interest in knowing about the spatial systems we live with, not realizing that such knowledge can have any use in art, or how to use it in art. So if we are not already fully aware of how these systems work, and why, it seems like a good idea to learn about these things consciously in order that we can make good use of all this in the art that we produce. And once we have it all in mind, then we need to understand how this knowledge can be useful to us - which I haven't written about here, but will in future posts.

Meantime, if you haven't already, you can read more about the Cartesian grid, and about how gravity influences our perception of the world and even the structures we make to live in, among many other things, in my post called Art, Gravity, Life, and the Cartesian Grid.

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NOTE: All pictures used in this post are in the public domain.

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Composition - Relating to the Outside Edges

Lessons from Edvard Munch's The Murderer in the Lane.

The outside edges of a painting play a major role in determining what your picture is about.

We can't just start painting without considering how the edges affect the subject we are trying to portray. What is inside the picture must be related to the outside perimeter of whatever we're painting or drawing on from the very beginning ... as well as to the center of the picture (but of course we only know where that center is when we know where the edges are).

Usually, when we are not just practicing we paint (or draw, etc.) in order to present a subject in such a way that other viewers might see it as we do and respond to it as we wish them to.

I think that all artists have these object in mind, though some who may be earnestly trying to get their message across may not realize how they are sabotaging their own efforts by ignoring the edges of their pictures, not taking them into account at all except as places where they must stop painting because they've run out of room.

Before we even choose the size and shape of the surface upon which we'll be painting, we must have in mind exactly what we're trying to say with our picture. What is it that has impressed us with regard to the subject that we want to impress upon others? Once we have that in mind, we can think about how we will accomplish this.

There are many things to think about when composing a picture, but one of the most important and probably the first to be considered is where the main subject will be placed and how large or small it will be, etc. in relation to the center and to the edges of the picture (as well as to everything else that's going to be in the picture). If you just paint whatever is "out there" that you are looking at (or what you're thinking about) until you get to the edges of your canvas, the intent of the picture will probably be unclear, to say the least. In fact my personal opinion is that it's not "art" unless you have planned for it (whether consciously or intuitively) to say what you want it to say.

If you have nothing to say, except perhaps that the subject of your painting is beautiful or interesting (though you can't think of exactly why and otherwise it has no particular meaning to you), you might as well just take snapshots or make sketches. You can always use the photos or studies later, after you've thought about what you want to say about this subject.

Why must we worry about the edges? Why can't we just put our main subject in the middle of the picture and paint outward from there until we reach the edges of the canvas? Because, as Rudolf Arnheim points out in his book The Power of the Center, "the nature of an object can be defined only in relation to the context in which it is considered." That context includes the surface you're painting or drawing on, right out to its outer limits.

"[T]he character, function, and weight of each object changes with the particular context in which we see it," writes Arnheim. Further, he says: "A frame of a particular size and shape defines the location of the things within its space and determines the distances between them." He is not talking here about the kind of frame you put a picture in and attach to a wall, but about the outside edges of the picture, or the "boundaries" of the picture, and how everything in the painting relates to those edges.

I'll give an example. If your subject was a very distressed murderer leaving the scene of the crime in great haste, would you put him in the middle of the picture? Perhaps. It depends on what else you do in the picture (with colors, values, rhythm, shapes, etc.) and what else you want to say about him. But take a look at the picture painted in 1919 by Edvard Munch (1863-1944), called The Murderer on the Lane.

Here you can see how large the painting is, as this page shows a recent photo of the original painting in a gallery with people looking at it -- Scroll down to the bottom picture on the page to see it.

In the painting we see just the head of someone hurrying down a dirt lane lined with frightening-looking trees, away from a dead body. His or her simple, almost cartoon-like face shows concentration and anxiety.

Assuming the head you see (a man's? a woman's?) at the bottom of the picture is that of the murderer (not a horrified passerby), you may wonder why (let's call this person "he") isn't somewhere near the middle of the picture rather than just barely seen at the bottom edge - After all, isn't the murderer the subject? I don't think Munch would put a murderer in the most "stable" part of the picture (the center), or anywhere near it. Whatever is in the center would look like it's not going anywhere soon, if at all; it would be as if planted there with no intention of movng away. The killer is crazy -- quite unstable -- and he's leaving the murder scene (and leaving it rather empty, except for that dead body), hurtling himself toward me (the viewer), in fact, and so near the bottom edge (with most of him out of sight) that his advance toward me seems unstoppable; he is "falling" right out of the picture, pulled by gravity, so to speak...as we associate the pull of gravity with the bottom of a picture (and the effect is even stronger if a significant amount of ground shows, as it does here).

In fact, if the murderer was in the center and also much larger in relation to the size of the painting, he might look like he was paralyzed, hardly able to move, the more so the bigger he was in relation to the outside of the picture. If his head filled the whole canvas so that it reached the edges it might look as if he were going to explode...but that is not the same as looking as if he were intent on getting the heck out of that place (and in fact there would be no space left in the picture in which the scene he was leaving could be depicted).

If he were situated very near or even touching the top edge of the picture rather than at the bottom he would probably not seem threatening to us at all. That edge would "hold him" up and away from us (like a helium balloon stuck to the ceiling), especially if it were toward the right side of the picture (the left side is where action usually begins, and it unfolds -- or appears that it will unfold -- toward the right, suggesting that whatever is happening will be completed by the time it reaches the far right side...unless it seems to be crashing down toward the foreground, perhaps, as in this painting).

Of course there are other things you can do with a picture to indicate the state of mind of someone, or the trajectory of his path, the likely escape route, or etc., but these are some of the ways in which the edges work ... you can modify or cancel the effects with other things you do, but let us see how the edges can work for us; it is useful to know these things if only to make sure we are not inadvertently saying something we don't want to say by where we're placing things in a picture.

In this painting the artist has made the murderer's head small in relation to the whole picture, and left plenty of room behind him so that we can see what he is fleeing from, and he has placed his head right at the bottom edge, almost out of the picture.

One reason that having the subject at the bottom edge of the picture is very effective is because, as mentioned, he seems to be uncontrollably leaving the scene. It's also effective because it's such an odd place to find the subject that it makes it very conspicuous...especially since it's only a head, with no body in sight. It's scary, and riveting.

The very dominant, large thick tree just to the left of the center of the picture is in a place and of a size such that it balances (visual weight-wise) the murderer's head that's just to the right of (and below) the center. (And the tree also looks something like a person, with a face on the thick branch at the right -- a witness to the murder, watching the murderer as he rushes away -- maybe it even represents the murderer in the act, with its branches upraised like arms perhaps wielding the knife.) There are other tree witnesses further up the lane. These trees not only play roles in the drama as witnesses, but they are lifting themselves and their branches up to the very top edge of the picture (and beyond), balancing the murderer who is running out of the picture at the bottom edge, so that the picture is not bottom-heavy, and so we look upward to the rest of the picture as there is so much in it that we need to see besides the murderer's head.

The picture shows the lane behind the murderer, where the dastardly deed was done (with the dead body still there to prove it), and although we see that the lane is not on a hill, there is still a "hill-like" effect that we feel since it starts at the horizon and comes toward the foreground (and continues beyond it out of the picture in our minds) ... Although we realize this is flat land being portrayed, we can't help but get a feeling that things are starting "high" (because the end of the path is up high in the picture) and coming "down" (to the bottom of the canvas) toward us. Also, we have a view of the murderer from slightly above his head, looking down on him, which increases the feeling that he is going downhill. What is in the foreground near the bottom edges of the picture is strongly affected by gravity in our "unconscious" minds if not in reality. An artist like Munch knows these things if only intuitively. And so the lane delivers (dumps?) the murderer into our laps.

The relatively calm (but not silent) area at the left side of the picture balances all the action on the right.

Note that the horizon (where all looks peaceful and humdrum) as well as the four edges of the picture (and the vertical trees - and there's even a square in the sky that appears to be the moon...what else could it be) are based on the Cartesian grid - These horizontal and vertical lines -- as I say, including those of the outside edges of the picture -- stabilize the picture and serve as contrast with and intensifiers of all that is bizarre and unnerving in the painting; they also determine for us what is up and what is down...We must know this in order to "feel" the gravitational pull at the bottom [this is something that we perceive below the level of consciousness] that is ridding the scene of the murderer.

All of the eerie, nervous lines and the sickening colors and so on in the picture that cause anxiety in us are more effective because of this contrast, i.e. chaos and anxiety contrasted with seeming permanence and stability of vertical and (especially) calm, non-threatening horizontal lines.

I have hardly begun to touch on the ways considering the edges (and center) of the picture can make our pictures more effective, but it's a beginning, and certainly enough for one post.

_____

NOTES:

1) The Power of the Center: A Study of Composition in the Visual Arts is a book by Rudolf Arnheim published by the University of California Press.

2) The Murderer in the Lane is also called The Murderer on the Lane and Murderer in the Avenue.

LINK:

The Artchive - Commentary on and Pictures by Edvard Munch. There is very interesting commentary here on Munch.

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Round Artworks

Before you start reading this post...

First (bear with me!), I'll provide a very short review of the Cartesian grid and the concentric system -- Not so boring as you may think! (Okay, maybe a little boring, but not complicated.) -- and then some examples of round artwork (tondos) are analyzed, below. You may be surprised at how helpful this might be if you're an artist and aren't already aware of how some subjects are more suitable for a round format than a rectangular format, and that there are different things to consider when you're composing a round picture.

There are two previous posts that you might want to read before you read this one (or you may prefer to go ahead and read this, then go to the others to understand this post a little better if the subject interests you). Here are the earlier posts:

Art, Gravity, Life, and the Cartesian Grid

The Tondo

In reading this present post (on this page) for the first time, you may want to zip through or even skip the first part (about the Cartesian grid and the Concentric system), or just look at the pictures and read the "In a Nutshell" parts. You can always come back to the first part if you're interested in learning more.

Planet Earth as seen from Apollo 17
Courtesy NASA/JPL-Caltech

We live on a round world but because of gravity we make use of a very non-round spatial system, the Cartesian grid, for practical purposes, in order to make things, understand things, etc. (see my earlier post, Art, Gravity, Life, and the Cartesian Grid to understand why).

IN A NUTSHELL: Although the earth is round, "in the parochial view of its small inhabitants, the curvature of the earth straightens into a plane surface, and the converging radii become parallels." (Rudolf Arnheim in the book The Power of the Center) -- The Cartesian grid represents the parallel verticals and horizontals that are so important in our lives here on Earth.

The Cartesian Grid "A co-ordinate system whose axes are straight lines intersecting at right angles"(Ref.)

However, when free of the constraints of gravity (either in real life or in our art), we use the concentric system to understand (and make understood) relationships between things.

IN A NUTSHELL -- "Cosmically we find that matter organizes around centers, which are often marked by a dominant mass.....A concentric system is, by definition, organized around a center....The central point allows for orientation....It creates a hierarchy." (Rudolf Arnheim, in POC) -- The concentric system represents matter or forces of some kind that are concentrated around a center, e.g. the planets circling the sun, or children surrounding their mother, or the fruit of a peach around its pit.

Concentric System (above)

In art we usually make use of both systems, combined.

IN A NUTSHELL: "Together they [the Cartesian grid and the Concentric/centric system] serve our needs perfectly. The centric system supplies the midpoint, the reference point for every distance and the crossing for the grid's central vertical and horizontal. And the grid system supplies the dimensions of up and down and of left and right, indispensable for any description of human experience under the dominion of gravity." (Rudolf Arnheim, in POC)

Combined systems (above)

Depending on what the subject is, what we're "saying" about it, and the shape of the "frame" (or outer edge of the artwork), the artist will focus more on one system, or more on the other.

A tondo (plural: tondi or tondos) is a round painting or sculpture or other circular work of art. The word comes from the Italian "rotondo" (round, or rotund). The tondo's round shape is particularly suitable for pictures that are not about life here on earth - that are, instead, about gods, fantastical space creatures, fairies, etc....things to which gravitational constraints do not apply.

"Not surprisingly we found that the concentric model of composition is enhanced by the tondo format. This does not mean that the Cartesian grid, so strongly advanced by all terrestrial subject matter, is simply suppressed. To be sure, the more fully realized are the compositional requirements of the tondo, the more the grid recedes as a self-sufficient system." (Arnheim, in POC)

Round (or spherical) things in nature and in art are considered "perfect" and "complete" and "stable within themselves" as well as able to be easily moved, intact, from one place to another (and if they're resistant to gravity, or even, at least effectively, not affected by it at all due to being out in space beyond gravitational pull, or in an imaginary realm where gravity doesn't apply, they have no real need for the horizontals and verticals of the Cartesian grid).

Some Examples of Tondos, Analyzed

Madonna and Child, painting by a follower of
Sandro Botticelli (Date c. 1500-1510)
El Paso Museum of Art

The tondo above clearly shows both systems being employed. Note the straight lines of the "throne" behind the Madonna and child. Those show strong evidence of the Cartesian grid system. It looks a bit awkward, as if the throne were painted in its entirety, then cut off using a circular template, but the straight lines of the throne do give a great deal of stability to the design, making the woman and child look very secure.

In this picture, the exact center does not just happen to be the point where the Madonna's womb and the child who came from it meet in the picture; if the artist didn't plan this consciously, he no doubt did so intuitively. This point is the center of the larger "center" which is made up of the child and his mother. The "throne" in the background snugs up around the larger center just mentioned, composed of the mother and child together. This is my own interpretation based on what I understand from the Arnheim books I have studied (as are the other interpretations below, except what is contained in quotes by Arnheim), but I feel quite sure that I am right.

A Desco da Parto Masaccio (1401 – 1428)

The tondo by Masaccio, above, also shows clearly that the Cartesian grid was the basis for the composition (note the strong verticals and horizontals and the perspective lines). It looks as though this "round" scene is just a portion of a rectangular scene, and while the arches are sympathetic with the roundness of the overall shape, and there is nothing "wrong" with using part of a scene that was first designed in a rectangular shape if it looks right, it shows that the artist had adapted his Cartesian-grid-based composition to the tondo shape rather than creating an idea for a picture of this scene that would be perfect for the round shape.

Greek kylix - Youth pouring wine with an oinochoe in Dionysos' kantharos
Triptolème painter

A very awkward composition for a round picture, above. Everything "fits" into the round shape, but only because it was all "squeezed" into place.

Kylix
Achilles tending Patroclus wounded by an arrow
Sosias - c. 500bc

I think that the scene just above is a much more successful composition in the round shape than the one of the "Youth pouring wine." The artist was much more sensitive to the circular edge. The subjects are bending over naturally, rather than tilting as if they're falling over, and there are some very interesting negative shapes around the edge (as well as within the composition). The center of the circle -- the area of most intense focus in a circular composition -- is well-used, too, as there you see exactly what is going on (the tending of the wound) without having to look any further. All the action is centered around this spot.

There is also reference to the Cartesian grid in the above picture, especially in the horizontal "floor" beneath the two men, and in Achilles' close-to-vertical lower back and "skirt." These provide the vertical and horizontal references that make the actions clear, and they also provide stability to the composition. The many diagonals in the picture make the composition appear lively, busy, and tense -- all the more so because they are compared with the "stable" Cartesian references of the floor and of Achilles' back.

Madonna della Seggiola (also known as Madonna della Sedia)
Rafael - 1513-1514

"In the Madonna della Sedia direct references to the angular framework are so thoroughly avoided that the one reminder of verticality, the upright post of the chair, looks almost like a safety device, needed to keep the picture from rolling out of control." (Rudolf Arnheim, in POC)

And note how the vertical post is topped by a ball shape, and also has curves below in different forms. Also note how the chubby baby's round toes relate to the rounded forms on the chair post, which relates to the faces and the baby's elbow, etc. You go from one to the other and go all around the picture, the round shape of the tondo encouraging this. As Arnheim pointed out, the post is the only thing that keeps it all from spinning.

There are so many things that can be written about round compositions that although I have have already written two posts on the subject, including this one, I have barely touched the subject (I may write more). Yet I hope that what I've written, and the illustrations accompanying it, will at least get across the idea that a round composition must be approached very differently than a rectangular one, and that some subjects are better than others in such a format. I also hope that people will be encouraged to try their own round compositions. I'm working on one myself that I started a couple of years ago and put aside. Now that I've learned a lot about composing for this shape, I'm starting over and hope to do it in a more intelligent way.

This animated snowglobe was created by Patti Wavinak of Moon's Designs, who has given permission to use this picture here.

Finally, here is an animated snowglobe. I looked through many, many snowglobe pictures before selecting this one. Most of the pictures didn't show the globes as I remembered them from long ago. The ones I remember had scenes such as this one, and here you don't have to imagine how it looks when you see the "snow falling."

To me this snowglobe picture illustrates something important about round (or spherical) compositions -- They are perfect at depicting another world, a self-contained world that is not where we live -- it is "out there" and not something we can join in (neither can anything in that world join us).

What is more "perfect" and "complete" than a world made up in the imagination -- a world that we sometimes wish we could enter and be part of, but know we can't? It's a world by itself. Something that we can only contemplate.

In order to join that world, we would need to be transformed into something that belongs within it and even then we may not gain entrance...it's hard to imagine entering (or leaving) a spherical "self-contained" object without destroying it in the process. We cannot usually make the leap, except maybe in our dreams.

I will write more about centers in another post. This post focuses mainly on the outer shape of the round artwork, or tondo.

My thanks to Rudolf Arnheim's fascinating books, eleven of which I now have in my own collection. It is because of his books that I have any kind of an understanding of this subject. His book The Power of the Center has been particularly valuable and is the one all quotes in this post are taken from.

Note: Where I have used the initials POC, above, I am referring to Arnheim's book The Power of the Center.

NOTE ADDED OCT. 4TH, 2009: I've written an "introduction" to this post that might be helpful in trying to understand the subject. If you're interested, you can read the introduction in the October monthly newsletter in the Thinking About Art Monthly Newsletter Archives. When you get there, click on the newsletter with the title Thinking About Art Monthly Newsletter - October 1, 2009.

Art, Gravity, Life, and the Cartesian Grid

I realize the title of this post is not very modest, but the post itself is, though I do touch on all of the subjects named. I don't presume to know everything there is to know about all of these subjects, but I want to introduce them and explain what they have to do with each other briefly. I will be writing more about these things, and related subjects, in later posts.

Here are a couple of pictures showing the Cartesian grid, so you'll have the grid in mind while reading what comes after.



The Cartesian Grid

"A co-ordinate system whose axes are straight lines intersecting at right angles"
(Ref: Ministry for the Environment, New Zealand)




3 Dimensional Cartesian Grid
Source: Wikipedia

Definition of a Cartesian grid: "A Cartesian grid is a special case [among grids] where the elements are unit squares or unit cubes, and the vertices are integer points." (Ref: Wikipedia Article on the Cartesian Grid)

Why is the Cartesian grid of any use to us? It doesn't look like much.

Awareness of the Cartesian grid is extremely useful to us, in our lives and in our art, because we live on Earth and so are very much under the influence of gravity (Gravity: The fundamental force of attraction that all objects with mass have for each other); it is gravity that makes those simple verticals and horizontals so necessary in order to understand and interpret our world (as viewed and experienced by inhabitants of our planet).

Gravity is a very strong force that pulls us, and everything we observe and live with, toward the center of the planet. In fact, it's what holds the planet itself together.

The artist who paints (or the sculptor who sculpts, etc.), if what they are depicting has to do with life as lived here on earth, has the effects of gravity in mind, whether he (or she) is consciously aware of it or not, as it is the dominant physical force in our lives. They might not plot their design on a Cartesian grid, yet they see and arrange and understand things as if they were doing so.

But the Cartesian grid looks so simple! (You say.) It's nothing more than vertical and horizontal lines! What do those lines have to do with life, and gravity, and art?

Let's start with the verticals.

The verticals in our lives

We live with gravity all our lives. We feel it as weight. Because we are constantly pulled from down below, we are very aware of what is "up" (pointing away from the center of the earth) and what is "down" (toward the center of the earth). Also, because we are aware (if only unconsciously) that everything on the surface of the earth is being pulled downward (or "has weight") we are inclined to infer that anything that's vertical (standing "up") has energy -- It is alive and alert and/or strong enough to resist the force of gravity.

The horizontals in our lives

Because we instinctively know how gravity works, things that are horizontal seem to us to be unthreatening, peaceful, meek, possibly even dead. They are not resisting gravity.



Photo Source: Wikipedia

When our energy is depleted, we lie down if possible, to sleep or just to rest. It requires no effort on our part to lie in a horizontal position.

The surfaces we walk and ride on are horizontal whenever it's possible to make them that way. Because of gravity, it's more difficult, and uses more energy (and is sometimes dangerous) to walk on or ride on an incline.

The places we live in (or prefer to live in) are usually as flat (i.e., horizontal) as possible because gravity makes it difficult for us to climb, or to descend with care (i.e., so that we will not fall). Even if the terrain is not flat, the floors of the buildings are; and, by the way, if we have flat floors the walls need to be vertical.


Building under construction
Photo Source: Wikipedia

If we lived in a place where gravity had no influence on us, there would be no up, nor would there be a down. There would be no definite verticals, nor horizontals. The verticals and horizontals of the Cartesian grid constitute the basic framework of our lives; everything is seen in relation to this framework.

Diagonals

If something is diagonal, that has meaning for us, too. Diagonals wouldn't have that meaning without the Cartesian grid showing us how they deviate from verticals and horizontals. A diagonal could be something rising, or something descending. (A vertical has already risen; a horizontal appears lifeless and not likely to make any moves.) So, diagonals mean "action" to us; something is happening (yes, diagonals can also imply depth).



Photo Source: Wikipedia
These diagonals do not look stable. It's alarming to see them like this. They're not vertical, nor are they horizontal, but they look like they're in the process of becoming horizontal. These diagonals make us nervous.

Relating vertical and horizontals (and diagonals) in life to those on the Cartesian grid

Standing people, trees, buildings, fenceposts, etc. look to us to be parallel to each other, as the vertical lines in the Cartesian grid are. Horizontals are connected at equal distances from each other to the verticals in the grid to make squares (in two dimensions), or make cubes (in three dimensions), making it simple to locate anything that is overlaid or represented by the grid.

The Cartesian grid helps us make many things that we use. Think of a map, or a pattern for a woodworking project or the grid you might use for transferring a picture from one surface to another. Graph paper is a Cartesian grid.
Furthermore, "The right angles of our living spaces, of chests and sheets, afford a visual order that helps make our lives simpler than they would be, say, in a primordial forest," says Rudolf Arnheim. "And, for the sake of order the Cartesian grid also remains present, actually or implicitly, in our works of art." (Arnheim: The Power of the Center, 1982 edition, paperback, page viii)

So we find the Cartesian grid very useful in measuring, planning, understanding, adapting to, representing and negotiating the spaces around us and in comprehending the meaning of what we see.

Two good links

1) I'm so glad I found this one. It's called The Coordinate Plane. It clearly and simply explains, and shows, how the two-dimensional Cartesian grid is used. Be sure to check what you want to see in the little boxes to the right of the diagram. Click "Grid" first, and you'll see it as it looks in the picture of the Cartesian Grid near the top of this post. Click each of the boxes to see what shows up. Also, you can move that little red dot around with your mouse pointer. When you are completely confused, click "Reset"
(under Quadrant 4) and it goes back to the way it was at the beginning. Be sure to read the definitions and suggestions below the grid. Also, there are other pages listed below that have to do with this subject. Just click on a link to get to what you want to see.

2) Wikipedia article on gravity

Quotations

"In daily perceptual experience, visual orientation in space relates to the Cartesian coordinates of the gravitational field." (Rudolf Arnheim in The Power of the Center, 1983, paperback, p. 197)

"The structure of visual space relies upon the framework provided by the vertical and horizontal. This framework is the visual 'tonic,' the zero base at which tension is at a minimum." (Rudolf Arnheim in New Essays on the Psychology of Art, 1986, paperback, p. 215)

"In the parochial view of its small inhabitants, the curvature of the earth straightens into a plane surface, and the converging radii become parallels." Rudolf Arnheim in The Power of the Center, 1983, paperback, p.vii)

"Parallelism and right-angled relation yield the most convenient framework available for spatial organization, and we cannot be grateful enough for living in a world that, for practical purposes, can be laid out along a grid of vertical and horizontals." Rudolf Arnheim in The Power of the Center, 1983, paperback, p.vii-viii)

"Were it not for gravity one man might hurl another by a puff of his breath into the depths of space, beyond recall for all eternity." -- Roger Joseph Boscovich, Philosophiae Naturalis Theoria, 1758.

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