Armature Example - Borrego Springs and a Tool.


I am beginning a series of shorter posts. Each post will concentrate on one topic and in an order such that they will build on each other. The series is open-ended but they will begin with topics on composition.  The underlying mathematics will be explained where ever possible or at various points.


 I want to preface this post with my usual 'disclaimer'. When I first began to paint I wanted to make sure that the left-side of my brain didn't take over, which -as a Mathematician- it's prone to do; I wanted to be expressive !  However, as the years went by I couldn't avoid seeing how often mathematics entered into discussions of composition, for example. So I decided to spend time investigating for my own self the symbiotic relationship of math and art.

My usual approach to a painting now is to start off analytically, with measurements and thoughts about proportions and unequal measures, and perspective in the landscape and the direction of light and the shadows.  While I paint, however, my thinking is much more intuitive, selecting colors and textures that 'feel right', perhaps with some cautions such as: does it need more warmth or cool, more light or dark, more gray or chroma? But if I begin with an analytically-induced design then perhaps I will be freer to invent/imagine/create other aspects of the painting.

My studies have led to different composition theories.

Composition Armatures

  • Checkerboard Grid
  • Rule of Thirds
  • Dynamic Symmetry
  • Harmonic Armature
  • Informal Sub-division
It is common practice to divide up the canvas into small square grids to transfer a drawing to the canvas accurately. But beyond this what can an artist do to help in designing a painting? Dow and others have provided guidelines with names such as Steelyard or letter-names such as L and O. General guidelines include unequal measures and thinking carefully about putting a focal point in the center of a painting.

This post describes the use of an Armature in general with a painting example that did not use a Dynamic Symmetry grid. Instead it used the Rule of Thirds to locate a focal point and a Fibonacci Spiral to set up guidelines. Could it have been improved with a Dynamic Symmetry armature during the design? The Dynamic Symmetry Armature is described below in more detail with an example.

 An Armature consists of lines criss-crossing on -or under- a painting to be used as guidelines for focal point(s) and lines leading to the focal point; the end result would be a painting that encourages the viewer to stay with the painting, traveling around it in harmonious way.  Perhaps one can think of an Armature as a scaffolding.

Dynamic Symmetry Example:

I've come across an iphone 'tool' that can help convey the idea of armature, Wise Photos, shown in this example. Most of these images in this post were produced using this tool. Take a photo and choose one of the designs -or armatures- from Rule of Thirds to Dynamic Symmetry as well as the Fibonacci Spiral to produce a photo with a selected overlay, such as Rule of Thirds or Dynamic Symmetry. 
Most artists have heard of and use the Rule of Thirds. Photographers and Architects like to use the Golden Mean with the 'Fibonacci Spiral' leading to the golden spot in the diagram/picture. The Dynamic Symmetry composition armature has also been used over the centuries by some artists. It's thought that the intersections of the lines offer good places for focal points and 'golden points'  as well as points along the grid lines that might lead the eye to the focal point. The focal point does not have to be exactly at one of these points of interest; perhaps next to it. We note in passing that the Golden Mean can be and is incorporated in Dynamic Symmetry.

One can set up the grid on a canvas before beginning the painting, perhaps preparing canvases for the field:

Theoretically, the pencil lines would be covered up by paint.

But we can also use grids to analyze existing paintings. And this is what I propose to do in this post.

I begin with a painting to be analyzed: Mountains. It was painted outside in Borrego Springs a few years ago with strong mountain shadows that lend themselves to interesting shapes and points to keep the viewer involved in the painting. At the time I probably used the Rule of Thirds (ROT) to mark the main mountain shadow; it's at the upper right intersection of the ROT. But I also used the Fibonacci Spiral to draw the eye around the canvas (sometimes referred to as the Golden Spiral - more on this later). So, is it obvious in this painting that these concepts were employed?

I would like to analyze "Mountains" also to see if the design could have been better. Should I have begun with an armature such as Dynamic Symmetry?

We have chosen as our example a canvas with measurements, 10 in high and 16 inches wide. The ratio of the two sides is 1.60 close to the Golden Mean of 1.618... (more about the Golden Mean in other posts).

Mountains, painting to be analyzed (10x16, oil).

It appears that the main mountain shadow was marked at the upper right intersection of the Rule of Thirds' grid. Is this a pleasing position for the focal point of the painting? Notice the main bush at the lower left intersection.

This spiral might lead ones eye around the canvas to end up at the center of the spiral. It looks like the main mountain shadow is slightly off, but perhaps close enough. Are the foreground bushes arranged to draw the eye around the canvas? Recall that at the time of this painting I was very aware of the Rule of Thirds and the use of the spiral.  

Dynamic Symmetry Armature Construction

The Dynamic Symmetry Armature is analyzed in detail on a site I came across years ago: Could this have helped me with a better design and composition? The theory behind this armature intrigues me as a mathematician, and I have been enjoying analyzing different, more complex grids for other rectangular shapes. 

An armature begins with the main diagonals of a canvas (rectangle). The diagonals cross in the center of the canvas. For the Dynamic Symmetry Armature we also use lines drawn at right angles to the main diagonals from the corners (called reciprocals).  The  reciprocals are considered effective lines since they act as balances to the main diagonals, creating dynamic interaction.  The idea that the reciprocals in general are at right angles seems to me to give them power, the power to 'thrust' the viewer's eyes around the canvas. So I like the idea of using reciprocals.

The four intersection points where these lines cross can be considered points of interest. One of them does lie almost at my main mountain shadow. A secondary point of interest is at the lower left intersection.  Is the design of the bush such that ones eye would be drawn up to the main shadow? 
The grid is symmetric, but the artist is advised to use the points of interest and the lines asymmetrically. And since I might not want to be encouraged to highlight the upper-left point of interest, I might not pencil in the reciprocal drawn from the lower left corner, at right angles to the main diagonal between the other two corners. 

One then constructs vertical and horizontal lines through the intersection points to complete the first phase of the Dynamic Symmetry Armature.

However, for unusually elongated  canvases - or in the other direction - near-square canvases, these reciprocals might not help much or at least might not lead to the ideal main focal point (to be analyzed later).

After a while, the artist can almost visual this grid when painting and not need to pencil in the lines.

This Dynamic Symmetry armature could be embellished with another design element, rabatment -or rebatement -of squares, which we shall explore later. Basically it adds a few more important verticals that will guide the artist further - and in fact lead to a finer or more detailed grid to use. A more elaborate Dynamic Symmetry overlay is not provided with this iPhone application so we will show a different grid overlay for this at another time.

Harmonic Armature

But before before concluding this take, I want to provide an example of a currently popular grid system called the Harmonic Armature. It consists of 14 lines drawn from the corners to mid-points of the edges, leading to a grid of lines that are seen to be excellent candidates for special points in the canvas, drawing ones eyes around the picture. Would this have helped with a better design?


These Harmonic Armature stars are located at the Rule of Thirds intersections. We will prove later that these intersection points always divide the canvas into thirds, whatever the proportions of the rectangles.

To be analyzed further: Does the 'harmonic' in the name of this armature lead to more harmonious paintings?  And what does this mean?

What are the pro's and con's of the two main armatures listed here: Dynamic Symmetry and Harmonic? And there's another that I have attempted over the years: Informal Subdivision by Andrew Loomis.  We will pursue this topic in another post.

We will add images of how to construct this Dynamic Symmetry Grid at a later time also though studying this example might be sufficient. 

In another post we will work with canvases of different proportions, noting again that this example uses an approximation to the Golden Rectangle, a 10x16-sized canvas.

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