The Visual Dynamics of Related and Unrelated Shapes (Rectangles)

Each shape has its own dynamics: each shape has its own energies and arrangement of those energies; the rectangle is the classic shape in the visual arts. Two classical divisions of the rectangle are handed down to the artist; but to the modern artist, these are for the most part curiosities: interesting but no necessary in composing – or rather, spewing forth a painting – at best, they are recipes on how to lay in a picture: where to conveniently hang objects. The reality is that these systems are maps of the rectangle’s dynamics.

The eye will naturally divide a line in half: the mid-point; in a rectangle, this leads to the bipartite system. The eye also naturally divides a line into thirds leading us to the tripartite system. Interestingly the bipartite system includes the tripartite: the latter is a subset of the former.

Yet, what about the shape area in terms of its nature divide into sub areas? Does the area easily divide into fourths and thirds?


  1. Is there a perceived relationship?
  2. Is this too subtle to consciously register?
  3. Does the eye grasp the relationships? Can the eye recognize a shape as based an original


  1. Create a rectangle with each side easily divided by three
  2. Enter the tripartite guidelines
  3. Create rectangular shapes based on those divisions
  4. Create an wholly unrelated rectangle having no proportional relationship with any of the rectangles or the master rectangle.
Rectangle with related rectangles and one unrelated


    • The eye does perceive the relationships: there is an harmony between shapes based on the initial rectangle;
    • The harmony and disharmony are immediately perceived. The red rectangle is perceived as out of harmony with the other rectangles.


  1. Can compositions be created that play off  the relatedness of different proportioned rectangles (or simply objects); for the eye is attracted to and tends to group by likeness.



[Edited 3/10/2017. This experiment was initially done as to understand why the eye quickly recognizes the misshapeness of a drawn human figure; but I have since come to understand that the mind has an internal sense of proportion. Yet, this is a possible way for the artist to create pleasing proportions of the human figure.]


I apologize for the delay in posting. The past few months have been consumed by clearing and moving out of the family home and moving to Greensboro, North Carolina. The studio – what there is – is still coming into shape; but the apartment is small and it is a humid August and poor air conditioning. That being said, the painting below was completed in May.

Seaside Heights Boardwalk Jitney

I originally meant this painting to be only a sketch; to be a quick study of creating the sense of movement across the rectangular field; at the time, I was bouncing off of Gerome’s “Duel after the Ball” wherein the artist used the grid of the rectangular force lines to create a stage and dramatic movement. Gerome played the tripartite canvas division against the bipartite: the former was the stage and the latter contained the action and interaction of the characters. Similarly in my painting, the background is placed within the context of the tripartite system and the characters and the jitney are laced within the bipartite system. The painting was to be done with think strokes of paint; but, I soon became concerned about the quality of the piece; and I also became more interested in how areas of color melded into related adjacent areas. Finally, I began to experiment is glazing in order to more intense colors.

As to the piece’s structure, the cart pusher initiates the movement. His back foot is planted on the vertical force line of the left (the bipartite system has three major lines dividing the rectangle into four sections). His forward foot crossed the leftward major dividing line of the tripartite system; and his head is just on the line. The pusher has set up the rightward movement. The back cart edge is released from the tripartite force line and comes under the influence of the center force line; the strength of this center line is increased as the back cart wheel is directly on the line as the head and torso of the female passenger. The forward struts of the cart’s cab come under the influence of the right side tripartite division line and, combined with the legs, increase the sensation of rightward movement. Because the eye seeks like relationships, the viewer’s eye is also cast back to the head and forward foot of the pusher. The forward section of the cart is elongated in order to increase the pull and release from the right hand force line on the quarter mark.

Overall, I think the painting achieved the initial goal of creating a sense of movement across the canvas.

In terms of glazing, I was able to increase my ability to predict how a color will change when overlaid by another. I was able to accurately predict the changes using the color mixing triangle.

The shadow under the cart was reworked four times in order to get a smooth transition from one color to the next. My initial thought was to use diagonal brush strokes as I applied the paint in order to recreate the planking of the boardwalk; but the result proved to be clumsy and distracting.

I also made extensive use of color fifths.

Over at a LinkedIn artists group, Stephen Cantrel asked the following question:
“Art can never loose its way it’s just up to us to keep up with it!”

I responded accordingly:
“Art is intimately connected to its parent civilization and culture; yet, it is also a tradition of intellectual/spiritual activity which goes all the way back to the cave paintings and sculptures. By examining this history, we can can see what are the basic requirements to being an artist; and, we can determine the aberrations, the degeneracy, and the highs and lows of a civilization. By being familiar with this history, the artist realizes what understanding and skills he needs to participate in the long history of art.

One things that can be determined from the history of art is that art has always served the master class; or, if that offends you, the class or group of people for which the artist creates work: their interests, their concerns, and their intellectual culture governs the output of the artist(s). If, upon examination, you decide that the art produced today under the current masterclass’ diktat (liberalism, progressivism, and political correctness) is an aberration and degeneracy, then you must re-establish the connection to the long history of art in your own work. And you must be prepared to face the consequences of snubbing the elite and the representatives of their culture.”


One of my Facebook friends posted a quote from Kierkegaard: “Because it is possible to create — creating one’s self, willing to be one’s self… — one has anxiety. One would have no anxiety if there were no possibility whatever.”

The conversation went on for a couple of postings; but my comments were, “Anxiety tells you that you are on the edge of your understanding: the creative step is beyond that; or, if you must use Kierkegaard’s phrase, it is the leap of faith;” and, “One must pass through anxiety; anxiety is the marker of your limits: it is the end of your current understanding. In art, one reaches a point where he does not know how to accomplish the next step and becomes anxious; one’s powers of understanding and knowledge must be marshaled; and then, though he doesn’t know what the end result will look like, he trusts his skill and judgment to make the leap.”

For the past few years, I have made use of a color’s fifths. By that I mean using the color triangle (as I wrote below in the entry “The Color Triangle: Mixing Pigments”) to determine the fifth colors from a root color and use that relationship to determine pigment mixtures.


The color-triangle_Yellow-Blue-Red-Orange; note that the colors purple, violet, red-violet, and red would be adjusted so that their intensity would lie along the edge of the shaded triangle.

Using yellow as the root and basing the chord on the Pythagorean right triangle of 3, 4, 5; the other chord colors are red-orange and blue; red-orange is three from yellow, blue is four. On the color/note wheel, yellow is A, blue is C#, and red-orange is F#. This gives us the following right triangle:


The yellow, blue, and red-orange chord with yellow’s fifths: red-violet and purple; the fifths of the other two colors are indicated.

it is also possible to keep yellow as the root color; but make the four side yellow to red, and the three side yellow to blue green. In this case, red-violet possesses the relationship purple had in the above figure; and purple now possess the relationship red-violet had.

The right triangle shows yellow at the right angle and the movement is clockwise to blue and then red-orange. Let’s call the right angle position the root position; therefore, yellow is the root color.

I then indicated with red lines the two colors that are fifths of yellow: red-violet and purple. As can be seen in the above figure, the fifths of the other colors in the triad are:

  • the fifths of blue are red-orange and yellow-orange;
  • the fifths of red-orange are blue and green.

Note that the fifth red-violet divides the hypotenuse – five color range – in a natural manner into three and two. Whereas, purple seems to be in a relationship to blue as though it was its sharp : C to C# so to speak. The natural division may be a reason why the yellow-red-violet relationship seems more attractive.


I played “put the fifths descending from yellow.”

I discovered in one of my failed acrylic paintings that using the fifth of a color gives air or breath to the painting at the same time it is creating distance between colors.

In painting these fifths, one’s eyes become accustomed to the relationship between a color and its fifth; so, it becomes easy to determine when one has mixed the true fifth. Here is a key understanding: one can train his eye to recognize the particular relationship he is seeking: the color relationship, when achieved just seems to harmonize; there is a visual “yes”; in fact, many times when the right color is found, the color just seems to disappear.

The relationship creates an implied line between the two colors; in fact, the color intensities withing the relationship can be adjusted to incorporate an emphasis on a compositional power line or intersection of the implied power lines.

My use of the fifth has become an integral part of my painting, not only because of the breath the fifth seems to give; but also, because the painting seems to come alive

September Composition 2013

September Composition 2013

The first of two created in September and October of 2013.

Seven rectangles make up the above work;These rectangles in turn create the levels or depths of the digital painting.The rectangle in the lower right is the key for the digital painting: it sets the color chords and the pattern of the shapes.

Each rectangle is organized using the bipartite method. The method is a means of describing the implied, energy lines embedded in the rectangle.

The basic principle used here is that the eye seeks out similarity in color, pattern, and shape. The viewer’s eye will of its own accord move to and from complete and incomplete versions of the key pattern found in the various rectangles; focusing on any one position of an element within that pattern moves the eye to its counterpart in the other rectangles. The same is true of the movement of color from rectangle to rectangle.

Finally, I used the empty energy loci within the larger implied rectangle to create a second movement to play against the first pattern.

October Composition 2013

October Composition 2013

The Second Composition

The principles used in the first painting apply to this one as well. I made three major changes: first I introduced a diagonal movement in each rectangle – other than the key – moving from the quarter point on the left side to the lower third point on the right; second, I removed the rectangle bounds and let the eye apprehend the rectangles; and third, I created another movement joining the key pattern and the diagonal pattern by darkening a glyph within each pattern.

Several years ago I created a web site for an artists’ guild to which I belonged to at the time; on that now defunct site, I created a page on how to hang an exhibition. The image below is a screen shot from that page.


Screen shot of instructions: click to enlarge.

The simple instructions were based on kinesthetic and visual principles:

  • The visual energy of an artwork is the key to placement in an exhibit;
  • Movement around the room is based on the focal length of the art work: this is the distance at which the piece is apprehended; the energy of the piece will force you to move the proper distance to perceive it;
  • Determine how the viewer is going to move naturally through the gallery space: clockwise or counter-clockwise;
  • Work should be arranged so that the movement around the room is a gentle flow: the shifting from one focal length to the next is not abrupt;
  • Keep similar energies together (back in the eighties, I was accused of having a corner for bad artists: no, it was based on energy: unfortunately a good artist was placed in the same spot because of similar energies);
  • The focal length of a piece should not force you against a wall: this would be the case if you hung a strong piece in a narrow hallway;
  • Use focal length to determine where to put a sculpture in a room with paintings: a viewer looking at paintings should not bump into someone looking at a sculpture; worse yet, the focal length of the painting should not lead the viewer to bump into the sculpture;
  • Use the energy of the works to determine spacing between pieces: keep moving the artwork apart until the energies release;
  • The longest focal length is where you are walking into the room; therefore, the strongest pieces – those having the most energy – are opposite the doorway;
  • The height of the artwork is determined by hanging the center of the piece five feet from the floor; if there is a group, arrange the group and have the center of the group be five feet high.