The following is a simple explanation of how to design your own composition with the dynamic symmetry proportional system. This method can be used to analyze other compositions.
This system, today termed "Dynamic Symmetry," is a very simple and useful way to proportion an area - any area. Dynamic symmetry is particularly useful to iconographers because it is so adaptable to any space needing decoration, and it allows for perfect enlargement of a composition without losing the "flavor" of the original. I believe that this method is an ideal one for the iconographer to use today. It can be utilized on any area and ensures that the resulting composition will have pleasing proportions. In addition, it has the ideal property of allowing for perfect reduction or enlargement of a composition. (See Figures I-1 to I-9 below)
How to develop your own dynamic symmetry composition
All you need in a compass, a ruler, and a pencil - that's all. To demonstrate:
Shown in Figure I-10 is a diagram of the continued progression of the development of the "root" rectangles. You will note that the "root-three" rectangle extension is a somewhat smaller length than that of the "root-two" rectangle extension. This method of adding onto the original (or "unity") square and extending the rectangle can be carried out as many times as needed or desired.
The progression is extended by the manner given in the directions above. By continuing to add diagonals to each new rectangle and extending it with a curved line to the base line and then drawing in the right-hand side of the rectangle, new "root" rectangles are formed. This can be done to infinity, but in modern times a "root-five" rectangle is usually the most common in use.
Plato's students used these rectangles up to "root-seventeen." The East Indian Hindus rarely if ever used more than "root-six" rectangles and did not commonly utilize the "root-five" rectangle in its many special properties as did the Greeks.
In general, there is no need of more than the "root-five" rectangle because it contains within its properties and boundaries all of the essence of the system of dynamic symmetry area proportioning.
The "root-five" rectangle has many of the same properties as the ancient Greek's "Golden Section" and "Golden Rectangle" but the Greek rectangle itself is derived by different means. The "Golden Rectangle" is a unit unto itself and is not part of a geometric progression, as is, for example, the dynamic symmetry's "root" rectangles.
Now that you can see how to construct your own dynamic symmetry "root" rectangles you can also see how various space arrangements can be developed with the use of these "root" rectangles. The themes very subtly with each "root" size difference. You may note that a "root-four" rectangle is equal to two squares and that a "root-nine" rectangle is equal to three squares.
The following paragraphs may seem to a non-mathematical person or any person who does not know the principles of geometry to be quite confusing. However, these simple lines can be made with a ruler and a compass and, if mastered, are followed by results that will make these dynamics clear.
Below are two diagrams demonstrating the formation of "root" rectangles from either outside of a square and thus making each succeeding "root" rectangle larger than the original square; or the formation of "root" rectangles from inside of a square, making each succeeding "root" rectangle smaller than the original square.
Each "root" rectangle has its own ratio. Ratio is the quantitative measurement comparison between two things belonging to the same kind; in this case, belonging to segments of straight lines. These ratios, in mathematics, are called "the proportion of the mean to the extreme." That means, you can divide the larger number by the smaller number, or the smaller number by the larger number, and the result is the ratio of the rectangle when the numbers measure the length of the lines.
You will notice that the beginning of both of these developments begin with a square (or "unity"). Again alphabetic letters locate the key points. For example, in review, AB means the line which connects point A with point B. Arc CF means the curved line which starts at C and ends at F, as in Figure I-10 below.