Kitty Gordon

Permutations

From Line Drawings To Three Dimensional Forms: An Explanation

A simple system acts periodically and returns to the same point over and over again.  For example, a pendulum moves from side to side, always returning to its starting point and then repeating.  If we introduce change to the system, tiny differences generate what appears to be chaos.  However, repetitive small changes within a system usually create a subtle form of order.  Multiple iterations result in so many minor and nearly imperceptible changes over time that this order is often difficult to see.

I was curious to see these patterns develop so I created a simple system in my mind that was composed of four points (1,1,1,1).  I then considered a system of number sets that would include all of the possible whole number combinations of four numbers (1,2,3,4).  From a starting point, each number represents a movement, first up, then to the right, then down, and finally to the left.  For the number set 1,1,1,1, the point would move up one unit, to the right one unit, down one unit, and to the left one unit, eventually making its way back to its starting position:

If I made a slight change to the set of numbers, then the point would end in a different location.  For example, the end point of number set 1,1,1,2 would be one unit over from the original number set:

As I continued to consider my number system, I realized that some sets of numbers, such as 4,4,4,4 or 2,3,2,3, would not change the end point because their ratios are proportionally equal.  Ultimately, I created the following defined number set system:

For my first number drawing, I began with the set 1,1,1,1 and moved the end point according to those numbers.  Then I moved down the column to the next number set and, using the end point of the previous number set as my new starting point, I moved the point through the second number set.  I continued to move the point through every set of numbers in the system.  Using this system, I created my first complete number drawing.  I was amazed to discover that when I got to the end of the drawing, I found myself back at my original starting point.  It was then I realized that within this odd and rather chaotic looking image there was an underlying order.  This discovery was both exciting and intriguing.

Next, I wondered what would happen if I changed the order of the number sets slightly.  For my second number drawing, I moved through the numbers horizontally rather than vertically.  This produced a different although not completely unfamiliar drawing.  I concluded that by making changes in the order of the number sets and moving the point around, I could create numerous images.  Even slight changes in the order of the number sets made completely new, but sometimes similar, images.

As I continued to vary the order of number sets within the system, I decided to set rules making changes to the number sets themselves, rather than just the order.  For example, I could create a drawing with a rule that replaced each “1” with a “2.”  Thus, 1,3,1,3 would become 2,3,2,3, even though it did not replace the already existing 2,3,2,3.  As I continued creating new rules, it seemed that the number of images I could create might be infinite.

Throughout my drawings, even slight changes in the order or rules made unique images.  No one image was exactly the same as any other image, even though many images contained parts of or similarities to other images.  In fact, the pattern I created in my first drawing is reflected repeatedly, but somewhat differently, in many other drawings.  In many cases, this pattern is only an echo of the first number drawing, but it is still apparent.  As with my first number drawing, I often finished a new drawing at its starting point.  Within each drawing, I discovered patterns underneath the image’s apparent random outcome.  This was when I knew that chaos and order are not only universally balanced, but are inseparable.  You cannot have one without the other.

After creating the number drawings, I wondered if the power of the drawings could be translated to three-dimensional images.  Could I create a deeper representation of the qualities of change?  If so, how could I express what was important to me?  I decided to use varying materials and techniques in order to bring life to these forms.  The process I have used to create these objects is as important to me as the drawings themselves.  First I had to decide if a drawing would translate well to another form.  Many images that did not interest me in two dimensions were fascinating, and far more powerful, in three dimensions.  As drawings, most of these images curl back on themselves, sometimes repeatedly.  In two dimensions, these overlapping layers are not apparent.  However, in a three-dimensional form, their patterns and structure become fully developed.  Conversely, many drawing do not work well as three-dimensional forms because they are so spread out that they are uninteresting.

Once I determined which drawings would translate well to three dimensions, I had to decide how to express each image.  Often I relied on nature’s own order to help me create new representations of the original drawing.  In the end, I went from a structured and ordered number system to the apparent disorder in my original number drawings and finally back to the universal chaos anchored by underlying order in my final forms and completed drawings.

Kitty Gordon
September 2006