Fractal
by
Mary Pfeifer

Art makes thoughts visible. Training the “eye” to see is an arduous process.  This process does not happen in one semester.  My exhibition “Fractal” represents a lifetime of seeing.

In 2002 I was privileged to become part of P.E.A.R.S. (Printmaking Education And  Research Studio).  That year, the visiting professor was Master Printmaker Elizabeth Dove.  She introduced a printmaking method that involved a product from DuPont which was developed originally for computer chips.  This method employed a dot pattern that had to be as non-repetitive as possible.  By the end of Dove’s stay at NDSU, I was hooked on finding the most chaotic dot pattern possible.  I exploited repetitive dot patterns in printmaking to emphasize the obvious.

In 2006 I read the novel Fractal Murders and was introduced to fractal mathematics.  I came to understand, in a very concrete way, how and why dot patterns are never random.  Through fractal mathematics, I came to understand (for the first time) dynamic dot patterns.  I began to learn to manipulate random patterns to create a better composition in my artwork.

The artist Paul Cezanne's instructions to young painters was "Everything in Nature can be viewed in terms of cones, cylinders, and spheres.”  In contrast to this, Mandelbrot, the mathematician who coined the word fractal, asserted that “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."  Fractal geometry is a method by which we can describe complex, irregular shapes that repeat themselves in nature.  Think about a needle on a fir tree.  The needle itself is a self-contained version of the whole tree.  If you look at the individual bits of the needle, they look like the needle (which looks like the tree).  Consequently, you have a complex mathematical formula that describes a pattern which continually repeats itself.  Thus, a single formula describes copious amounts of data.  So it is with Art as explored through the artist.

These seemingly isolated occurances include another experience with a visiting P.E.A.R.S. professor, Master Printmaker Laurie Sloan.  Under her direction, I experimented with various plastics, shapes, and patterns to create form.  This inspire me to tackle the ideas represented by the work in this exhibition.

In my most recent work, I examine my relationship with my mother (now deceased), who had Alzheimer’s disease; the ever-changing relationship I have with my siblings; and my own, personal struggle with the aging process.  These highly personal relationships are revealed in complex background images; my point here is that rarely, if ever, is the means to an end simple.

My work has a particular look to it.  When asked to make any shape, I made female figures and placed them in a row.  These shapes vary slightly in size and outline.   Often they appear in a connected row.  Sometimes an obvious dot pattern, or a pattern within a pattern, appears.  These patterns appear in every piece in the “Fractal” exhibition.

In the traditional and non-traditional prints, you will see a male figure that I have called “North Dakota White Male.”  He reminds of the fractal “Brownian Motion: According to Perrin” (1909), in which fine particles in a liquid, which has been disturbed frequently, are always in a perfectly irregular motion.  "They go, stop, start again, mount, descend, and mount again, without the least tending toward immobility." 

Traditional and Nontraditional Printmaking

Traditional and non-traditional printmaking is a process by which a repeatable image is made on paper.
The four traditional types are:  relief printing, in which the image is created by carving into the material and inking the raised area; intaglio, in which a dot pattern is made into the material and ink is forced into the wells; screenprinting, in which ink is forced through a dot pattern burned onto material, and; lithography, which is about oil and water not mixing.  Each repeatable image is hand pulled and considered original.

The repetitive patterns used to make the traditional prints in my exhibition “Fractal” are influenced by the mathematician Mandelbrot.  Part of my fascination with this is that Mandelbrot’s definition is a simple one for a complicated idea.  Mathematically, fractals are just a set of complex numbers which repeat.  When numbers are lined up in rows and columns, it becomes a matrix.  The Mandelbrot set, in general, is not always perfectly self-similar; small, slightly different versions of it can be found randomly.  Such picky little differences are what make a mathematician happy and a printmaker frustrated. 

In addition, I considered a fractal known as the Cantor set.  It is mathematically tied to self-similarity, and is the reverse of the printmaking method.   The mathematician or artist (in this case) take a line and remove its middle third.  Then one removes the middle third of that truncated line and so on. This repeating pattern can go on for ever.  The Cantor set repeated for “X” long is called Cantor dust.  Traditional Printmaking is additive, therefore the print becomes darker when repeated “X” times.

For a printmaker it becomes “What if I added another layer? What if I placed it just this way? What would happen if I …”

I created traditional woodcut prints in Fractals by repeating layers of ink.  Each layer was made with a base of approximately 80% transparency and 20% cyan, processed magenta, or primrose yellow.  Between each layer, the wood was manipulated to create variation in layers.  The board was then drilled with two inch holes to make a matrix.  Subsequent layers were inked with 95% transparency, 5% cyan, processed magenta, or yellow.  Registration marks were not used so there would be a slight variation in the matrix on each layer as well as on each print.  Each print was evaluated for composition and balance before it was placed on the drying rack.

I am actively involved in and fascinated by Technology, Education, and Fine Art.  I want to make real these very diverse methodologies.  To understand what makes an image visible in non-traditional printmaking (the way I did in this exhibition), I designed an image that I repeated using the computer and a software program called PS3 (photoshop3) developed by Adobe products.  The image was printed on a plotter and was therefore untouched by the human hand until it was finished.  Conceptually I wanted to show how the dot pattern, landing on paper, can create virtually any color from only three or four colors.  How these colors (cyan, magenta, yellow, and black or red, green, and blue combinations) are positioned on the paper make result in an almost infinite number of color variations.

Since the viewer may not understand basic color theory (uch as yellow and blue make green)and might not know the difference between PPI (pixels per inch) and DPI (dots per inch), I made very large green images.  Since computers make PPI and computers make DPI, I changed the pixel, which is square, into a circle.  I used a halftone pattern, which was the pattern used in the first offset color printers.  With the computer, I was able to isolate the dot pattern of each color.  I then changed each dot so there would be 8 dots per inch and the entire image was 90 inches tall.   Here is an isolated yellow dot at 8dpi.

Here is that same dot magnified. As you can see, the majority of the dot is yellow with the blue dot overlay making the green.  The magenta in the lower right is making the dot appear darker but not at this magnification
Taking the blue dots first, I converted each dot into an image. The image I used was a fetus.  The second dots isolated were the magenta ones which I turned into the repeating male pattern.  The largest number of dots were yellow since the image I began with was the repeating green female figure.  The black was comprised of very few dots so I changed those dots into small figures.

Here is that yellow dot with the fetus. The blue is still showing so you will actualize where the other colors fall to make green.  The next image shows the fetus in context.  The conventional printer prints in a matrix (rows and columns).

xx
Showing here is a figure replacing a dot pattern. This  appears as the color is printed as a diagonal.  The matrix dot pattern may print in rows and columns but the dot pattern is not a random or dither dot pattern it is printed in rows and columns.

This is the image replacing the color so non color theorists can see how the dots lay to make the different colors.
This color that I have isolated and replaced with the figure of Esther looks like this . In this three color separation you can see how the dot patterns lay in relationship to the other dots in that same color pattern.

As you can see in this image there are white areas.  The ones inside the individual images would not be white on the paper. The white areas  are shown in the following Image as blue.

The white area, colored blue in this example would not contain any color.  This dead space is what makes an image appear out of focus or fuzzy.  The images used here and in the exhibition FRACTAL are not actually 8dpi  but  made using the ratio 8 dots per inch, and printed using 72 dots per inch as a magnification.

In the Exhibition, Fractal, there were five female images plotted showing various aspects of non-traditional printing. 
Repeating Behavior Patterns Presented in Portraiture
In keeping with the use of repetitive patterns, the female form, the number five, and to demonstrate my abilities as an artist, I used oil, acrylic, and copper etching as media to convey jealousy, using our bodies to gain favor, genetics, mothering, and oppression as repetitive behavior patterns.    

  
The first two of the five portraits come from stories handed down orally and later in the written word.  There are a few variations in the different versions of these two accounts.  In Greek mythology, Medusa was the sister of Athena; as the result of a lover’s triangle, Athena turned Medusa’s beautiful hair into snakes and made her face so ugly that when men looked at her they were turned to stone.  I began by painting my face, then added my version of snakes (her head is full of them). 

After I completed the painting, it was brought to my attention that I did not paint venomous snakes, which are more appropriate for jealousy.  I realized that I have no relationship with snakes other than through books or movies.  Their impact is not as great for me as it would be for someone who has been bitten by one, but I do understand jealousy.  A face that could turn men to stone came home to me as, each morning, I looked in the mirror at my wrinkles.

The second image and story comes from a Biblical story of an event that supposedly happened about 400BC.  The title “Esther” refers to an orphan girl raised by her cousin Mordecai.  When she was old enough to become one of the virgins rounded up for the king, she was encouraged to go but to hide her ethnicity.  The king found pleasure with her and she was allowed to live in the palace as a concubine, but not as a wife because she was not royalty.  Later, when she wanted to ask a favor of the king, she prepared herself for presentation to the king to gain favor.  The repeating pattern is one we still use today:  we prepare ourselves in our attitude and with the clothes we wear to win favor.

The third image is of my mother.  “We belonged to a book-of-the-month club when I was growing up.  Mother read to us every night after dinner.  I listened intently.  When she finished the book, she read the encyclopedia to us.  My oldest sister and I were intrigued by everything.  My sister Marie fell asleep or tried to sneak off. When my Moother was diagnosed with Alzheimer’s, I dreamed of reading to her.  When I visited her, she held her hand just so in front of her face, as if she could pluck the word she needed from the air.  The repeating pattern is DNA.  We are genetically predisposed to certain conditions.  DNA contains the instructions for the development and function of all living organisms.

“Me” is the title of the fourth image in the series.  I think of this image as the repeating image of my mother.  Not only do I laugh like her, I have faced many of the same life challenges that she faced.  I think I have more in common with her and other women who have given birth, have aging husbands, and discover wrinkles on their own faces than I have with anyone of the same IQ or any other comparison factor. 

The fifth in this series is about oppression.  The roles of women have changed in my lifetime, but change is not static in and of itself.  The essence of change is dynamic, so like a pendulum, it can swing both ways.  While thinking about the sisterhood circle, the diversity council at NDSU, and the diversity training I have received on campus, I decided that there are things we just do not understand. 

Here is my take on the topic:  Nelson Mandela was sent to jail for his beliefs on equality.  When he went into prison, he was virtually unknown in the western world.  By the time he was released, he and the word apartheid were both globally known.  My image is modern day mythology , but it is plausible. Let us elevate an American woman of color to sainthood.  We cannot elevate her as high as Mary or Mother Theresa, but we can give her a job historically given to women of color.

 I call her “Our Lady of Lost Socks.”  It is neither too exalted, nor is it too ordinary.  Then, just as she becomes established, she is raised higher and higher. People everywhere turn to this new saint because we simply cannot find those stray socks.  Soon her name is on the lips of the leaders of every country and wealthy people everywhere cry out to this saint.  This painting, too, started out as a self-portrait. I  changed the image slightly to create a woman of color.

Large Acrylic Paintings
The final five images in my exhibition are about relationships.  They are painted in acrylic, a medium that is changed by water.  Water is a medium used in cleansing rituals.  Water is a means of transport.  Water is necessary for life.  The fetus is about creation.  Not only the creation of the universe, and of life, but the creation of oneself.  It repeats as we change and we recreate ourselves.

  The repeating green woman is about the various styles, shapes, and forms of womankind.  When a picture is painted it becomes more than a mere image.  It should be something that continues to talk each time that you look at it.  I do not live in a box regardless of how hard society, ideology, politics, tradition, and rules try to put me in one and close the lid.  I hang my hat on the non-traditional, and I am inspired by that.  Since I have a creative nature, I am bound to express the mundane and the ordinary with a heightened sense of awareness.

I do not create art for the pleasure of others because I usually cannot see into or feel their souls enough to create for or through them.  My art is personal.  As I create, I may use oil, acrylic, ink, or graphite.  I may wipe my hands on a paper towel, and that towel then becomes part of my art.  I spend time and study the texture, line, form, or color as demanded by my formal training.  From the tube or from a palette, one brush or three, I paint on canvas, paper, or wood.  Intaglio, chine colle, serigraph, and monotype are made in shared studios with exacting procedures.  I am an energetic mark-maker and leave marks on my hands, face. clothes, and work area.

I am art because as an artist there is no separation or line to cross.  I become a means of transmission. The rendering makes my art visible.  Some art seems beyond my control because it is meant to be.  The end product is meaningless to others unless it is viewed.  Then the interpretation is up to the viewer.  At that point, my thoughts are usually resolved, and I am whole.