It is my personal mission as an artist to illuminate the intrinsic beauty of mathematics in a purely aesthetic realm. Translating mathematical subject matter to the picture plane of my drawings, I strive to enable viewers to appreciate this aesthetic, regardless of their mathematical background. I express the grace and beauty I find in mathematics through symmetries, patterns and proportions in my art. Many of my drawings are related to growth patterns such as the Fibonacci sequence and binary growth. I begin my work process by creating a plan or an algorithm. I make all of the decisions for the work beforehand and make a detailed plan in a large spiral drawing tablet that I refer to as my plan book. After I write out all of the specifications, I generate the actual drawing by hand using the rules from the plan. Through my drawings I hope to express both the aesthetics of my mathematical subject matter, as well as the aesthetics of the process of algorithmic generation.
In the past few years I have become interested in generating drawings using fractal forms based on the repetition of similar shapes. I begin with a largest instance of a shape and incorporate copies scaled by powers of ½. I developed a drawing based on the four quadrants of the Cartesian coordinate system. Each drawing begins with 8 spokes. The line segments fall on the coordinate axes and the lines y=x and y=-x. Once I have drawn the initial shape, each spoke becomes the starting point for a new 8-spoke shape in which the line segments are ½ as long as the original spokes. Then those 64 spokes become the starting point for 8-spoke figures with line segments ¼ the length of the first line segments. Next, the 512 spokes each become the bases for an 8-spoke shape with line segments 1/8 the length of the original spokes. This process creates a circular fractal network of lines. While producing these drawings, I have developed a type of mantra to remember where I am in the drawing. I need to keep count and this becomes quite complicated and rhythmic, especially when I reach the third iteration.
Mathematics and art both enable humans to better understand the world around them by uncovering patterns and structures. Chaos Theory is one of the topics in mathematics that, I feel, particularly throws light on the intricacies of the human condition. Chaos Theory shows that even within apparent disorder there can often be found both order and structure. My investigation took me to the earliest ideas on Chaos Theory. In 1961 Edward Lorenz inadvertently discovered the phenomenon of sensitive dependence on initial conditions by noticing the effect of rounding off decimals had in a computer-generated sequence of calculations for weather prediction. This event marked the (re-) discovery of what is now commonly known as Chaos Theory. I decided to visually interpret this phenomenon in my drawings, by using my basic 8-spoke pattern and continuing with multiple iterations using stencils with a small margin of error. The errors accumulate to create these cloud-like, chaos- derived drawings. If the viewer spends a few moments gazing into what at first appears to be a chaotic cloud they will begin to see the pattern of the fractals develop. There is a hidden structure to these drawings, as well as a sense of growth through time. This process of layering iteration on top of iteration takes weeks of work and through the process the drawings go through interesting changes and developments. I wanted a way to incorporate this sense of time and change into my art. It was time to make a movie.
I started with a fresh large black sheet of paper. Then I installed a digital camera over my drawing table. I began my drawing process, but after each line I took a still shot of the drawing. I continued this process over months. I wanted the movie to have an organic handmade feeling to it so I made a number of changes throughout the process. The frequency with which I photographed the drawing fluctuated. Sometimes I would take a picture after each line, sometimes I would complete a small cycle of lines before taking a picture. This change produced skips and jumps in the rhythm. Occasionally, I moved the camera closer to or farther away from the drawing. I also included myself in the photos as the generating mechanism: there are a few shots where you can see my hands. At a point where the drawing was getting quite complicated, I adjusted the camera so you could see my feet coming and going from view: the drawing was becoming a dance. Leaning over to draw and then pulling away to take a picture created a very physical element to this work and I wanted to express that physicality. Thousands of still digital photographs were taken during the drawing process. These photographs were put into consecutive order and then repeated in reverse to create the sense of both growth and decay. The edited product is a 6 minute video titled “Chaos Night”.
I knew from the beginning of the process that I would add music into the final production. I contacted composer Max Schreier, and discussed the structure and mathematics I wanted incorporated into the music. I wanted to make sure the number 8 played a major role in the structure of the music to mirror the 8 spokes of the drawing. Max agreed to write and perform a 6 minute composition based on these specifications. Influenced by Arnold Schoenberg, he based the music on a series of 8 sequential notes. While the bottom voice of the organ plays a drawn out rhythm associated with the first iteration of the drawing, the violin accelerates with the increased speed of the smaller iterations. The right hand of the organ creates small disturbances, each catalyzed by the random insertions of hands, feet and rulers in the video.
– Susan Happersett
Originally presented at Bridges Art Exhibition – Banff, Canada – July 2009;
Sonnabend Gallery is exhibiting large wooden sculptures by Robert Morris. Morris is one of the most important American artists and preeminent practitioner of Minimalism. The twelve sculptures in this show are from his “Hardwood Series” and they are all recent reinterpretations of plywood constructions from the 1960’s. Craftsman Josh Finn facilitated the actual production of the work. I was particularly drawn to three totem-like sculptures that were each stacked columns of square planks. In “Serrated Column” (2012) each consecutive plank is rotated 90 degrees. Each square has diagonals that are parallel to the sides of the squares above and below.
Morris – Serrated Column – 2012 – Wood
“Twisted Column” (2012) is a stack of 40 squares that rotate a total of 90 degrees. Each square is only rotated 2.25 degrees. This subtle rotation gives the illusion that it is a smooth surface instead of separate square planks.
Morris – Twisted Column – 2012 – Wood
In “Spiral Column” (2013) the squares are rotated around a corner instead of the center. One full turn of the spiral is formed by planks. This work is an engineering marvel. Standing in front of this sculpture in the gallery it seems like magic that it does not tip over. Morriss’ column sculptures illustrate the many visual possibilities that can be explored using the repetition of a single geometric element.
Morris – Spiral Column – 2012 – Wood
Beth Campbell at the Project Room at Josee Bienvenue Gallery
In the Project Room at Josee Bienvenu Gallery, Beth Campbell is exhibiting her drawings and mobiles in an exhibition titled “My Potential Futures”. The works on paper are handwritten text-based diagrammatic drawings. The wire mobiles are a 3-D extension of the drawings. The structure of the mobiles create a binary fractal pattern. Each mobile is attached to the ceiling by a single wire that then divides into two wires, then each of those wires split again into two wires each. The 4 wires split into two wires each (now 8 wires). This continues through 7 iterations. Start at the top and then there is a choice of two possible routes, a yes or no question or ones and zeros if you are thinking in binary code.
A few days ago, I discussed a few of the artists exhibiting at the art show that was part of the Joint Mathematics Meeting in Baltimore. Here are my other favorites from that show.
I have been a fan of Robert Fathauer‘s sculptures for years, but I feel Three-Fold Development is one of his best works. This ceramic vessel has a top lip sculpted to depict the development of a fractal curve through five iterations. Starting with a circle, then a three-lobed curve, then a nine-lobed curve. In each subsequent iteration the number of lobes triples.The sculpture has a wonderful organic quality, while still maintaining an elegant complexity. Fathauer has skillfully kept the spacing quite even between the ribbons of clay creating a graceful relationship between the positive and negative space.
Fathauer – Three-Fold Development – Ceramic
Mathematics enthusiasts have been fascinated with Magic Squares for centuries. Magic Squares are grids. Each grid square contains a number. The grids are constructed so that the sum of the numbers in each column, row and diagonal of the square are equal. Margaret Kepner‘s Archival Inkjet print “Magic Square 8 Study: A Breeze over Gwalior” is a an intriguing representation of a Gwalior Square: an 8 by 8 magic square which contains the numbers 0 to 63. The sums of the rows, columns and diagonals all add up to 252. Kepner has translated each of the numbers 0 to 63 into graphic patterns using her own system, and formatting the numbers in either base 2 or base 4. The resulting print has a great optical effect of patterned color block grids that are both horizontal, vertical and across the diagonal. It reminds me of a Modernist quilt or a contemporary twist on some of Al Jensen’s paintings that resemble game boards. Kemper refers to her artistic process as “visual expression of systems”. I think that this print goes beyond merely expressing the Gwalior Square it celebrates the Mathematics in a bold field of shape and color.
Kepner – Magic Square 8 Study: A Breeze over Gwalior – Inkjet print
At the Art Exhibition at the JMM conference quite a bit of the art was digital printing on paper. Petronio Bendito – in contrast – prints his work on canvas, giving the prints more of a painterly feel. Bendito has developed algorithms to define his color palette, but there is also an element artistic expression in establishing the final images.”Color Code, Algorithmic lines n.0078″ is so vibrant that it beckoned me from across the room. Bendiito’s use of color and line creates a cacophony of bright straight and curved thin ribbons of paint. The use of the black background makes the exuberant frenzy of color jump out to the viewer.
Bendito – Color Code, Algorithmic lines n.0078 – Digital print on canvas
Lilian Boloney is a textile artist who uses crocheting to explore the geometry of hyperbolic figures.There is an elegant simplicity to the off-white cotton thread she used to crochet the sculpture “Boy’s surface”. This allows the viewer to explore the complex topology of the figure with out the distraction of patterns or color. Boloney not only has a clear understanding of her Mathematical subject, but she transposes their beauty into graceful objects. Instead of models of Hyperbolic figures I see them crocheted portraits.
Boloney – Boy’s surface – Crocheted cotton
I hope you enjoyed the samples of work from the JMM exhibition as much as I did. The Art Exhibition at the JMM conference was organized by the Bridges Organization, an international organization that promotes the relationship between Art and Mathematics. Each year they have a conference where Mathematicians, Artists and educators meet to discuss, explore and learn about Math Art.
This year’s Bridges 2014 conference will take place in August in Seoul, South Korea. This is the first Bridges conference to take place in Asia. It is a wonderful opportunity. I encourage all artists who are interested in Mathematics to attend and participate at this conference. The deadlines for paper and art submissions are fast approaching all info is on the Bridges website.