Last week I visited the Metro Show in New York. This is an art and antiques fair where 35 dealers display a wide range of items including folk art, outsider art, and ethnic antiquities. I did not necessarily expect to find Mathematical Art in this venue. Much to my surprise the first thing that caught my eye, as I walked into the exhibition hall was a Peruvian textile in the William Siegal Gallery area, made by weavers from the Nasca Culture (sometimes spelled “Nazka”) from the Southern coast of Peru. It was made somewhere between 200-600 AD from camelid wool and natural dyes. This Stepped Mantle has interesting symmetrical properties. If you only look at shapes and ignore the colors, this is a great example of order 2 rotational symmetry, also called a “point symmetry”. Rotating at any point where all four colors meet you can rotate the four rectangles 180 degrees and still have the same pattern (disregarding colors):
On another wall in the booth of the William Siegal Gallery there was a Stepped Cushma (one piece dress) also Nasca 200-600 AD. This textile demonstrates reflection symmetry, also referred to as “mirror symmetry”. There are 7 vertical lines of symmetry that can be drawn through this example. If you consider each on the four columns of V-shaped chevron patterns, they have lines of symmetry through the center. Then, each of the two pairs of adjacent columns have a line of symmetry between them. Finally, the complete textile has a line of symmetry down the middle:
E.A.T Experiments in Art and Technology 1960 – 2014 is the current exhibition on display at the Payne Gallery at Moravian College in Bethlehem, Pennsylvania. This small show documents the collaborations of artists with scientists and engineers from Bell Labs in NJ. Two Bell Labs engineers, Billy Kluver and Fred Waldhauer, started working with artists, providing them access to the newest technology. In 1966 they helped bring together 30 scientists and engineers with 11 artists to produce a cutting edge performance art series called 9 Evenings: Theater and Engineering in NYC. Through these partnerships, the engineers were trying to do two things. They wanted to address the effects of technology on society, and they were looking for new ways to explore this technology. Not all of the work was performance art, it also included sculpture, drawing and architecture.
The Brooklyn Museum – Experiments in Art and Technology – Poster – 1968
What does this have to with Math Art? If you look at the time line for these collaborations you see that in 1966 computers were the new technology. Some of the art work done in these experiments was based on Mathematical algorithms.
Robert Rauschenberg was one of the artists closely involved with E.A.T. One of his projects was a series of six “Revolvers”. “Revolver II” from 1967 is on display in the center of the gallery. It consists of 5 plexiglass circles that have been printed with silk screen. They rotate independently when one of five buttons is pushed. Because the circles are transparent, the different rotations (1, 2, 3, 4, or 5 circles at a time) create interesting geometric patterns.
Rauschenberg – Revolver II – Silk screen on plexiglass – 1967
Andy Warhol was also involved with these Art Technology Experiments. On the second floor of the gallery there are 3 prints of Mao from sequentially produced photocopies made in 1973. Warhol started with a photocopy of a drawing of Mao Tse-tung and made a photocopy of the photocopy, then a photocopy of the second photocopy, etc. The copying machines 40 years ago did not make true to size copies, each copy enlarged the image .01%. By the 300th iteration of his process only an enlarged abstract portion of Mao’s face was visible.
Also in the exhibition are photos and ephemera from the largest collaboration undertaken by the engineers and artists: The design for the Pepsi Pavilion at Expo’70 in Osaka Japan. The exterior of the structure was a white Geodesic dome shrouded in a Fujiko Nakaya cloud sculpture. The photos made the structure look ethereal, almost delicate, like a folded paper origami dome. The interior was lined with Mylar, and there were some great photos of visitors in the spherical mirror room showing unusual perspectives.
Although there was no mention of Mathematics in the wall text of the gallery, it is clear that Mathematics, through algorithms and geometry, played an important role in the creation of the art work made through Experiments in Art and Technology.
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.
In this blog, I will be sharing my observations on Mathematical Art that I see in galleries museums exhibitions and art fairs. What is Mathematical Art? I will choose work that meets at least one of the following three criteria: The art
is based on a Mathematical phenomenon, or
it is generated by a Mathematical process, or
it is a personal response to Mathematics by the artist.
JMM – Baltimore 2014
Each year in January, thousands of Mathematicians gather at the Joint Mathematics Meeting (JMM) to discuss current issues in their field. For the past 11 years, an exhibition of Mathematical Art has been part of the event. This year the Joint Meeting was held in Baltimore at the convention center. The art exhibition was held at one side of the general exhibition hall.
Joint Mathematical Meeting – 2014 Art Exhibition
I have participated in the exhibition five times in the past six years and over that time the exhibition has matured, both in the range of work exhibited, and in the quantity of interesting – or even exciting – work.
Exhibitions like this are really a mixed bag of prints, drawings, paintings and sculpture of all types. You can find full catalogs of the shows online. here I will discuss just a few of my favorites from this year’s show.
Kolam-93X93 is a painting on canvas based on the fractal patterns of Kolam drawings. Shanthi Chadrasekar has incorporated the rules of Indian Kolam drawings into her artistic practice. Kolam drawings are traditionally drawn by women, each day, at the entrance of their homes. In this painting, Chandrasekar has created an elaborate 93 by 93 dot grid with a single thread-like line that gracefully winds around each dot, completely enclosing the dots in a web. I find the intricacy of this painting mesmerizing. Spending a few moments with this work, the viewer feels as though they too could be encircled by this unbroken thread. The patterning on this painting is so dense that a small image of the entire piece will not do justice to the work so I am providing just a close up of a small section.
Chandrasekar – Kolan 93X93 – Paint on Canvas – 24″ x 24″ (detail)
Karl Kattchee has developed a unique process to use Mathematics to create his digital prints. His work starts with hand drawn abstract drawings that are then multiplied and manipulated using a camera, a computer and a printer. He creates reflections, translations, etc. until the image appears to have fallen into chaos. Kattchee then builds patterns using these chaotic elements. What I find very interesting about these prints is that the whole process begins with what Kattchee refers to as” abstract automatic drawings”. The freedom of this stream-of-consciousness type of drawing lends a whimsical quality to the initial pictures. After they have been subjected to all of the technical process, they retain a playful quality: the drawings dance across the page.
More about the art exhibition at JMM in Baltimore next time.