This year the Joint Mathematics Meeting was held in Baltimore Maryland. There has been a lot of discussion into the mathematics involved in the patterns of knitting, crocheting and other needle crafts. One of the featured events at the conference was a Knitting Circle, where people could work on, and share, their fiber arts projects. Much of the work being produced had a mathematical component. Here are a few photos from the gathering.
Much more from JMM next week.
The gallery area at JMM was full of interesting work. Here are two more excellent examples.
Elizabeth Whiteley work is often related to botanical drawing and painting. In this new work she explores the geometry of of plants, but also the symmetries of design. Through her study of Frieze Group Symmetries she is developing a series of drawings that tackles the challenges that occur at the corners of the page. A Frieze Group is the mathematical classification for 2-D patterns that repeat in only one direction. Often seen on building as border decoration. There are seven symmetry groups that relate to Frieze patterns involving combinations of rotations reflections and translations.
The silverpoint drawing “Halesia carolina I” (above) features a central figure of three blooms surrounded by a border pattern of single blooms. This frieze pattern features reflected translations with a line of reflection at the center of each side. Whiteley’s drawings call to mind the decorative use of borders in illuminated manuscripts. By referencing the patterns of the central figure in the design element of the border, the symmetries become more connected to the central theme.
The clean lines of Clayton Shonkwiler’s digital animation “Rotation”drew my attention. Using circles and lines, the video presents undulating, almost sensual, geometric images.
I am providing a still shot I took in the gallery, but his videos are available on Shonkwiler’s website.
Although the geometric figures, circles packed into the square grid of the video frame, are basic, the mathematics for this visual feat is quite complex (Shonkwiler utilizes a Möbius transformation of the hyperbolic plane to the Poincaré disk model). I think it is the purity of the clean lines of the circles that allow the grace of the more complicated mathematical processes to translate into a really beautiful video.
This year the huge Joint Mathematics Meeting was held in Atlanta Georgia with over 6,000 attendees. A section of the exhibition hall was turned into a gallery space to present art work with mathematical connections. There were also dozens of talks presented by both mathematicians and artists on the topic of Mathematical Art.
During one of these talks, Sarah Stengle presented work from her collaboration with Genevieve Gaiser Tremblay. The large series of works on paper, titled “Criterion of Yielding”, uses stereoscopic images from the 1850’s as the background for drawings of diagrams from the book “Mathematics of Plasticity” written by Rodney Hill in 1950.
The work “Criterion of Yielding, Winter Scene” features a mathematical schematic based on the deformation of metals that creates a visual bridge between the solitary figure on each side of the stereoscopic card. To enhance the feeling of antiquity, the artist uses ground peridot gemstone to make the pigment. This process gives the color a sense of stains instead of paint alluding to the paper as artifact.
The topic of plasticity revolves around the measurement of stress, strain, bending, and yielding. All these ideas are poetically associated to the human condition, both as individuals and with regards to our interactions. The layering of mathematical material over existing images presents an unexpected dichotomy. The additional process of pigmented staining and mark making instills each work with a sense of time.
Andrew James Smith developed a unique process of drawing regular polygons to create a spiral called a Protogon. The process to form a Protogon begins with a triangle and progresses with each new polygon sharing a side with the previous polygon and having one more side.
“Proto Pinwheel” is a digital study for a large acrylic painting and is a pigment transfer on wood. For this work Smith has started with a yellow opaque Protogon shape and then rotated 120 degrees and layered subsequent Protogon shapes in varying transparent colors. The result is a spiral pulsing with energy.
More from JMM in a few days.
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.
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.
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.
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.
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.
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.
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.