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.
The use of computer generated drawing processes and inkjet printers is a popular means of expression at the Bridges conference. Some of the more interesting examples on display were created by David Chappell. The artist builds a system of rules to generate graceful line drawings that are mathematically to related plant growth through space and time. The lines begin from a rooted position at the horizontal bottom of the picture plane and playful grow up into reaching tendrils. In order to achieve this lyrical organic quality (not an easy feat using mathematical algorithm computer generation) Chappell modifies the rules throughout the process. This extra attention allows the drawings to change and develop in a more free-form manner.
David Chappell -untitled – 2014 33 x 40 cm – Archival Inkjet Print Picture courtesy of the artist and the Bridges Conference
Another means of creating computer assisted art is the use of laser cutting. In his work “Islamic Fractal Starflower”, Pill Webster has cut a lace-like pattern into a clear light blue acrylic sheet. The mathematics behind this pattern is a combination of two geometric themes: the symmetry in Islamic patterns and the recursive properties of fractals. This combination requires some heavy weight mathematics, but Webster’s choice of materials transforms the complex theories into an ethereal presence. It has the appearance of being built from delicate and complex ice crystal. The juxtaposition between the serious mathematical generation and delicate physicality of the work create an interesting tension.
Phil Webster – Islamic Fractal Starflower – 2014 38 x 38 cm – Laser cut acrylic, light blue Picture courtesy of the artist and the Bridges Conference
Nathaniel Friedman is one of my favorite artists for two reasons. First, he creates wonderful sculptures and prints and second because he is a very supportive of other artists. As the founder of the organization ISAMA – The International Society of Art, Mathematics and Architecture, he contacted me years ago to speak at one of the first Math Art conferences. This was my introduction into a whole community of other artists and mathematicians devoted to the aesthetics of Mathematics. I will be eternally grateful to Nat.
Nathaniel Friedman – Triple Twist Mobius – 2014 29 x 29 x 7 cm – Aluminum Picture courtesy of the artist and the Bridges Conference
But back to the sculpture…. “Triple Twist Mobius” consists of three equal-sized aluminum bars each with a single twist. They are joined to form a triangle shape. The clean lines and the simplicity of the form are deceiving, this is a powerful shape. The 2-D photo does not do it justice. In the gallery each vantage point offers a different geometry, it seems to change depending on where your stand. This act of looking at something from different perspectives is referred to as hyperseeing (a concept Friedman taught me, Thank You!)
Every Summer the Bridges organization holds a conference devoted to Mathematics and the Arts. Bridges is an international organization whose sole mission is to foster and explore these interdisciplinary connections. This year the meeting was held in Baltimore Maryland in the beautiful University of Baltimore Law building. Each year the Art exhibition is one of the highlights of the gathering. This year was a particularly impressive display of work in a light and open space over three floors. Here are two photos of the gallery.
It has been very difficult for me to just single out a few art works to write about, for a complete overview I suggest checking out the Bridges website. Today I will focus on two works by two different artists that struck me particularly.
Taneli Luotoniemi – “The Hyper Cube” – 2015 Pencil on paper – 42 x 40 cm Image courtesy of the artist and Bridges
I will start with a pencil drawings by Taneli Luotoniemi. I have a real affinity for hand drawing and I feel Luotoniemi is able to achieve a remarkable subtly of line form and grey scale using only a pencil. “The Hypercube” Is a 2-D representation of a 3-D depiction of a 4-D cube. There have been many example of two dimensional art referencing hyper cubes but this is definitely a a more organic representation then most. This is achieved by the use of thick curved lines that meet at crossings of more solid shapes, instead of small points. By adjusting the grey scale of the pencil mark Luotoniemi gives the lines the appearance of weaving over and under each other. This is one of the most graceful visual interpretations I have seen.
David H Press – “Three ¾ Great Circles in Orange” – 2015 Laminated wood and cotton thread – 40 x 40 x 40cm Picture courtesy of the artist and Bridges
David H. Press builds elegant hanging sculptures that are a type of 3-D line drawings. The support structures are curved shapes but the wires within these frameworks are straight lines that form what appear to be curved surfaces. Symmetry plays a major role in Press’ work. In “Three Great ¾ Circles in Orange” the use of three circles would have created a sphere, but the ¾ circles create an asymmetrical frame work. Within the wire line work, however, there are some smaller areas with symmetrical properties. We are used to seeing complicated symmetries in Mathematical sculpture, but the use of the ¾ circles rips open the sphere, granting the viewer a fresh look.
There were so much interesting work on display this year it is hard to discuss it all in one blog post, I will write more next week.
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.