There were so much interesting work at the JMM Art Exhibition that I needed to write a second blog post.
Amanda Owens’ “Links” is painted on a wood panel with the grain and an underlying drawn grid exposed. The structure of the geometric pattern features repetitive tessellation. What makes this painting unique is the use of a hombre technique for the blue squares,changing gradually from light blue on the top row to the dark blue on the bottom row. This alters the expected symmetries.
“A Unit Domino” a print by Doug McKenna explores symmetry vs asymmetry. We expect the two points of the triangles to line up along a vertical axis but the are both off center. The mathematics behind this bold pattern is quite complex. This space filling curve was developed using a pair of double spirals and a half-million line segments. McKenna has also published an electronic, interactive,illustrated app/eBook that allows the viewer to explore his intense and beautiful patterns.”Hilbert Curves: Outside -In and Inside-Gone” is available at Apple’s App store.
This January the 2020 Joint Mathematics Meeting was held in Denver, Colorado. Every year the Art Exhibition at the Convention seems to get better and better.
I will present a small sampling of the work on display. Anne Ligon Harding and Clayton Shonkwiler created this lino cut print featuring trefoil knots. The knots both have 3 fold rotational symmetry. The use of parallel lines gives the illusion of under and over in 3-D space.By flipping the prospective 180 degrees the viewer can see the trefoils from different angles. Having one knot on a white background and the other on a black background juxtaposes positive and negative space.
James Stasiak used the process of digital photo improvisation to create this print on metal. According to Stasiak a photograph of railroad tracks was manipulated using “tessellations and polar projections” to the form this striking image.
Here are two more great selections from the Art Exhibition at JMM.
Uyen Nguyen creates computer generated origami. Using precise Mathematical calculations, “Wiggle” presents a raised modeling of a non-linear curve. It can be folded up accordion style into a compact pattern.
“Symmetrical Studies 19” an Ink on acetate drawing by Olivia Bridget O’Mahoney has an interesting order 9 rotational symmetry. The artist incorporates both a curvilinear wave type of illustration as well as a straight edge cubic rendering. O’Mahoney states that this piece was inspired by the work of both Leonardo Da Vinci and Stephen Hawking.
Once again this year the most popular venue in the conference hall is the Art exhibition. There were dozens of exciting art works on display and here are just a few of my favorites.
Matt Enlow’s prints “Breaking The Ruled” have been shaped to mimic the old school, student wide-ruled binder paper. In an interesting twist Enlow questions the confines of parallel lines. In this example the vertical red margin stays in its traditional location but the blue lines are no longer all horizontal instead the distance between them becomes smaller from left to write across the page. There is the perception that these might be parallel lines going into the distance, utilizing rules of perspective.
Stephen Kenny explores the concept of nine point circles in his color pencil drawing “Nine Point Circle and Euler Line for an Acute Angle”. A Nine Point Circle is constructed in reference to a particular triangle. The nine points consist of : the midpoints of each of the three sides, the foot of each of the three altitudes, and the mid point between each vertex and the orthocenter (the point where the three altitudes intersect). Kenny incorporates these complex geometric constructions to define the abstract shapes and create straight-edge wedges of color.
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.
There were so much interesting work on display at the JMM that I wanted to explore a few more.
Tom Bates – “Six Easy Pieces” – 30 x 28 x 25 cm -Bronze – 2010
Tom Bates’ cast bronze sculpture “Six Easy Pieces” is based on one of the Chen-Gackstatter minimal surfaces. Mathematical minimal surfaces are skin-like surfaces where the area is locally as small as possible. Quite often when minimal surfaces are represented as sculpture they are shown with a smooth surface. Bate’s bronze is unpolished and rough. I really like this more organic form. It adds an unexpected hand made feel to the work.
Elizabeth Whiteley -“Euclidean Arabesque 1” 41 x 51 cm – graphite + color pencil on archival paper – 2017
One of the exciting things about returning to the JMM show over a number of years is being able to see how artists’ work changes. This year Elizabeth Whiteley is showing elegant geometric drawings. These new renderings were produced using two circles with radii in a 1:0.75 ratio and arcs measuring 180 and 270 degrees. The drawing references Euclid’s Elements Book Three: proposition 12. The series of colored lines Whiteley has used to illustrate chords on the imaginary surface brings the form to life. The shape seems to float over the surface of the paper.
In case you are wondering what I brought to the JMM this year… I had one of my new lace drawings in the exhibit. “Syncopated Hexagons” features elements created on six axis (instead of four). These elements possess order 6 rotational symmetry.
Susan Happersett – Syncopated Hexagons 35 x 11 x 4 cm – Ink on paper – 2017
It is Januar and that means it is time for the Joint Mathematics Meeting. This year the conference was held at the San Diego convention center and had an attendance of over 5000 participants. The JMM Art Exhibition is always a great way for me to start of the year. There is always a very diverse selection of art on display, featuring many different themes, techniques, and materials. I was not disappointed this year. I will only be able to mention a sampling of the of the great work…but here are a few of my favorites.
James Stasiak – “into the sun” – 38 x 50 cm – Archival glicée print – 2017
Photographer James Stasiak’s print “into the sun” transforms an original photograph into a mandala type abstraction through the use mathematical manipulation. Photo editing software allows Stasiak to carry out his prescribed sequence of rotations and reflections to create symmetrical properties. The result is a dense web of color that draw the viewers eye into the center of the print.
Yvette Kaiser Smith – Excerpts from pi (187-210) (554-580) (685-711) 29 x 45 x 5 cm – Laser-cut acrylic sheet, nylon spacers, capped hardware. Three panels: clear with green edge, 31% light transmission white, and fluorescent green. – 2016
Yvette Kaiser Smith has created a language of shapes to represent digits and then laser-cuts these shapes into colored transparent acrylic sheets. The sequence of these shapes is based on the sequence of particular sets of digits found within the irrational numbers e and pi. Irrational numbers are numbers that cannot be written as a fraction and have never ending, non repeating decimal representation. The work in the exhibit “Excerpts from pi (187-210) (554-580) (685-711)” features three panels The top panel shows the 187th to the 210th digit in the number pi. By layering the panels of different colors with space between them Smith has created a complex arrangement of shape light and color. The irrational numbers and especially pi have a type of mysterious reputation and a history of human fascination. This sculpture examines the number at it’s most finite level and then through technique and material expresses the beauty within.
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.
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.