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.
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 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.