The largest of all of the Art Fairs in New York City last week was the Armory Show that was on two huge piers (92 and 94) on the Hudson river. A wide range of work was exhibited, I have just chosen a sampling of more recent work with Mathematical themes.
I was still in line to check my coat when I spotted Bernar Venet’s steel sculptures across the aisle. The title of the work above, “11 Acute Unequal Angles”, is a perfect description of the geometric theme of the work. It is always exciting to see work that so directly embraces the mathematics.
This next work, by Shannon Bool, is a large- scale oil and batik on silk. The fabric is slightly transparent and backed with a mirror which creates an interesting repetition of the design, as well as a slight ghost of the reflection of the viewer. Through the use of grids and diagonals, there is a reference to the geometry of architecture.
This eight foot tall painted plywood column by Brandon Lattu consists of 12 stacked prisms. Each prism has a regular polygon as its base. The top form has is triangular, the second is square. The third one has a pentagonal base, and so on. Each subsequent prism has bases with one extra side. The prisms are stacked in such a way that a vertex from each prism lines up to create a vertical line.
Brandon Lattu, “Columns, White, Natural Progression”, 2016 (detail) Courtesy of Koenig & Clinton Gallery
When you walk around the structure you can see the different angles. This work is a great visual example of a numeric progression in terms of the number of sides in each section. It also compares the different angles found in regular polygons.
Jim Iserman’s acrylic painting is a pulsating homage to hexagons. This work is made like a tiling. Each hexagon is created using three rhombi. By situating the yellow bands to meet at the center, Iserman creates a Y-pattern. The forms take on the presence of cubes jumping off the surface.
Jim Iserman, “Untitled” , 2013-2014 (detail) Courtesy of The Breeder Gallery
The Armory show is an overwhelming experience. It takes hours to even get a superficial overview. There were a myriad of other works of art that relate to mathematics at this venue. It was difficult to chose just a few.
Renowned Mexican painter Francisco Castro-Leñero has a long history of abstract geometric themes. His current exhibition at the Howard Scott Gallery features a brilliant selection of painting created between 2004 and today.
Francisco Castro-Leñero – “Mandala (tres tiempos)” – 2016 Picture courtesy of the artist and the gallery
“Mandala (tres tiempos)”, which was painted this year, uses a 12 by 12 square grid format. The length of the side of the squares become the length of each of the radii used to create circular arcs, with the centers of the circles located at the corner of grid squares. The arcs have measurements of 90 degrees, 180 degrees, or 270 degrees. This technique allows Castro-Leñero to create undulating ribbons. The outer rows and columns of the painting have a white background with colored arcs on the left side and black and grey arcs on the left. The 6 by 6 grid at the center of the canvas features a a black background with white and grey arcs. This center square reinforces the contrast between the linear and curvi-linear geometry, as well as positive and negative space. By mapping a vocabulary of squares and circles, and displaying a virtuosity of color Castro-Leñero’s paintings build intricate geometric structures.
The David Zwirner Gallery’s 20th Street branch in Chelsea is presenting a large show of the work by one of the most influential Dutch artists of the last half of the twentieth century, Jan Schoonhoven. A member of the Nul Groep in Holland, Schoonhoven was connected to the international art movement “ZERO Group”. The artist members of these groups worked to develop a type of art that was more objective then the more emotionally expressive art created after WWII. Schoonhoven established techniques to create monochromatic wall sculptures that relied on clean geometric lines to explore form,light, and shadows.
Jan Schoonhoven – “R70-28” – 1970
The rectangular grids like the ones seen in “R70-28” from 1970 are probably the types of structures that became most famous. A square relief sculpture with 5 columns with ten rows each. The white walls are the grid lines, creating rectangles with a 1:2 ratio of height to width. The exhibition at David Zwirner is quite inclusive and includes works on paper, earlier geometric work, as well as work featuring more complex geometry.
Schoonhoven used latex paint, paper, cardboard and wood to assemble these sculptures. The hand of the artist has given these 3-D spaces an ageless quality. Although the geometry is all straight edges there is a softness to the lines of these shadow boxes.
Jan Schoonhoven – “R69-33”
The work “R69-33” from 1969 has a rather complex pattern made up of trapezoidal surfaces. They are positioned into rows with horizontal axes of symmetry. The longer side of each trapezoid is closest to the viewer. This work offers a dramatic example of Schoonhoven’s use of shadows.
Jan SChoonhoven – “Diagonalen” – 1967
“Diagonalen” from 1967 is one of my favorite pieces in the show. The grid format is intact but by bisecting each grid square on alternating diagonals the artist has created a lattice of right triangles. One of the most exciting elements of Schoonhoven’s wall sculptures is that they change depending on the angle from which you see the art. As the viewer moves around the gallery the shadows are changing.
The Danese Corey Gallery is currently exhibiting the abstract geometric paintings of Warren Isensee. The artist uses a playful vocabulary of color to achieve an exciting sense of light. The straight edges are all hand painted without the aid of taping and Isensee uses adjacent colors that create enough tension that the work pulses with energy.
“Dark Heart”, 2014
The large square canvas “Dark Heart” provides an interesting perspective on the grid. Floating in a field of steel blue, the yellow black and red figure is made up of solid and striped squares. Alternating from horizontal to vertical of striped squares, the patterning draws the viewer’s eye to the two central horizontal bands. This work features both horizontal an vertical axises of symmetry through its center .
“Surface Noise” offers the viewer an optical trick. At first glance it appears to have a nice neat four-fold rotational symmetry. The artist has painstaking created detailed elements of the composition that possess four-fold rotational symmetrical patterns. Only after close inspection you realize that the small center form is a rectangle and not a square. This painting has horizontal and vertical axises of symmetry, but it is not four-fold rotational symmetry. I think the slight deviation makes “Surface Noise” more interesting. It becomes a commentary on the visual expectations of symmetry.
The artist Jacob Hashimoto has created a breathtaking installation at the Mary Boone Gallery in Chelsea NYC. “Sky Farm Fortress” fills the entire main room of the gallery.
This huge 3-D grid environment is comprised of a multitude of kite-like square, circular, and hexagonal elements. These small elements consist of thin paper over bamboo support bars that cross in the center.
The paper panels are suspended from the ceiling with black thread. The arrangements of these panels are based on the structure of the cube. They hang in a series of rows and columns, sometimes with large gaps, where only the thread is visible so the viewer can see the next series of shapes in the background.
The ceiling of the gallery is completely filled with the paper grid, that trembles as the air circulates through the room.
Jacob Hashimoto has created two different dichotomies in his “Sky Farm Fortress” installation. The work incorporates the rigid structure of a 3-D Cartesian system grid, but the individual elements are not static, they move in response to air flow of the gallery. Hashimoto uses small ephemeral paper elements that appear fragile in nature to construct a monumental work of art. I have already visited the gallery twice to experience this exhibition and I plan to go again. It will be on display until October 25th.
All pictures courtesy of the artist and the gallery.
There was so much interesting work at the Bridges Conference Art Exhibition it is difficult to select just a few but… here are a few more of my favorites.
John Hiigli is a New York based artist whose work I have admired for years. His Contribution to the exhibition included an outstanding black and white painting titled “Chrome 203 Homage to De Barros I: Translation”:
Hiigli – Chrome 203 Homage to De Barros I: Translation Picture courtesy of the artist
This painting is a great study of the power of positive and negative space. Hiigli uses 3/4 squares in alternating black and white to build a square pattern that he then uses to create a 3 by 4 grid of these square elements. I really like the concept of using a 3/4 fraction of a square, the general outline of the square remains even though 1/4 has been removed. These patterns are based on the work of Brazilian painter Geraldo De Barros.
There were a lot of sculptures at the conference that were made using 3-D printers. One artist whose work stood out was Henry Segerman. His “Developing Fractal Curves” figures had a graceful presence and conveyed the narrative of the Mathematical sequences in an interesting linear fashion.
Segerman – Deloping Fractal Curves Picture courtesy of the artist
These four structures start at the top with the basic iterations of the fractals clearly defined. As the viewer’s eye travels down into the curves the patterns become more and more complex. These small sculptures do an excellent job of conveying the nature of fractal curves.
Mike Naylor has created an interactive Mathematical pattern generator called “Runes” that can be used on a tablet or smart phone. This program allows the participant to explore the operation of multiplication by making curves within a circle that is divided like a numbered dial. The more numbers on the dial the more complex the patterns become. ”Runes” is available here. Naylor has created an excellent tool to show students how a simple mathematical process, used in different permutations, can result in a wide variety of visual images.
Matteawan Gallery in Beacon, New York is currently exhibiting works on paper by Dominick Talvacchio, in a show named “The Eros of Mathematics”. Talvacchio has a background and education in mathematics. His work has been exhibited extensively throughout the United States and Europe. The visual dialog in his print and drawings express his interest in the inherent beauty of the order and structure found in mathematics.
Arcs Missing Arcs – 2012 Giclée Print Picture courtesy of the artist and the gallery
In the print “Arcs Missing Arcs”, Talvacchio has created a 4 by 4 grid of touching circles with only sections of the circles visible. These arcs create a series of graceful and organic curves. The viewer senses the existence of the underlying grid pattern, but is allowed to enjoy the sensual aesthetics of the segmented curves.
Kairovan Below – 2012 Drawing on paper Picture courtesy of the artist and the gallery
The drawing “Kairovan Below” features two elements. First, an underlying, lightly-drawn tiling. Second, a selection of line segments from the tiling, drawn in a darker black. The tiling has a four-fold rotational symmetry. Within this symmetrical pattern there are five-point non-symmetrical stars. The juxtaposition of the overall symmetry of the tiling against the not-quite-symmetrical stars creates an interesting tension. By making some of the lines darker and more pronounced, Talvacchio allows a simplified but elegant pattern to emerge.
Artist talk and reception
On June 1st from 2-4 at Matteawan Gallery there will be an artist talk and closing reception for “The Eros of Mathematics”. I will be there to participate in the discussion about the relationships between mathematics and art. All are welcome.
Matteawan Gallery is located in Beacon. A small city north of New York City, situated on the Hudson River. It is the home of DIA Beacon, a museum dedicated to displaying long-term, large-scale gallery presentations of single artist displays, with emphasis on conceptual art and minimalist work. They have an excellent selection of Sol LeWitt’s wall drawings currently on view. I would suggest DIA Beacon as an excellent destination for a day trip for any math art enthusiast. While you are in town, check out the galleries on Main Street.
The German artist Pius Fox is having his first solo exhibition in New York City at Pablo’s Birthday Gallery. The title of the show is “We expected something better than before” and features wonderful abstract paintings, whose geometries are based on interior architectural elements. I have chosen two works that seem to me to have the most mathematical significance.
Pius Fox – Zeitland Schaft – Oil on Canvas – 2014 Picture courtesy of the artist and the gallery
The first painting is “Zeitland Schaft”, an oil painting from 2014. This work features four rectangles. Each is bisected diagonally to form eight right triangles. What I find interesting about this work is how it relates to the work of Piet Mondrian and Kazimir Malevich. Malevich used the geometric forms as his subject matter: the paintings were traditional in the fact that, even though he was depicting abstract themes, they were still pictures of shapes within a background. In Mondrian’s square canvases the square itself becomes both the format and the subject. There is no longer a delineation between subject and artwork. I feel that in some ways Fox’s work is taking this use of geometric forms a step further. In this painting rectangles and triangles might – at first glance – seem to be the subject of this work, but in fact it is much deeper. The geometric shapes are a vehicle for Fox’s use of layers of color and his lush painting technique. The symmetrical properties of the painting – for example the glide reflections in the placement of the pink and yellow triangles – enhance the relationships of colors, making them seem to glow.
Pius Fox – Untitled (PF 1403-41) – Oil on canvas – 2014 Picture courtesy of the artist and the gallery
The next painting I would like to discuss is an untitled oil on canvas also from 2014. I Particularly like the use of both line and solid shapes this painting. Dividing the rectangular canvas into four columns and four rows, Fox has set up an interesting grid to draw lines connecting the points of intersection on the grid. Lightly drawing in both diagonals of each rectangular grid cell, he fills in a dark isosceles triangle in the top half of each. This creates a strong pattern that superimposes the other lines of the painting. Behind the triangles there is a 180 degree rotational symmetry to the red blue and gold lines. Looking at this painting the viewer gets the feeling that it is about more than just the geometry. Again,the shapes are the language that Fox is using to convey a sense of place.
Pavel Zoubok Gallery is exhibiting the hand and laser cut mylar 3-D drawings of Imi Hwangbo. Using layers of colored mylar sheets, Hwangbo creates intricate geometric reliefs that have both depth and line. In the piece “Azure Seer” (2004), a grid of squares is meticulously cut from each sheet of mylar. Sheets with larger squares are at the front. With each sheet the squares get ever so slightly smaller until the farthest sheet has no cutout. This method creates a grid of inverted pyramids. It is very common for Math enthusiasts to cut and fold paper to make 3-D geometric solids. Hwangbo’s process of cutting into the layers to make geometric voids is a fresh approach.
Imi Hwangbo – Azure Seer (2004) Courtesy of the artist and Pavel Zoubok Gallery
In a more recent work named “Lens 2” (2013) Hwangbo has layered a series of net-like webs of patterns in hand-colored red and blue sheets. In the pattern there are intersecting blue circles with perpendicular diameters. These diameters run diagonally across the work creating a diamond grid. Then, in red layers there are two different sizes of smaller circles. Looking at a small section you can see the order 4 rotational symmetry around the center of each blue circle.
Imi Hwangbo – Lens 2 (2013) – DETAIL Courtesy of the artist and Pavel Zoubok Gallery
Hwangbo has been influenced by ornamentation from religious and spiritual architecture. This inspiration enables her work to transcend the flatness of the mylar and create environments of space, light, and pattern.
Richard Kalina at Lennon Weinberg Inc.
My fascination with MathArt goes beyond art whose direct theme is Mathematics. I am also intrigued by work that is inspired by, or is a reaction to, the systems in Mathematics. Richard Kalina‘s new work falls in this category. Lennon Weinberg Inc is currently exhibiting his works on paper, as well as collages on linen. Using a background grid consisting of overlapping rectangles of white paper in “Nominal Space” (2012) Kalina paints a collection of brightly colored circles. These circles interact through a network of black straight lines that connect them. The lines have one of three possible directions: vertical, horizontal or diagonal, from lower left corner up to upper right corner. Each circle can have one, two, or three connecting lines radiating out from it, creating angles of 45 degrees. 90 degrees, 135 degrees, or 180 degrees. The patterns of connections seem like an homage to the molecular and geometric models we made in high school.
Richard Kalina – Nominal Space (2012) Courtesy of the artist and Lennon Weinberg Inc.
For the collage on linen “Neochrome” (2013) Kalina changed the rules with regard to the angles of the connecting lines. There are many more possible angle structures and the circles can have up to six connections. “Neochrome” has the energy of a complex flow chart with many possible routes to connect different elements within the network. Richard Kalina has had a long and esteemed career in the Arts. His work is included in many museum collections including the National Museum of American Art, the Fogg Museum, and the Wadsworth Atheneum. Kalina has also served as a contributing editor for Art in America magazine.
Richard Kalina – Neochrome (2013) Courtesy of the artist and Lennon Weinberg Inc.
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.