Math Art in Finland

Last week the Bridges organization held their annual conference in Jyväskylä, Finland. This international conference features lectures and workshops that highlight the connections between mathematics, music, art, architecture, education and culture. My favorite part of the five day event is the art exhibition. This year there was a wide range of styles, techniques and mediums on display. it is difficult to select only a few for this blog but I will try.

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Sharol Nau

Sharol Nau repurposes unwanted hard cover books to create sculptures that contain parabolas. A parabola is a curve with reflective symmetry, in which each point on the curve is the same distance from a fixed focus point and a fixed line. The artist  carefully measures and folds each page to the common focus point. The resulting portable sculpture preserves the exterior shape of the book but creates a new visual story for the interior.

 

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Nithikul Nimkulrat – “Black & White Striped Knots” – Knotted paper – 2015

Nithikul Nimkulrat hand-knots sculptures using paper string. Inspired by mathematical knot diagrams, the artist employs two colors of string to better indicate the positions of each stand within the knot structures.”Black & White Striped Knots”examines properties of knotted textiles.

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Nithikul Nimkulrat – “Black & White Striped Knots” – Knotted paper – 2015 (Detail)

Looking closely at the work, the circular patterns emerge. Overlapping circles cross to form four equal arcs. This creates a series of monotone circles with the arcs of adjacent circles forming a pattern with order-4 rotational symmetry. Nimkulrat’s intricate structure is a wonderful exploration of the mathematical possibilities in textile and fiber art.

Susan Happersett

Judith Braun at McKenzie Fine Art Gallery

Homeostasis is the current solo exhibition of Judith Braun’s charcoal and graphite drawings at McKenzie Fine Art Gallery. This work is all part Braun’s series titled “Symmetrical Procedures”, a long term commitment to the exploration of symmetry. Since 2003 the artist has been creating abstract drawings that use the rich gray scale attainable through the use carbon based materials. On one wall of the gallery there is a particularly intriguing installation. Four square framed drawings are presented within a large wall drawing.
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Each of the four squares contains a circular figures with order-8 rotational symmetry. Here are two examples:

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“Symmetrical Procedure” NE-21-3, 2014, Graphite on Dura-lar
Picture courtesy of the gallery

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“Symmetrical Procedure” NE-21-4, 2014, Graphite on Dura-lar
Picture courtesy of the gallery

In these examples there is a secondary symmetry, each of the eight lace-like elements around the central circle possess reflection symmetry. The intricate use of positive and negative space in this work demonstrates the complexity and richness that can be achieved with just black and white.

The wall drawing, in contrast, uses the gray scale to allow the large circles to fade away into the top of the wall. There is an allusion to the underlying symmetry of the forms, but it is incomplete. The lower of the two circles has the semi-circles forming on the exterior. The upper circle has the semi- circles going into the interior. This is a great demonstration of convex and concave curves. The marks of this drawing are the artist finger print, created by the artist pressing her charcoal covered finger directly on to the wall to create varying shades of grey. This tactile method creates an emotional connection to the viewer, adding another more human element to the exhibition.

McKenzie Fine Art Gallery is at 55 Orchard Street. Judith Braun’s exhibition is up through April 24.

Susan Happersett

Larry Zox at STUX + HALLER Gallery

The exhibition “LARRY ZOX: Master of Color and Form” is currently on display at the STUX + HALLER located at 57th street in Midtown Manhattan. This neighborhood has a number of blue chip galleries that show the work of established and often historically significant artists. Zox’s acrylic paintings from the late 1960’s are all about hard edge geometry on a flat plane.

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“Untitled” from the “Double Gemini Series”, 1969
Picture courtesy of the gallery

This large scale rectangular canvas has adjacent sides in a 2:1, ratio creating a format consisting of two equal squares. From each side of the squares an obtuse isosceles triangle has bee drawn. An obtuse isosceles triangle has two sides and two angles of equal measure, and the third  angle  measures over over 90 degrees. All Isosceles triangle have a line of reflection symmetry.  The triangles with vertical bases have a greater height than the triangles with horizontal bases. This gives the illusion of stretching the plan across the canvas. All but one of the triangles have been painted a different color than the central form. The left central vertical triangle is only defined by a white line outline. This painting is a very important piece, MOMA owns a similar work from this series. It is quite gratifying to be able to enjoy it in an intimate gallery setting.

More From The Bridges Conference 2015 in Baltimore

 

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.

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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.

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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.

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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!)

Susan Happersett

Karen Schiff at BravinLee Programs

At their Chelsea gallery, BravinLee has a vitrine dedicated to the display of Book Arts. Works that address the topics of typography and linguistics are considered part of the Book Arts genre. Currently on display are recent prints by Karen Schiff. These works are created using alphabetic and numeric rubber stamps. The artist prints on various types of commercial stamp album graph paper in a very small scale grid.

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Karen Schiff – “oOo” 2015 Ink graphite, and watercolor on stamp album paper
Picture courtesy of the artist and the gallery

“oOo” from 2015 is a type of tiling constructed out of zeros and capital letter O’s. The artist takes advantage of the two-fold rotational symmetry of these forms. By rotating the figures 90 degrees and overlapping the edges, Schiff has filled the rectangular plane with ellipses. This print is an exploration of the geometry of these two typographic elements.

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Karen Schiff – “mmm…” 2014 Ink, graphite, and gouache on stamp album paper
Picture courtesy of the artist and the gallery

“mmm…” made in 2014 is composed using only one type of rummer stamp, the lower case “m”. At first glance, the image appears to be a horizontal rows of vertical marks, but upon closer inspection you see the top curves of the m’s. What makes these rows of m’s interesting is the fact that the letters have no symmetry, but lined up appear to create a consistent pattern.

Schiff hand stamps each of these letters individually to form detailed images. The imperfections of the printing process create slight discrepancies in the patterns. This is an important part of Schiffs artistic process. By removing the letters and numbers from a traditional text format of works or calculations they lose their direct linguistic and numeric connotations, becoming abstract forms. This allows the viewer to explore the abstract shapes geometrically. We look at numbers and letters all day with out thinking mathematically about their shapes. In this his new series of prints Schiff has invited us to look at numbers and letters in a different way.

Susan Happersett

Sol LeWitt at the Metropolitan Museum of Art

Sol LeWitt’s ” Wall Drawing #370″ is currently on display in a long  corridor on the first floor of the museum.

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The directions for”Wall Drawing #370″ are: “Ten Geometric Figures (including right triangle cross X, diamond) with three-inch parallel bands of lines in two directions”. LeWitt wrote the conceptual plan for these drawings in 1968.

Each of the ten panels feature alternating black and white lines that run either vertically or horizontally. The shapes depicted, however,  feature curves and non-right angles, and lines that cross do so in a perpendicular fashion.

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Each shape also has some type of symmetry either reflective or rotational.

I have always been a huge fan of Sol Lewitt’s Wall Drawings. Besides the obvious geometric mathematical elements to the work LeWitts underlying conceptual process shares theoretical similarities with Mathematical Algorithms.

In 1967 Sol LeWitt published his “Paragraph’s on Conceptual Art” in Artforum magazine. Here is an excerpt:

“In Conceptual Art the idea or the concept is the most important aspect of the work….all planning and decisions are made beforehand and execution is a perfunctory affair. The idea is the machine that makes the art.”

As a comparison I want to look at what David Berlinski  writes about algorithm in his book “The Advent of Algorithm”:

“As Algorithm is  a finite procedure, written in a fixed symbolic vocabulary governed by precise instructions, moving in discreet steps,1,2,3…whose execution requires no insight, cleverness, intuition, intelligence, or perspicuity, and that sooner or later comes to an end.”

I feel there is definitely a relationship between Sol LeWitt’s description of Conceptual Art and the way that mathematical algorithms perform, I also see a connection in this early work of LeWitt and the birth of the computer age….. But I will leave that for another blog.
If you are going to be in NYC anytime in the next 14 months, go see the Wall Drawings at the Metropolitan.  They are powerful and graceful and up until January 3, 2016!

— FibonacciSusan

Matt Keegan Wall Sculptures at Andrea Rosen Gallery

The Andrea Rosen gallery in NYC is exhibiting the work of Matt Keegan. I found two of the powder coated steel wall sculptures of particular interest. These structures originate as folded paper cut-outs that are then fabricated in steel. The type of fold that is used to make the paper forms is called a French fold. To make a French fold you take a sheet of paper and fold it in half. Then without opening the paper you fold it in half again perpendicularly to the first fold. When you unfold the paper you have two types of folds: valley folds, which are concave, and hills folds that are convex.

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In the sculptures Untitled (Navy) and Untitled (Neon) the French fold technique creates horizontal valley folds running through the centers. The top portion of each sculpture shows a vertical hill fold through the center, and the bottom half has a vertical valley fold through the center. Disregarding the fold directions both sculptures have two lines of reflection symmetry, vertical and horizontal.

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Keegan celebrates the simplicity of the folded and cut paper by transforming the patterns into substantial steel structures .

Till next time,

FibonacciSusan

Charles Thomas O’Neil at Howard Scott Gallery

Charles Thomas O’Neil

The Howard Scott Gallery in Chelsea NYC is currently exhibiting a selection of Charles Thomas O’Neil’s recent abstract paintings.

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Untitled 2740, 2013
Picture courtesy of the artist and the gallery

The painting “Untitled 2740” (2013)  has a vertical line of reflection symmetry running through the center of the canvas. The top section of the features a rust colored bridge-like shape enclosing a white rectangle. The bottom section of the painting has a variation of the bridge shape in dark grey.

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Untitled 2741,2013
Picture courtesy of the artist and the gallery

The oil painting on panel “Untitled 2741” (2013) is a 2-D rendering of what appears to be a 3-D impossible object. It looks like a rectangular bar with square ends positioned so both ends are visible to the viewer. This work has 180 degree rotational symmetry.

O’Neil’s geometric designs are enhanced by his use of saturated colors that immediately draws in the eye of the viewer. I also appreciate his use of visible painterly strokes which keep the work from looking flat and static.

More MathArt next time.

Susan Happersett

Rachel Garrard at Klemens Gasser & Tanja Grunert Gallery

Mitra Khorasheh has curated a fascinating exhibition of the paintings, sculptures, videos and performance art of Rachel Garrard title “VESSEL” at Gasser Grunert. All the work in the show is about geometry, a very personal geometry, based on the physical measurements of the artist’s body. In the press release from the show Garrard is quoted as saying: “I see the human body as a microcosm, a seed encompassing all the geometric and geodesic measures of the cosmos, as a container for something infinite”.

One of the geometric forms used by Garrard is the isosceles triangle.

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The work “Convergence 2004” (quartz dust on linen) features layers of transparent isosceles triangles, 4 with the bottom of the canvas as the base and three with the top of the canvas as their base. The vertex angles are lines up on a vertical reflection line of symmetry that runs through the center of the canvas. This expresses the symmetric nature of the human form, with a vertical line of symmetry, but also the non-symmetrical nature, i.e. the absence of a horizontal line of symmetry.50-2

The geometry for “Blue II” (Ink on canvas, 2004) is takn diretcly from the outline of the artist’s body. Garrard uses various rectangles to create a structure that relates the proportions of her body and again displays a verical line of reflective symmetry.

Garrard has also created videos and performance works that are based on her techniques of dividing up her body into a sort of grid of points. The artist then connects these points with either tape lines, directly on her body, or paint lines on a clear panel.

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The sculpture “Geometric Void” (paint on perspex) is the result of an 8-hour performance from 2010. Rachel Garrard has created a new way to express geometry based  on the proportions of her body. Although the nature of this work is very personal, the essence of these symmetries and proportions reveal universal truths.

 

Transmutations – Benigna Chilla at Tibet House NYC

Benigna Chilla has incorporated mathematics into her art practice throughout her career. Her recent, large scale canvasses on display at Tibet House are inspired by her stay in Bhutan in 2011.

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Overview of the exhibition
Picture courtesy of the artist and the gallery

Chilla has included small segments of cultural pattern and textiles into the texture of these paintings. This enhances the connections between the bold symmetries and traditional Tibetan Art. In the painting “Two black Triangles” there is the obvious reflection symmetry of the black triangles, but there are also subtle almost-reflective symmetries. Near the bottom of the canvas there two added sculptural elements, but the right one is higher than the left. On the right hand side of the bottom border there are two red triangles with grey circles on top. On the left hand side, the triangles re grey, but the circles  are red.

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Two Black Triangles – Mixed Media – 8′ x 6′ – 2012
Picture courtesy of the artist

The painting “Full Moonstone” features a large central Mandala with 8-fold rotational symmetry.

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Full Moonstone – Mixed Media on Canvas – 8′ x 6′ – 2013
Picture courtesy of the artist

In the press release for this exhibition, Chilla discusses the importance of both the meditative and physical processes involved in the creation of these works. There are not many artists who can discuss creating mathematical symmetries and meditation, and I personally find that combination very inspiring.

Susan Happersett