The Beautiful Brain: The drawings of Santiago Ramón y Cajal

The Grey Art Gallery at NYU is currently presenting the scientific drawings of Spanish neuro-scientist Santiago Ramón y Cajal. Created at the end of the 19th century into the beginning of the 20th century the accuracy of these drawings are unsurpassed . These images are still used for scientific purposes.
This example is a pen and ink drawing of a Purkinje neuron from the human cerebellum from 1899 shows the scientist’s skills as a draftsman. These works were all done freehand looking through a microscope there is a more to these pieces than just research. Ramón y Cajal had an artistic sense of line and pattern.
This next drawing depicts a cut nerve outside the spinal cord from 1913. I think this work is a excellent representation of the contrast between an ordered system and chaos. The lines used to show axons in the center take on an almost lyrical sense of disorder.
This exhibition could be seen more as a Science/Art show then a Math/Art show. I feel however that the neurological systems examined in Santiago Ramón y Cajal’s work possess mathematical themes, including set theory. It is an exquisite exhibition and one of the best examples I have seen of scientific research in which the final product is Art that can be appreciated on it’s own merits. Special Thanks to Elizabeth Whiteley who sent me the info. If you can not see the show in NYC it will be on display at MIT in May
Susan Happersett

Mark Reynolds at Pierogi Gallery

Mark Reynolds creates complex drawings of intense networks of geometric grids. The exhibition provides the public with some some sketches and studies to reveal some of the artist’s processes.
There are two different ways Reynold’s starts his patterns. One of the techniques utilizes historic images. This vitrine contained a small reproduction of a Botticelli painting with a sheet of tracing paper on which a series of guide lines have been drafted. There is also a notebook with a studies for the drawings that are based completely on Mathematical phenomena.
The drawing “Double Phi Series, Ideal Mathematical Space 23,11,16”, from 2016 employs both linear and curvilinear grids to fill the plane. This particular piece is more orderly then some of the other drawings at first glance it seems as though there might be two axises of reflective symmetry, but on closer inspection the two points on either side from which a series of rays emanates are not in the center of the side. There is only a vertical line of mirror symmetry.
“Square Series: Generation of the Harmonic Mean, 3-4-6, 11-29-12, from 2012 presents two opposing ideas. The sequence of rotating squares provides well ordered geometric shapes while the underlying cacophony of line work gives the feeling of disorder.
The detailed and precise complexity of the many layers of grids within Mark Reynold’s work unveil the order within chaotic patterning.
Susan Happersett

Cristina Camacho at Praxis

Using a process of making precise cuts through canvas Cristina Camacho creates a very unique type of dimensionality to straight edge drawing.
This example is based on a line drawing of an irregular pentagon with a vertical line of reflective symmetry. A series of lines have been drawn emanating from the two upper corners of the form featuring the same reflective symmetry. The top layer of canvas has been sliced in parallel line segments allowing the fabric to hang and drape off the 2-D plane.
The underlining canvas has a series of bars parallel to the top two sides of the pentagon cut completely away. This creates both positive and negative space as well as a shadow box effect.
What I find so interesting about this work is the way the shadows and especially the hanging drape of canvas make us look at a flat geometric figure in a very different way. The sculptural quality has been augmented by the obvious presence of light and gravity which play an important role in the transition from 2 to 3 dimensions.
Susan Happersett

Barry McGee at Cheim & Read Gallery

Known for his free-for-all type of installations, Barry McGee is consistent in his unpredictability. His newest display at Cheim & Read Gallery consists of hundreds of objects. There are stacks of objects and dozens of paintings on canvas wood and cardboard. There is one prevalent theme throughout the space and that is the use of geometric patterning.

“Untitled”, 2017

This collection of shaped paintings is a single work of art. Each shape is filled with a tiling of  geometric patterns.
Here is an example of a tiling made up of  yellow Rhombuses and isosceles triangles in two shades of red.
This black and white design features squares set on the diagonal with alternating bands of black and white.

“Untitled”, 2017

Here is another wall in the gallery, consisting of a collection of framed works on paper. The wall has been sculpted to bulge out at the bottom. In this assortment of drawings there are more of the tilings, but there are also illustrations of geometric figures.
Within the random nature of McGee’s installation the impressive use of mathematical patterning becomes a unifying factor.
Susan Happersett

Kantha Recycled and Embroidered Textiles at the Mingei International Museum

While I was in San Diego for JMM, I went to Balboa Park to visit the Mingei Museum. The museum is currently presenting a beautiful exhibit of vintage kantha, embroidered textiles from Bengal.
I was taken by the interesting uses of symmetry in some of the work.

Baytan Kantha – late 19th or early 20th century – Bengal

This particular Baytan Kantha is from the late 19th or early 20th century. It features lotus flower and star patterns. All of these from possess order-8 rotational symmetry if you disregard coloring. The corner lotuses and the stars have order-4 rotational symmetry when color is taken into account. Although lotuses  and stars are very traditional forms of patterning, to me this textile has a very modern abstract quality.
Susan Happersett

More Art from JMM – San Diego

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

Susan Happersett

JMM 2018 San Diego – Art Exhibit

Happy New Year!
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.
Susan Happersett

SEEING MATH – Flaten Art Museum, St. Olaf College

Math Art Workshop January 6, 2018
Author of this blog post, artist Sarah Stengle will teach a Math Art Workshop from 10 a.m. to 12 noon on January 6, 2018, at the Center for Art and Dance, which is in the same building as the Flaten Art Museum. Everyone is welcome to attend. Further information can be found here

Seeing Math at Flaten Art Museum at St. Olaf College, in Northfield, Minnesota, is a masterfully curated interdisciplinary exhibit featuring six contemporary artists who are clearly comfortable working creatively with mathematical concepts. Curator Taylor Davis selected works by Daniel Dean, Tracy Krumm, Emily Lynch Victory, Ben Moren, Margaret Pezalla-Granlund, and Roman Verostko that span a wide range of media, from video through painting to fiber art. The works incorporate mathematical topics such as algorithms, infinity, geometry, counting systems, and the fourth dimension.

Emily Lynch Victory, P1: Number System Base 16, 2016

Emily Lynch Victory’s P1: Number System Base 16 is a complex set of grids of linear marks that resemble scraffito. At a distance her work appears to be an imposing minimalist painting with a densely worked surface. Upon closer examination the grid turns out to be a visual mapping of numbers expressed in different base systems. Visitors can appreciate the beauty of the accumulated markings with or without unraveling the system of numerical notations that generated the imagery.

Daniel Dean, Infinity, 2015

At first glance, Infinity, by Daniel Dean, also closely resembles a minimalist work of art. The pristine construction and electric blue glow are reminiscent of Donald Judd’s light sculptures. The title Infinity combined with the circular motion of the light can be interpreted as metaphor for the cycle of life. But the image in the lighted panels is a painfully familiar one: the one that appears when our computer gets stuck in processing a task. Dean plays with the sublime notions of infinity and light using an image that is also an everyday symbol of frustration, an image that simultaneously evokes the feeling of things taking “forever” while waiting around in the prosaic realm of electronic dysfunction.

Ben Moren, River Suspension, (Analysis), 2015

Ben Moren’s video installation River Suspension (Analysis) captures multiple images of the artist apparently hovering in mid-air over a river. The effect is starkly surreal. Using a very high-speed camera developed by the military for analyzing the trajectory of ballistic weapons, he instead tracks the trajectory of his own leaping body. The frames are so numerous that motion is nearly frozen, confounding our sense of time and gravity. Usually talk about the trajectory of an artist is in reference to a career path, not the physical body of the artist in motion. Moren elicits a complex emotional response to his fairly simple action, jumping, by modeling his trajectory physically and technically in a context where one expects pure metaphor.

This highly engaging exhibit also includes examples of book art, fiber art, algorithmic art and models of tesseracts (cubes imagined in the fourth dimension). Attendees who linger will be rewarded both by the masterful work exhibited and by the varied depth of information provided. The text panels are unusually well written, and additionally there is a table with an array of enjoyable mathematical puzzles, models, and books.

Seeing Math is on view through January 15, 2018, at Flaten Art Museum, St. Olaf College, Northfield, Minnesota. It is inspired by works of mathematically themed art acquired with The Arnold Ostebee ’72 and Kay Smith Endowed Fund for Mathematical Art. Established in 2014, this fund supports the acquisition and display of mathematically themed art at St. Olaf College. The museum will be closed during winter break, December 10, 2017 through January 2, 2018.

Sarah Stengle


My Artist’s Statement in the Journal of Mathematics and the Arts

The current (December 2017) issue of the Journal of Mathematics and the Arts (JMA) is introducing a new feature, highlighting individual artists through their statements. The fist artist covered is yours truly.

Publisher Taylor & Francis is making the article available to everyone. You can read it here. The accompanying picture is also on the cover of JMA this issue.

Happy Holidays!

Kelsey Brookes at the Jacob Lewis Gallery

Kelsey Brookes current solo exhibition at the Jacob Lewis gallery is titled ” The Mathematics Underlying Art”. I was so happy to see that the Fibonacci Sequence is a major theme for these large scale paintings. Each square canvas is divided into thirteen (13 is a Fibonacci Number) wedges radiating from the center point. Then dots are made along each dividing line at intervals that correspond to the Fibonacci Sequence.

”1.618 ( Golden Ratio) Indigo”, 2017

An intricate concentric pattern is painted around each dot, filling the surface.  The waves and undulations in this detailed work allude to the fact that Brookes is also microbiologist.

”1.618 ( Golden Ratio) Indigo”, 2017 (detail)

There are two sets of systems at work in this series. There is the overall predetermined structure, which features order 13 rotational symmetry and the uses the Fibonacci Sequence and the Golden Ratio to place each circle. Within this architecture,when you look more closely at the paintings you see the freer, expressive style . The mathematical structure creates a sense of order to contain the movement of the patterns.

“1.618 (Golden ratio) Red” 2017

Susan Happersett