Christoph Ohler’s sculpture “MBC” was created fom a flat sheet of steel. Curved sections were cut away. Then the form was bent and soldered resulting in eight connected Moebius strips. One of the cool things about the Moebius strips is how much their appearance changes depending on the viewers vantage point. “MBC” enhances the property of multidimensional visual perspective.
“Towards Infinite Smallness in layered Space” by Irene Rousseau is a 3-D paper construction. This work illustrates the negative curvature on a hyperbolic plane. The repetitive forms become increasingly small as they reach out to the boundary of the round disc. The paper shapes are not applied to create a flat surface, but instead the elements are of differing thicknesses, giving the work a complex surface.
This year the annual Bridges Math Art conference was held in Stockholm Sweden. Along with a busy program of lectures and workshops, the art exhibit is always a highlight of the event. There was so much interesting work on display that is hard to select just a few to write about in the blog. I encourage everyone to take a look at the on line gallery available on the Bridges website.
Martin Levin’s brass and aluminum sculture “Altogether II” was particularly fascinating to me because it includes all five of the platonic solids. By using thin rods as lines in 3-D space, Levin outlined the figures so you can see the shapes stacked inside each other. Platonic solids are comprised of faces that are regular polygons and at each vertex there are an equal number of faces meeting. The five Platonic are: Tetrahedrons with 3 equilateral triangular faces at each vertex, Cubes with 3 square faces at each vertex, Octahedrons with 4 equilateral triangle faces at each vertex, Dodecahedrons with 3 pentagons at each vertex and, Icosahedrons with 5 equilateral triangles meeting at each vertex. In Levin’s structure the shapes with triangular faces all share a common face plane, and the solids that have three shapes meeting at the vertices share common vertices.
“Triboid” is a resin sculpture by Alfred Peris that is a ruled surface, which means that on any point of the surface there is a straight line that lies on the curved surface. Peris generates these curved surfaces by taking a 2-D curve with no end points and then projects it into paraboloid of revolution to get a 3-D curve. The resulting sculpture has an elegant organic floral presence.
There are a number of artists who have been making mathematical art for many years. I have been following the work of Carlo H. Sequin and John Hiigli since I first became interested in the field. It was great to see some of their new work on display.
Sequin’s sculpture , “Pentagonal Dyck Cycle”, uses 5 connected elliptical Dyck disks to create a single sided surface (like a Moebius Strip). This complex form was designed on a computer and produced in ABS plastic formed by fused deposition modeling. The undulating curves create a sensuality not often found using this method. Sequin has successfully created an emotionally charged object using Mathematics and technology.
John Hiigli”s painting “Chrome 209” depicts a icosahedron, a polyhedron with 20 faces inside an octahedron, a polyhedron with 8 faces. The icosahedron is twisted, so that 8 of its faces share a plan with on of each of the 8 faces of the octahedron. Using transparent oil paint Hiigli lets us see inside of the shapes, creating an elegant geometry of color within the delicate straight line schematic drawing.
Christopher Arabadjis used only blue and red ballpoint pens to create this drawing. Using 2-D depiction of octahedrons in square at the bottom of the image, Arabadjis begins a process of projecting 3-D forms onto a 2-D plane. The squares become parallelograms. Then after the 6 by 6 grid of octagons is complete, Arabadijs adds two more rows to give the illusion of another dimensionality.
Once again there was a lot of interesting art on display at the Bridges Conference this year. Way to much to write about in my blog. To see more work the entire gallery is available on the Bridges website.
It is always difficult to pick a few pieces, but I will choose six over two blog posts.
Veronika Irvine’s sculpture “Delle Caustiche (Sagittarius Star Cloud)” incorporates the art of bobbin lace making into a 3-D surface. The hexagonal lace pattern has been altered to create a disc formation with larger hexagons at the outer edge of the curves. It required 3 rotations of this disc process. Copper wire has been used to give the lace structure. Irvine’s intricate band of lace graceful curves up and out of the plane.
Guy Petzall’s “Obloid Whorl” pop-up model is masterful created, using a single sheet of paper. Cutting and folding along a grid format, Petzall creates what he refers to as “a whorling meander motif”. The flat paper has been transformed into a rising spiral.
Lee Angold used water-soluble carbon to hand paint “Pinus nigra”. It is a an exploration of Fibonacci spirals found in cones of the Austrian pine, but with a twist. Cones with imperfect Phylotaxis are also included.
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.
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.
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.
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.
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.
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.
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.
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!)
Every Summer the Bridges organization holds a conference devoted to Mathematics and the Arts. Bridges is an international organization whose sole mission is to foster and explore these interdisciplinary connections. This year the meeting was held in Baltimore Maryland in the beautiful University of Baltimore Law building. Each year the Art exhibition is one of the highlights of the gathering. This year was a particularly impressive display of work in a light and open space over three floors. Here are two photos of the gallery.
It has been very difficult for me to just single out a few art works to write about, for a complete overview I suggest checking out the Bridges website. Today I will focus on two works by two different artists that struck me particularly.
Taneli Luotoniemi – “The Hyper Cube” – 2015 Pencil on paper – 42 x 40 cm Image courtesy of the artist and Bridges
I will start with a pencil drawings by Taneli Luotoniemi. I have a real affinity for hand drawing and I feel Luotoniemi is able to achieve a remarkable subtly of line form and grey scale using only a pencil. “The Hypercube” Is a 2-D representation of a 3-D depiction of a 4-D cube. There have been many example of two dimensional art referencing hyper cubes but this is definitely a a more organic representation then most. This is achieved by the use of thick curved lines that meet at crossings of more solid shapes, instead of small points. By adjusting the grey scale of the pencil mark Luotoniemi gives the lines the appearance of weaving over and under each other. This is one of the most graceful visual interpretations I have seen.
David H Press – “Three ¾ Great Circles in Orange” – 2015 Laminated wood and cotton thread – 40 x 40 x 40cm Picture courtesy of the artist and Bridges
David H. Press builds elegant hanging sculptures that are a type of 3-D line drawings. The support structures are curved shapes but the wires within these frameworks are straight lines that form what appear to be curved surfaces. Symmetry plays a major role in Press’ work. In “Three Great ¾ Circles in Orange” the use of three circles would have created a sphere, but the ¾ circles create an asymmetrical frame work. Within the wire line work, however, there are some smaller areas with symmetrical properties. We are used to seeing complicated symmetries in Mathematical sculpture, but the use of the ¾ circles rips open the sphere, granting the viewer a fresh look.
There were so much interesting work on display this year it is hard to discuss it all in one blog post, I will write more next week.