Math ImageryThe connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius ands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.

Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.

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"Spring," by Jeff Suzuki and Jacqui Burke (Brooklyn, NY)24" x 36", quilt, 2011

Our quilts are based on "Rule 30" (in Wolfram's classification of elementary cellular automata), applied to a cylindrical phase space. "Winter" is the basic rule 30 to produce a two-color pattern. The successive patterns combine the history of two ("Spring"), three ("Summer), or four ("Fall") generations to produce a palette of four, eight, or sixteen colors. In this quilt, "Spring", the colors are determined by the history of a cell at times t = 2k and 2k + 1, treated as a two-bit number between 0 and 3. --- Jeff Suzuki and Jacqui Burke (Brooklyn College, NY,
May 14, 2012
"Lawson's Minimum-Energy Klein Bottle," by Carlo Séquin (University of California, Berkeley)9" x 6" x 4.5", FDM model, 2011
Third Place Award, 2012 Mathematical Art Exhibition

My professional work in computer graphics and geometric design has also provided a bridge to the world of art. This is a gridded model of a Klein bottle (Euler characteristic 0, genus 2) with the minimal possible total surface bending energy. This energy is calculated as the surface integral over mean curvature squared. --- Carlo Séquin (University of California, Berkeley, CA,
May 14, 2012
"Process Print 3 from Trefoil," by Nathan Selikoff (Orlando, FL)4" x 6", Archival Pigment Print, 2011

I love to experiment in the fuzzy overlap between art, mathematics, and programming. Seeking to extract and visualize the beauty that I glimpse beneath the surface of equations and systems, I create custom interactive programs and use them to explore algorithms, and ultimately to generate artwork. When I prepare an image from my Aesthetic Explorations series of strange attractors for print, the first step is rendering a very high resolution, high quality 16-bit grayscale image from my custom software. While these images are destined to spend some time in Photoshop in a process of recoloring and enhancement, I find that they are very beautiful in and of themselves. The nature of algorithmic artwork (and fractal phenomena in nature in general) is that there is captivating detail at all scales. This is a crop from "Trefoil". --- Nathan Selikoff (Artist, Orlando, FL,
May 14, 2012
"Round Möbius Strip," by Henry Segerman (University of Melbourne, Australia)152mm x 62mm x 109mm, PA 2200 Plastic, Selective-Laser-Sintered, 2011

My mathematical research is in 3-dimensional geometry and topology, and concepts from those areas often appear in my work. The usual version of a Möbius strip has as its single boundary curve an unknotted loop. This unknotted loop can be deformed into a round circle, with the strip deformed along with it. This shows a particularly symmetric result. The boundary of the strip is the circle in the middle, and the surface "goes through infinity", meaning that the grid pattern should continue arbitrarily far outwards. To save on costs, I have removed the grid lines that would require an infinite amount of plastic to print. --- Henry Segerman (University of Melbourne, Australia,
May 14, 2012
"Seven Towers," by Radmila Sazdanovic (University of Pennsylvania, Philadelphia)16" x 16", Digital Print, 2011

This tessellation of the hyperbolic plane is inspired by Japanese pagodas but realized in classical black, red and white color scheme, emphasizing local 7-fold symmetry. --- Radmila Sazdanovic (University of Pennsylvania, Philadelphia,
May 14, 2012
"Kharragan I," by Reza Sarhangi (Towson University, Towson, MD)16" X 20", Digital print, 2011

I am interested in Persian geometric art and its historical methods of construction, which I explore using the computer software Geometer's Sketchpad. I then create digital artworks from these geometric constructions primarily using the computer software PaintShopPro. Kharragan is an artwork based on a design on one of the 11th century twin tomb towers in Kharraqan, western Iran. The artwork demonstrates two different approaches that are assumed to have been utilized centuries ago to create the layout of the pattern, which is at the center of the artwork. From left to right, the artwork exhibits the construction of the design based on a compass and straightedge. From right to left, we see another approach, the Modularity method, to construct the same design using cutting and pasting of tiles in two colors. --- Reza Sarhangi (Towson University, Towson, MD)
May 14, 2012
"Snail Shell," by Ian Sammis (Holy Names University, Oakland, CA)20" square, Digital Print on metal, 2011

I am particularly interested in creating visualizations of data and of mathematical structures, and more broadly in the creation of art directly from code. It has long been observed that a logarithmic spiral describes a snail shell quite well. I created this image as part of a series of pieces based upon logarithmic spirals. --- Ian Sammis (Holy Names University, Oakland, CA,
May 14, 2012
"Pythagorean Tree," by Larry Riddle (Agnes Scott College, Decatur, GA)16" X 20", Digital print, 2011

The traditional Pythagorean Tree is constructed by starting with a square and constructing two smaller squares such that the corners of the squares coincide pairwise (thus enclosing a right triangle), then iterating the construction on each of the two smaller squares. When viewed as an iterated function system, however, one can start the iteration with any initial set. For this image I began with a common picture of Pythagoras as the initial set. The trunk of the tree was constructed using 10 iterations of a deterministic algorithm based on an iterated function system with three functions - the identity function, a scaling and rotation by 45 degrees, and a scaling and rotation by 45 degrees with a reflection. This gives a reflective symmetry for the trunk. The leaves consist of 500,000 points plotted using a random chaos game algorithm and colored based on a "color stealing" algorithm for iterated function systems described by Michael Barnsley in a 2003 paper. To give the leaves a realistic shading, the colors were from a digital photograph of a field of green and yellow grass. -- Larry Riddle (Agnes Scott College, Decatur, GA,
May 14, 2012
"SPHERE," by Dominique Ribault (Paris, France)60cm x 60cm, Digital Print (Hahnemuhle Canvas Goya)

Eleph-Zero and its clones are tessellations of the plane made with the crystallographic group P3. With this work I wanted also to illustrate links between Algebra and Topology. Eleph-Zero walks on two spirals from the south to the north. --- Dominique Ribault, Artist, Paris, France
May 14, 2012
"Laplacian Growth #1," by Nervous System generative designers8" x 8" x 8", Selectively Laser Sintered Nylon, 2011

We designers at Nervous System are attracted to complex and unconventional geometries. Our inspirations are grounded in the natural forms and corresponding processes which construct the world around us. Laplacian Growth #1 is an instance of growth using a model of 3D isotropic dendritic solidification. The form is grown in a simulation based on crystal solidification in a supercooled environment. This piece is part of a series exploring the concept of laplacian growth. Laplacian growth involves a structure which expands at a rate proportional to the gradient of a laplacian field. Under the right circumstances, this leads to instabilities causing intricate, fractal branching structure to emerge. This type of growth can be seen in a myriad of systems, including crystal growth, dielectric breakdown, corals, Hele-Shaw cells, and random matrix theory. This series of works aims to examine the space of structure generated by these systems. --- Nervous System generative designers (
May 14, 2012
"Parabola-C for curve," by Sharol Nau (Northfield, MN)9" x 6" x 12", folded book, 2011

Folded Book Sculpture. The collection of folds forms an envelope to the parabola. The abounding waves emanate as the book is opened and spread out. --- Sharol Nau (Northfield, MN)
May 14, 2012
"Broken Dishes, Mended Edges," by Margaret Kepner (Washington, DC)6" x 16", Archival Inkjet Print, 2011

The traditional quilt pattern “Broken Dishes” and certain edge-matching puzzles share a common visual element – a square subdivided along its main diagonals to form 4 right triangles. This work presents 4 puzzle solutions using this visual element in a format suggesting Broken Dishes quilts. Edge-matching puzzles based on the square were introduced by MacMahon in the 1920s. One challenge was to arrange a set of 24 three-colored squares (all the possibilities) in a rectangle with same colors matching on the edges and a single color appearing around the border. If this is generalized to four colors, the complete set of puzzle pieces jumps to 70. These can be arranged in a 7x10 rectangle, providing a nice quilt proportion. This set of four designs is based on different matching “rules” ranging from strict matching to random placement, while maintaining the border requirement. To produce richer colors, each design is overlaid with a translucent scrim of the next design in the sequence. --- Margaret Kepner (Artist, Washington, DC)
May 14, 2012
"Triaconthedron sphere," by Richard Kallweit (New Haven, CT)12" x 12" x 12", printed paper, 2011

My artworks are based on investigations into mathematical form concerning the arrangements of units in space. This is a model of a triacontehedron using minimal surface planes with an infinite regression pattern. --- Richard Kallweit (New Haven, CT,
May 14, 2012
"Pleated Multi-sliced Cone," by Thomas Hull (Western New England University, Springfield, MA), Robert Lang (Robert J. Lang Origami) and Ray Schamp (Ray's Origami)16" x 16" x 5", elephant hide paper, 2011
Second Place Award, 2012 Mathematical Art Exhibition

Imagine a long paper cone that is pleated with alternating mountain and valley creases so that its cross-section is star-shaped. Now slice the cone with a plane and imagine reflecting the top part of the cone through this plane. The result is exactly what one would get if we folded the pleated cone along creases made by the intersecting plane. Doing this repeatedly can result in interesting shapes, including the origami version presented here. This work is a collaboration. The concept and crease pattern for this work was devised and modeled in Mathematica by origami artist Robert Lang ( The crease pattern was then printed onto elephant hide paper by artist Ray Schamp ( The paper was then folded along the crease pattern by mathematician and origami artist Thomas Hull ( Part of the charm of paper folding is its capacity for simple, elegant beauty as well as stunning complexity, all within the same set of constraints. This mirrors the appeal of mathematics quite well. Geometric origami, which is where most of my artwork lives, strives to express in physical form the inherent beauty of mathematical concepts in geometry, algebra, and combinatorics. The constraints that origami provides (only folding, no cutting, and either one sheet of paper or further constraints if more than one sheet is allowed) challenges the artist in a way similar to being challenged be a mathematical problem. --- Thomas Hull (Western New England University, Springfield, MA,
May 14, 2012
"Color Wheel with a Twist," by Diane Herrmann (University of Chicago, IL)12" diameter, needlepoint canvas, 2011

"Color Wheel with Twist" is more than just a stitched version of the artist’s color wheel, and is also more than the mathematician’s non-orientable manifold. The colored leaves flow all around the band in their natural order on the color wheel; yet this mysterious shape has only one side. I wanted to capture both color theory and geometry in this piece. --- Diane Herrmann (University of Chicago, IL)
May 14, 2012
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