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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 bands, 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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riddle-2011.jpg
"Sierpinski Theme and Variations," by Larry Riddle (Agnes Scott College, Decatur, GA)Counted cross stitch on fabric (25 count per inch), 13.5" x 13.5", 2009

The Sierpinski Triangle is a fractal that can be generated by dividing a square into four equal subsquares, removing the upper right subsquare, and then iterating the construction on each of the three remaining subsquares. That is our “Theme”, shown in the upper left. The “Variations” arise by exploiting symmetries of the square. The three variations in this piece were generated by rotating the upper left and lower right subsquares at each iteration by 90 or 180 degrees, either clockwise or counterclockwise. The self-similarity of the fractals, illustrated by the use of three colors, means that you can read off which rotations were used from the final image. Each design shows the construction through seven iterations, the limit that could be obtained for the size of canvas used. --- Larry Riddle (http://ecademy.agnesscott.edu/~lriddle/)
Mar 10, 2011
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"Traveling Ribbons," by Irene Rousseau (Irene Rousseau Art Studio, Summit, NJ)Painted wood and paper collage with gestural expression, 17"x17"x5", 2010

The sculpture "Traveling Ribbons"© 2010 is composed of geometric symmetry and interweaving patterns. The alternating overpasses and underpasses at crossings result in graceful curves and transitions between straight and curved sections. The repeating ribbon patterns are arranged in a three-dimensional lattice form and can be viewed from many different directions. The voids between the ribbons become a part of the form and also create a symmetrical pattern. The ribbons are painted in complementary colors of orange and purple with markings, which lead the eye on a continuous path. --- Irene Rousseau (http://www.irenerousseau.com)
Mar 10, 2011
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"Sierpinski's Doughnut," by Ian Sammis (Holy Names University, Oakland, CA)Digital print on canvas, 15" x 12", 2010

A Sierpinksi curve is a space-filling curve that fills a triangle. Sierpinski curves may be chained together to construct a continuous path from triangle to triangle. The correct arrangement of triangles allow the construction of a single path that fills the unit square while following an Eulerian path along a graph with the topology of a torus. Mapping the square onto the torus in the usual way gives us a space-filling closed circuit on the surface of a torus. The image is a render of a tube following such a circuit. --- Ian Sammis
Mar 10, 2011
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"Calm," by Reza Sarhangi (Towson University, Towson, MD)Digital print, 16" x 20", 2008

"Calm" is an artwork based on the “Modularity” concept presented in an article “Modules and Modularity in Mosaic Patterns” (Reza Sarhangi, Journal of the Symmetrion, Volume 19, Numbers 2-3, 2008/. Another article in this regard is “Modularity in Medieval Persian Mosaics: Textual, Empirical, Analytical, and Theoretical Considerations” (Sarhangi, R., S. Jablan, and R. Sazdanovic, Bridges Conference Proceedings, 2004). The set of modules with extra cuts used to create this artwork is presented in this figure: http://gallery.bridgesmathart.org/sites/gallery.bridgesmathart.org/files/Reza/Calm_figure.jpg. --- Reza Sarhangi (http://pages.towson.edu/gsarhang/)
Mar 10, 2011
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"Tryptique," by Radmila Sazdanovic (University of Pennsylvania) and Aftermoon studio (Paris, France)Ink/brush, 24" x 8", 2010

Tryptique is a drawing of three different kinds of diagrams used in categorifications of the one-variable polynomial ring with integer coefficients. These diagrams are elements of three distinct algebras: on the level of Grothendieck rings, projective modules spanned by these diagrams correspond to Chebyshev polynomials, integer powers of x and (x-1), and Hermite polynomials. Asgar Jorn's comment about Pierre Alechinsky's work could as well apply to the signs Aftermoon studio created based on our diagrams.



"L'image est écrite et l'écriture forme des images... on peut dire qu'il y a une écriture, une graphologie dans toute image de même que dans toute écriture se trouve une image." --- Radmila Sazdanovic (http://www.math.upenn.edu/~radmilas/)
Mar 10, 2011
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"Æxploration (Aesthetic Exploration)," by Nathan Selikoff (Digital Awakening Studios, Orlando, FL)Real-time Video Projection, variable, 2009

Æxploration (Aesthetic Exploration) is a real-time, interactive video projection. This custom software visualizes a variety of two- and three-dimensional strange attractors, allowing the viewer to control the coefficients, color, and translation of the attractor. Until recently, my goal has been to generate high quality still images of strange attractors, and my interactive software has been geared towards that purpose alone - an artist's tool that is a byproduct of the process, viewable only by myself. But recently, in the course of a single day, I made some changes to my code that completely revolutionized what I was seeing on the screen while using my software, and I am excited to share the results. The image above is a screen capture. Video is available at http://nathanselikoff.com/251/strange-attractors/aesthetic-exploration. --- Nathan Selikoff (http://www.nathanselikoff.com)
Mar 10, 2011
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"Torus Knot (5,3)," by Carlo H. Séquin (University of California, Berkeley)Second Place Award, 2011 Mathematical Art Exhibition

Bronze with silver patina, 10" × 8" × 16", 2010

Torus knots of type (p,q) are simple knots that wind around an invisible donut in a regular manner – p times around the hole, and q times through the hole. By using a somewhat more angular shape for the donut and a variable-size, crescent-shaped cross section for the ribbon, this mathematical construct can be turned into a constructivist sculpture. The challenge was to find a way to make a mold for casting this highly intertwined structure. The solution was to cast three identical pieces, which were then threaded together and welded to each other. --- Carlo H. Séquin (http://www.cs.berkeley.edu/~sequin/)
Mar 10, 2011
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"Hyperbolic Twistslug," by Mickey Shaw (Le Roy, KS)Fiber, 9" x 22" x 13”, 2009

This crocheted fiber soft sculpture is based on non-Euclidean geometry. It represents a variation of the hyperbolic plane ruffle effect. The piece was created using basic crochet stitches, which were increased at a rate great enough to create exponential growth. Attention was given to pushing the construction into a form of varying volume, irregular shape and an integration of pattern and color. The end result is simultaneously geometric in its basic nature and organic in its form. This creation used over two pounds of fibers. The structure is malleable, allowing the form to morph into numerous shapes. The hyperbolic soft sculpture is a further exploration of what forms can evolve in combining hard-edged geometric concepts with the fluid, textural aspects of fiber and stitches. This combination creates a three-dimensional visual and mental juxtaposition of the interconnection of the two elements. --- Mickey Shaw (http://FullLunaCreations.etsy.com/)

Mar 10, 2011
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"Quarthead," by Bob Sidenberg (Minneapolis, MN) Wood, 16" h x 16" w x 16" d, 2002

This one is trying to be a rhombic dodecahedron, but hasn't quite emerged from its tetrahedral beginnings. --- Bob Sidenberg (http://www.silkmountain.net)
Mar 10, 2011
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"Fractal," by Bradford Hansen-Smith (Chicago, IL)Folded 9" paper plates, 8" x 8" x 8", 2009

This is formed using twelve 9" paper plates all folded to the same equilateral triangular grid and reconfigured to the same design with slight variation between the four units that make the center tetrahedron pattern and the eight circles that form the outer cubic arrangement. This is one of many explorations using fifty-four creases rather than the twenty-four creases I usually work with. The higher frequency triangular grid allows greater complexity in a single circle which when combined in multiples forms designs that would not be possible otherwise. --- Bradford Hansen-Smith (http://www.wholemovement.com)
Mar 10, 2011
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"Chaos - The Movie," by Susan Happersett (Jersey City, NJ)Video, 19" flat panel monitor (about 18" by 12"),

"Chaos - The Movie" is a stop-motion animation movie in which I create a line drawing based on Chaos Theory. The drawing--and the movie--were made over a period of six months. Music is an original composition made for the movie by Max Schreier. Meejin Hong did the video editing. --- Susan Happersett (http://www.happersett.com)
Mar 10, 2011
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"Fibonacci Scroll," by Susan Happersett (Jersey City, NJ)Video, 19" flat panel monitor (about 18" by 12"), 2010

Fibonacci Scroll is a stop-motion animation of a long scroll drawing based on the Fibonacci Sequence. Susan Happersett has been creating mathematical, counted marking drawings for a number of years, but this is the first time her markings come to life. The sound track was composed specifically for the movie by Robert van Heumen, an accomplished composer and musician. --- Susan Happersett (http://www.happersett.com)
Mar 10, 2011
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"Ball and Chain," by George Hart (Museum of Mathematics, New York, NY)Nylon (selective laser sintering), 6" x 6" x 6", 2009

Ball and Chain is a ball made of triangular chain mail mesh containing twelve flexible regions in a rigid dodecahedral framework. There are 3,722 small rings, which interlock to form a sphere with chiral icosahedral symmetry. At 920 places, six triangles meet, but at 12 special points (at the center of the twelve dimples) only five triangles meet. The ball does not collapse down to a disk because the dodecahedral structure of ribs (made by having some of the rings lock to form a skeleton) is rigid. But in twelve circular regions the rings are free to hang freely. No matter how it is turned, the top six regions hang to make concavities while the lower six regions are convex and blend in with the overall spherical form. The complete structure was created as one unit in its assembled state by selective laser sintering. --- George Hart (http://www.georgehart.com)
Mar 10, 2011
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"Hyperbolic Planes Take Off!," by Vi Hart (New York, NY)Oil paint on canvas, 20" x 16", 2010

What does it look like when you crease the hyperbolic plane? This painting is an attempt at visualizing simple origami done with hyperbolic paper. Each plane has a mountain and valley fold perpendicular to each other. Done with your average Euclidean sheet of paper, it would be impossible to have both creases folded at a non-zero angle, but the hyperbolic plane can fold both ways at once. The creased plane can then be manipulated into different "birds", or so I imagine. --- Vi Hart (http://vihart.com)
Mar 10, 2011
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"Hyperbolic Twist: Forever in Memory," by Charlotte Henderson (A.K. Peters, Natick, MA)Acrylic yarn and glass beads, 6 × 6 × 4 inches (3d work), 2010

This model is a hyperbolic Möbius band. The starting “spine” consists of 20 chain stitches, and the outer single edge has over 1600 single crochet stitches. The negative curvature of the surface allows the width of the band to be much greater than if the curvature were zero. The surface can move freely through the “hole” in the center. The bead work highlights the nonorientability of the surface. In isolated sections, it looks as if the beads are on two sides of the band; but if one traces the line of beads, one will return to the chosen starting point having traced all of the beads. The same amount of yarn is used for the red and the pink, to display the exponential growth of the surface. (There is a greater amount of white yarn, to have a constant final row for aesthetic purposes.) The color scheme arose from the fact that, at an earlier construction stage, the silhouette of the model resembles a heart. --- Charlotte Henderson

Mar 10, 2011
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