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"Hyperbolic Coasters," by Mikael VejdemoJohansson (University of St. Andrews, Scotland)Laseretched glass, 14 items, 12cm diameter each, 2011
The advent of accessible automated tools opens up a number of new approaches to art: especially algorithmic and mathematical art works. The computational control allows us to write algorithms to generate concrete physical art; and their precision allows a higher resolution than what the eye can discern. These pieces highlighting and reifying different mathematical concepts, giving them physical presence and accessibility and turning abstract geometry into handson displays and objects. Among the most successful of the reified mathematics artpieces I produced where thesehyperbolic disk tilings with the Poincare disk model were etched onto glass disks, producing a collection of reified hyperbolic geometries and symmetries.  Mikael VejdemoJohansson (University of St. Andrews, Scotland, http://mikael.johanssons.org)May 14, 2012


"Great Ball of Fire," by Eve Torrence (RandolphMacon College, Ashland, VA)Craft Foam, 2010
I love the symmetric beauty of polyhedra and enjoy creating models to study. Through the process of building a model I am able to truly understand its form. I like to use color to help reveal the structure and patterns of an object. This sculpture is based on the third stellation of the dodecahedron. A stellation of a regular polyhedron is formed by extending the faces until they intersect and enclose a region of space. The faces of the dodecahedron will intersect three times as they are extended, forming the small stellated dodecahedron, the great dodecahdron, and the great stellated dodecahedron. Twelve identical pieces of craft foam were slotted at the edge of each stellation and then tightly woven. This open skeleton allows one to follow each face to view the intersections and the outline of the dodecahedron and the three stellations. Six colors of foam are used and parallel faces are the same color. Each of the five arms of each face intersects three others to form 20 colorful "flames" in an icosahedral arrangement.  Eve Torrence (RandolphMacon College, Ashland, VA)May 14, 2012


"Lisbon Oriente Station," by Bruce Torrence (RandolphMacon College, Ashland, VA)Panoramic Photograph, 2011
I've been exploring recent developments in digital imagery which allow me to utilize mathematics and computer programming to solve visual problems. This is a projection made from a panorama of 13 photographs. The individual photos were shot from precisely the same point in space, and when stitched together they comprise the entire "viewable sphere" centered at that vantage point. That is, the panorama has complete coverage of the scene360 degrees around, and 180 degrees from top to bottom. Stereographic projection was then applied to the spherical panorama, with the projection taken from the North Pole so that the point directly overhead becomes the point at infinity. This produces a lovely "little planet" effect, with the geometry of the roof structure framing the scene. The panorama was shot at Oriente Station in Lisbon, Portugal.  Bruce Torrence (RandolphMacon College, Ashland, VA, http://www.flickr.com/photos/thebrucemon/, http://faculty.rmc.edu/btorrenc/)
May 14, 2012


"101smooth numbers," by Graeme Taylor (University of Bristol, UK)Print from digital, 2011
'The smoothness spiral' is an interactive applet (see http://maths.straylight.co.uk/archives/453) that plots the first 10,000 integers on an Archimedean spiral. Each point has a brightness depending on its numbertheoretic smoothness (its largest prime divisor), controlled by a userselected threshold. Curves of smooth numbers emerge, whilst large primes are conspicuous by their absence, causing 'missing' curves. This print from 'the smoothness spiral'; the threshold is set to show values which are at most 101smooth, with brightness proportional to smoothness.  Graeme Taylor (University of Bristol, UK, http://straylight.co.uk)May 14, 2012


"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 twocolor 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 twobit number between 0 and 3.  Jeff Suzuki and Jacqui Burke (Brooklyn College, NY, https://sites.google.com/site/jeffsuzukiproject/)May 14, 2012


"Lawson's MinimumEnergy 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, http://www.cs.berkeley.edu/~sequin/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 16bit 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, http://nathanselikoff.com)May 14, 2012


"Round Möbius Strip," by Henry Segerman (University of Melbourne, Australia)152mm x 62mm x 109mm, PA 2200 Plastic, SelectiveLaserSintered, 2011
My mathematical research is in 3dimensional 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, http://www.ms.unimelb.edu.au/~segerman/)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 7fold symmetry.  Radmila Sazdanovic (University of Pennsylvania, Philadelphia, http://www.math.upenn.edu/~radmilas/)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, http://www.hnu.edu/~isammis) 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, http://ecademy.agnesscott.edu/~lriddle)May 14, 2012


"SPHERE," by Dominique Ribault (Paris, France)60cm x 60cm, Digital Print (Hahnemuhle Canvas Goya)
ElephZero 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. ElephZero walks on two spirals from the south to the north.  Dominique Ribault, Artist, Paris, FranceMay 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, HeleShaw cells, and random matrix theory. This series of works aims to examine the space of structure generated by these systems.  Nervous System generative designers (http://nervous.com)May 14, 2012


"ParabolaC 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



