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"Fractaled Fire," by Christopher Shaver, Rockhurst University, Kansas City, MO (2008)Digital photography, 11" x 14". "This work is a collage of photos taken during the fireworks display at Fair St. Louis on July 4, 2008. Each firework is somewhat self-similar and recursive in nature, with a common pattern appearing at both the center and the outer edges, and each piece having almost the same appearance. The shape is complex even on a small scale. The dimension of a firework is difficult to comprehend since its shape is constantly changing over time, but is a three-dimensional display. The change over time can be viewed and even is part of the overall image because of the appearance of the smoke left behind in the same shape as the colored flame. These art pieces are the product of a student research project I was a part of, exploring the relationship between art and math by a study of fractals." --- Christopher Shaver, Student, Department of Mathematics and Physics, Rockhurst University, Kansas City, MOApr 14, 2009

"Chinese Button Knot," by Carlo H. Sequin, University of California, Berkeley (2007)Bronze, 8" tall. "The Chinese Button Knot is a nine-crossing knot, number 9-40 in the knot table. It actually has more symmetries than one would infer from the usual depiction in these tables. This has been brought out in this 3D sculpture, which has one 3-fold and three 2-fold rotational symmetry axes. It has been implemented as an alternating over-under path on the surface of a sphere, realized by a ribbon of continuous negative Gaussian curvature." --- Carlo H. Sequin, Professor of Computer Science, EECS Computer Science Division, University of California, BerkeleyApr 14, 2009

"Equinox," by Anna Ursyn, University of Northern Colorado, Greeley (2008)Fortran, photosilkscreens, photolithographs, photographs, etc., 8" x 10". "I explore dynamic factor of line. I find computers to be a perfect tool to explore the regularity of nature. I use the computer on different levels. First I draw abstract geometric designs for executing my computer programs. Then I add photographic content using scanners and digital cameras. The programs that produce two-dimensional artwork serve as a point of departure for photolithographs and photo silkscreened prints on canvas and paper. All of these approaches are combined for image creation with the use of painterly markings." --- Anna Ursyn, Professor, University of Northern Colorado, GreeleyApr 14, 2009

"Figure-8 Knot," by Carlo H. Sequin, University of California, Berkeley (2007)Second Prize, 2009 Mathematical Art Exhibit. Bronze, 9" tall. "The Figure-8 Knot is the second simplest knot, which can be drawn in the plane with as few as four crossings. When embedded in 3D space it makes a nice constructivist sculpture. This particular realization has been modeled as a B-spline along which a crescent-shaped cross section has been swept. The orientation of the cross section has been chosen to form a continuous surface of negative Gaussian curvature." --- Carlo H. Sequin, Professor of Computer Science, EECS Computer Science Division, University of California, BerkeleyApr 14, 2009

"Universe Before Big Bang," by Clifford Singer, Clark County School District, Las Vegas, NV copyright 1989Acrylic on plexiglass, relief, 36" x 36" x 2". "This painting as a model entitled, Universe Before Big Bang, 1989, is intended to reconstruct the universe prior to the Big Bang. My concept in 1989 was to take a snapshot of the universe encapsulated in a non-Euclidean square. Thus, matter is then present before the Big Bang. Origins of the cosmos are found in supersymmetries and further understanding of concepts for their elucidation. As an artist and geometer 'infinity' has taken an important place in my life in terms of abstraction. My art combines both ancient and modern mathematical foundations ranging from Pythagoras to Einstein." --- Clifford Singer, Artist/Fine Art Teacher, Clark County School District, Las Vegas, NVApr 14, 2009

"Star Birth," by Nathan Selikoff (2007)Lightjet print, 24" x 18". "Underlying this artwork is a two-dimensional plot of the 'typical behavior' of a chaotic dynamical system, a strange attractor. The base image is computed with a set of iterated functions, which serve as a numerical approximation to integrating the underlying differential equations. The iterated functions contain four coefficients, which are controlled by sliders in interactive custom software and control the appearance of the attractor. Once the particular form is chosen, it is rendered as a high-resolution 16-bit grayscale image, colorized using gradient mapping and edited to enhance contrast, control composition, and add special effects. I love experimenting in the fuzzy overlap between art, mathematics, and programming. The computer is my canvas, and this is algorithmic artwork--a partnership mediated not by the brush or pencil but by the shared language of software. Seeking to extract and visualize the beauty that I glimpse beneath the surface of equations, I create custom interactive programs and use them to explore algorithms, and ultimately to generate artwork." --- Nathan Selikoff, Artist, Orlando, FLApr 14, 2009

"Chinese Dragon," by Nathan Selikoff (2007)Lightjet print, 18" x 24". "Underlying this artwork is a two-dimensional plot of the 'typical behavior' of a chaotic dynamical system, a strange attractor. The base image is computed with a set of iterated functions, which serve as a numerical approximation to integrating the underlying differential equations. The iterated functions contain four coefficients, which are controlled by sliders in interactive custom software and control the appearance of the attractor. Once the particular form is chosen, it is rendered as a high-resolution 16-bit grayscale image, colorized using gradient mapping and edited to enhance contrast, control composition, and add special effects. I love experimenting in the fuzzy overlap between art, mathematics, and programming. The computer is my canvas, and this is algorithmic artwork--a partnership mediated not by the brush or pencil but by the shared language of software. Seeking to extract and visualize the beauty that I glimpse beneath the surface of equations, I create custom interactive programs and use them to explore algorithms, and ultimately to generate artwork. " --- Nathan Selikoff, Artist, Orlando, FLApr 14, 2009

"Caught in a Dual Net," by Radmila Sazdanovic, The George Washington University, Washington, DC (2008)Digital print, 16" x 16". "This computer graphic represents three superimposed tessellations. The edges of a tessellation (6,6,7) are hidden below two nets consisting of tessellations (7,7,7) and (3,3,3,3,3,3,3), both dual to the original one. My inspiration stems from the rich geometric structures found in tessellations of the hyperbolic plane. Mathematical objects can be manipulated in many ways (superimposing, dualizing, breaking symmetry) to create aesthetically pleasing computer graphics brought to life by the unusual combination of colors." --- Radmila Sazdanovic, Graduate student, The George Washington University, Washington, DC
Apr 14, 2009

"Ellipse Lace," by Susan McBurney (2005)Computer-generated graphic art; digital print, 14" x 14". "This complex and intricate design is created very simply from just one element--the ellipse. The width and height are varied and the sets are rotated, but the result is not at all what one might expect. In particular, the interior circles are generated entirely by the interaction of the parts. There are no circles drawn at all and the complexity of the design is entirely natural and unpredicted. It is my intention to use the computer as a tool to generate designs that are not only aesthetically pleasing, but that also reveal the order, structure and beauty inherent in mathematical objects. Additionally, if an attractive design can be made from the simplest of elements, then the generating process itself becomes an object of beauty as well. Complexity from a simple beginning via an elemental algorithm is a common, fascinating and universal process."--- Susan McBurney, Western Springs, ILApr 14, 2009

"Five Left Tetrahedral Cosets," by Francisco Lara-Dammer, Indiana University, Bloomington (2008)Digital print, 20" x 20". "This is a Klein diagram (named after the nineteenth-century German mathematician Felix Klein) that represents A5, the group of symmetries of the icosahedron. Another way of describing A5 is as the alternating group on five elements, namely, the group of all even permutations of five entities. This diagram emphasizes A5's tetrahedral subgroup A4 (the group of symmetries of the tetrahedron, also the group of even permutations of four entities), which has twelve elements, plus the four left cosets of A4. The general diagram is obtained by centrally projecting an icosahedron onto a sphere (with the center of one face projected onto the north pole) and then making a stereographic projection of the sphere down onto a horizontal plane. Each coset has been identified with one color. The circle contains a hundred and twenty regions from which sixty correspond to the dark blue background, and the other sixty are split with the five left cosets. The reason I have realized Klein diagrams is to understand more clearly the beauty of Group Theory." --- Francisco Lara-Dammer, Research assistant. Center for Research on Concepts and Cognition, Indiana University, Bloomington, INApr 14, 2009

"The Path Crumpled Paper Takes," by Jeanette Powers, Rockhurst University, Kansas City, MO (2008)Ink and paper, 11" x 15". "A classic example to explain fractal dimension is the piece of crumpled paper. In this example, one takes a sheet of paper to be 2 dimensional (ignoring the very thin thickness). This then is a good representation of the mathematical plane. However, if we crumple the paper into a ball, as seen below the frame, it seems to take on a volume, or third dimension. Now, there is a meta-level to the inter-dimensionality of this system. If one flattens the paper back into the two dimensional sheet of paper, then one can draw a continuous line ( in blue) of all the folds that happened during the crumpling process. Now a line is considered to be one dimensional, but is the space this line takes up really best described with only one dimension?" --- Jeanette Powers, Student, Physics and Math Department, Rockhurst University, Kansas City, MOApr 14, 2009

"Uniqueness--and Infinity," by Jo Niemeyer (2008)Prints, 20" x 20". "To realize the concept of 'uniqueness' in art is a true challenge. And no easy task for an artist. This could be said for the concept 'infinity' as well. As a visual experiment with both of them, this problem is shown systematically in two steps in the following two graphics: The top image shows the overlapping of two geometrical grids. The size of the mesh corresponds to the relation 1 : 0.625. Or the Fibonacci numbers 5 and 8. There are nine grid elements, which overlap accurately. Furthermore the constellations of overlappings reiterate themselves. The two grids behave periodically. There is infinity - but no uniqueness. The bottom image shows the overlapping of two grids as well. Very similar to the top image, but the size of their meshes correspond here exactly to the relation of the golden section. 1 : 0.6180339... As the last number is an irrational number, the two grids behave aperiodically. Only the upper left two grid elements overlap accurately. Each overlapping constellation of the elements is unique, even if the size of the grid would be extended to infinity!" --- Jo Niemeyer, Freelance artist, Schluchsee, GermanyApr 14, 2009

"Pulse," by Jeanette Powers, Rockhurst University, Kansas City, MO (2008)Acrylic, 6" x 24". "This piece explores Hausdorff Dimension. Chaos and dynamical systems collapse in ordered ways. A nebula coalescing into a galaxy, a frozen molecule tossing through the tumult and falling as a six-sided crystal, the Mandelbrot Set. As an artist, I've tried to use chaotic interactions as a tool to express the limitations of our control and the beauty of chaos. This painting uses cellophane crushed into wet pigment to create the random patterning of the surface. The result is a chaotic landscape reminiscent of leaves, cells, rivulets, the cracked dirt of arid lands. All chaotic processes which leave a recognizable mark. The pattern is not exact, but exhibits self-similarity." --- Jeanette Powers, Student, Physics and Math Department, Rockhurst University, Kansas City, MOApr 14, 2009

"Valley of Serenity," by Ghee Beom Kim (2007)Digital print, 12" x 12". "'Valley of Serenity' has been created using semicircles based on fractal concept with a touch of Op art element. Within a semicircle two smaller semicircles fit in. This process (iteration) continues on until it is visually meaningful. The resulting image conjures up an extraterrestrial terrain of a faraway planet. The smaller semicircles bear a resemblance to a horizon by giving it the effect of perspective." --- Ghee Beom Kim, Freelance artist, Sydney, Australia
Apr 14, 2009

"The Empty Paradox," by Kaz Maslanka, D3 Technologies (2008)Digital print, 16" x 20". "The equation is the familiar function of x equal to 1/x which yields a hyperbolic curve when graphed and results an asymptote when x = 0. Compassion multiplied by Wisdom is equal to 1 over X as the limit of X approaches Buddha's mind. Buddhist philosophy tells us that Buddha's mind is emptiness yet the philosophy also tells us that emptiness is different than nothingness or zero. In fact it is quite paradoxical for we are told that emptiness is very much something. This piece also uses visual imagery for poetic expression with Buddhist symbolism of flexibility and eternity represented by bamboo and pine trees respectively. As an artist, my interest in correlating experience through language spawned my desire to study mathematics and physics. I am currently pursuing my interest in using mathematics as a language for art." --- Kaz Maslanka, Mathematical poet and Polyartist, D3 Technologies, San Diego, CAApr 14, 2009

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