Intersection of Art and Science

INTERSECTION OF ART AND SCIENCE Exhibition September 14, 2015 through December 22, 2017 Lawson Computer Science Building 3rd Floor Exhibition Space Purdue University West Lafayette, IN USA

This educational exhibition examines a wide range of expressive approaches that emerge in the intersection of art, science, and technology. It is a joint collaboration between the Department of Computer Sciences and the Patti and Rusty Rueff School of Visual and Performing Arts at Purdue University. The exhibition is curated by Dr. Tim Korb and Dr. Petronio Bendito.

Department of Computer Science www.cs.purdue.edu Patti and Rusty Rueff School of Visual and Performing Arts cla.purdue.edu/academic/vpa

Purdue University Department of Computer Science 305 N. University Street West Lafayette, IN 47907-2107 Phone: (765) 494-6010 Fax: (765) 494-0739

Intersection of Art and Science Exhibition September 14, 2015 through December 22, 2017 Lawson Computer Science Building 3rd Floor Exhibition Area Purdue University West Lafayette, IN USA Intersection of Art and Science Exhibition Catalog Curated by Petronio Bendito and Tim Korb Published by the Department of Computer Science and the Patti and Rusty Rueff School of Visual and Performing Arts Purdue University, West Lafayette, Indiana 47907 USA Printed and bound in the USA by Purdue Print and Digital Services, delivered by Xerox Cataloguing Information: Art and Science Exhibition Petronio Bendito and Tim Korb (Curators, Introduction) Artists: Sergio Albiac, Patrick Bingham-Hall, Anne Burns, Conan Chadbourne, Hans Dehlinger, Brian Evans, Richard Hassell, John Arden Hiigli, So Yoon Lym, Gabriel Meyer, and Robert M. Spann.

ISBN 978-0-692-52729-0 Exhibition, Art, Computer Science, Math, Mathart, Technology, Science, Technology and Civilization, Aesthetic, Geometry, 21st Century, New Media, Painting, Photography, Digital Printmaking

Merging Reason and Emotion through Mathematical and Computational Thinking Petronio Bendito and Tim Korb

This exhibition focuses on the possibilities that are enabled by merging art, science, and technology. It is the latest in a series of collaborations between the Purdue Computer Science Department, artists, and designers.

Collaborations began in earnest during the design of the Lawson Computer Science Building in 2005. These collaborations contributed to the creation of a teaching, learning, and working environment that incorporates exhibition spaces to inspire and engage students, faculty, and visitors—beyond the usual traditional spaces of academic buildings. In addition to the current exhibition documented in this catalog, works currently on display in Lawson include the “Echo Spiral” (John Misler) stainless-steel sculpture in the Kurz Lobby, “A Parade of Algorithmic Mathematical Art” (Greg Frederickson) featuring geometric dissections, “The Quartet Collection” (Clifford Peterson) of original art that has been altered and multiplied using digital tools, and “Experience Color” (Petronio Bendito) that uses computational processes to explore digital color aesthetic.

are used by the artists for self-expression. Some artists are mathematicians who visualize mathematics in their works, whereas others are artists who are inspired by mathematical processes and geometry.

From a pragmatic point of view, the Intersection of Art and Science exhibition is part of a broader educational goal to inspire computer science students to realize that communication through computer technology—from user interfaces, to geometric visualization, to program expression—can also provide an engaging human experience in a more aesthetic and even emotional way.

Likewise, for art and design students, the exhibition showcases a broad range of interdisciplinary expressive possibilities with science and technology.

Thematically, the works range from figurative to abstract and non-functional to architectural. Processes and themes include not just algorithmic, but also generative methods, often using random number generators. In computer-based art, randomization triggers the human fascination with the unknown and fosters aspects of surprise in the creative process. Some works represent the mapping of mathematical principles via computer programs, whereas others are mathematical applications enhanced by the artist’s own hand, re-digitized, or digitally refined using computer tools.

The Intersection of Art and Science exhibition features works from an international pool of artists that exemplify the use of sophisticated mathematical concepts and computational input to provide output for inspiration and contemplation. It is our hope that this exhibition will not only inspire and educate, but also act as a resource for students at Purdue as they incorporate aesthetic principles into scientific and engineering design. The increasingly visually centered society we live in demands that they build products that work not only on a rational and functional level, but also have experiential appeal and are emotionally engaging.

The influence of mathematics on art and music is clear throughout history, from the golden ratio used in the Great Pyramid of Giza and art by Leonardo da Vinci, to the numerical ratios used in musical scales, and beyond. As showcased in this exhibit, the pervasiveness of computational methods provides new and exciting possibilities for the creative thinker. As the next generation of artists and scientists internalize the processes of computational thinking and become more code literate, we expect to see an increased use of algorithmic processes in conjunction with digital technology to create both simple and complex expressions, whether for artistic or functional purposes.

At a fundamental level, the exhibition serves to expose the underlying mathematical, logical, and algorithmic thoughts that are present in a range of artistic forms that bridge emotion and reason. The artworks were purposefully selected to represent a broad range of processes, methods, and styles. Equations and geometric techniques commonly associated with mathematics 3

Monique – Monolithic fragility (2012)

by Sergio Albiac Snap to grid version 25” x 25” Originally 72 cm x 96 cm Digital – Code Art

code art generative randomness

My main media is computer code. I personally develop the programs that generate my artwork. It could be argued that the programs themselves are the works of art, as they contain in their code a description of the universe of possible artworks. Modeling and abstracting with formal (programming) languages involves some of the skills required in mathematics. I use scientific concepts as inspiration for my work in an attempt to capture the rational side of human experience and artistically exploit the conflicts that arise when reason is confronted to emotion.

Sergio Albiac // Spanish visual artist Albiac experiments at the intersection between generative computer code and traditional media. He writes computer programs that transform reality to express ideas about beauty, chance, and human emotions.

The illusion of control in a world much governed by randomness and the existing tension between reason and instincts are recurring themes in his work. The final result of this artistic process is not always preconceived: it can be a painting, a giclée print, a video art piece, a digital portrait, or an interactive installation. Albiac does not feel constrained to a single medium or style and he uses either traditional or new media to express his artistic vision.

Art made with computer code using random number generators achieves unexpected visual results and explores the universe of possible artworks contained in the code. It makes use of Delaunay triangulation, a concept of computational geometry. Images are generated with a custom program created using Processing, an environment, framework, and language (based on Java) designed for artistic creation.

www.sergioalbiac.com

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portrait triangulation geometry

www.anneburns.com

Visual Proof (2014)1 (cover art) Circles on Circles (2011)2 (left page)

by Anne Burns Snap to grid version 25” x 25” 1. Originally 1800 x 1800 pixels 2. Originally 1200 x 1200 pixels Digital Print

visual complex analysis Möbius transformation dynamical systems

Visualization is an important aid in the study of mathematics. Often a diagram or graph can be understood more easily than pages of computations. In many of my courses, particularly those in math education, I have the students buy an inexpensive set of colored markers and use them in a variety of topics from abstract algebra to complex roots of a function. They are amazed at the beauty and art that results.

All of my computer-generated art is a result of programming mathematical processes; most are various topics from Complex Analysis: Mobius transformations, dynamical systems, or interpreting a complex function as a fluid flow. Colors and values are assigned in various ways; for example, in a fluid flow the color of a vector can be a function of its direction or its length, or some combination. In other applications, parameters can be “continuously” changed with color and value depending on parameters.

In Visual Proof, each of the disks in the 3x3 matrix of disks is a picture of the first five backward iterations of f(z) = zn + c / zm, where c is a small positive real number.

The rows represent n = 2, 3, 4 and the columns represent m = 2, 3, 4. The black disks in the center consist of the set of points z, such that | f(z) | > 1.1. The second largest sets of disks are blue; they are the inverse images of the black disks under f; ochre disks are the inverse images of blue disks; red disks are the inverse images of ochre disks, etc. First, notice the n+m symmetry in each disk.

Next, can you identify n and m by this pattern? Hint: Choose one blue disk in each entry and count the number of pre-images closer to the center and the number of preimages further away from the center.

complex flows mathematics-art-nature

Anne Burns // Long Island University. Burns began her studies as an art major, but after taking her first calculus course, she fell in love with mathematics. She received a Ph.D. in Mathematics at the age of 40 and taught math at LIU for 38 years.

Burns bought her first computer in the mid-eighties and immediately became hooked; programming in Basic, she made simple stick figures of trees and plants.

Computer programming allowed her to combine her two passions, mathematics and art, and to explore the visual beauty of mathematics.

In Circles on Circles, a loxodromic Möbius transformation has two fixed points, one attracting and the other repelling. Starting with a small circle around the repelling fixed point and repeatedly applying the Möbius transformation results in a family of circles that grow at first, each containing the previous one. Successive images eventually pass over the perpendicular bisector of the line connecting the fixed points and shrink down as they are attracted to the other fixed point. Each circle in a second family of circles passes through the fixed points and is mapped to another circle in that family. Each circle in the second family is orthogonal to every circle in the first family.

www.anneburns.net

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Journey II (2014)

by Conan Chadbourne Snap to grid version 25” x 25” Originally 24” x 24” Archival Digital Print

Cayley diagram icosahedral group Hamiltonian cycle

My work is motivated by a fascination with the occurrence of mathematical and scientific imagery in traditional art forms, and the frequently mystical or cosmological significance that can be attributed to such imagery.

Mathematical themes, both subtle and overt, appear in a broad range of traditional art, from medieval illuminated manuscripts to Buddhist mandalas, intricate tilings in Islamic architecture to restrained temple geometry paintings in Japan, and complex patterns in African textiles to geometric ornament in archaic Greek ceramics. Often, this imagery is deeply connected with how these cultures interpret and relate to the cosmos, in much the same way that modern scientific diagrams express a scientific worldview. I am especially interested in symmetry as a mechanism for finding order in the universe, from its intuitive appearance in ancient cosmological diagrams to its important role in modern theoretical physics, and my recent works explore various forms of symmetry.

Conan Chadbourne // Chadbourne and Park, LLP. Chadbourne was born in Hobbs, New Mexico in 1978, and received a BA in Mathematics and Physics from New York University in 2011. He has worked in experimental physics research, digital imaging and printing, graphic design, and documentary film production. He draws inspiration for his work from his experience in mathematics and the sciences. He lives in San Antonio where he works as a freelance graphic designer and documentary film producer. www.conanchadbourne.com

This image is part of an extended series of meditations on the structure of the icosahedral group. In this image, a Hamiltonian cycle is drawn in the Cayley diagram of the icosahedral group, shown here based on generators of order 2 and 3. The image is composed of multiple handdrawn images that are digitally composited and output as an archival digital print. The initial plan for this image was calculated using Mathematica software, creating projections of various polyhedra to act as guides. These guides were used to make several hand-drawn images, which were subsequently scanned and composited using Photoshop. The final image was then printed digitally.

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fib_13_w (2014)

by Hans Dehlinger Snap to grid version 25” x 25” Originally 20 cm x 40 cm Digital Print

generative art algorithmic art generative line drawings

I imagine drawings to be sorted into two distinct universes: “hand-made” and “machine-made”. Rulesystems are mandatory for the machine-universe, but they can be in place for the hand-universe, too. This observation places generative/algorithmic art into the historic continuum of art. They are not new inventions of our time, but rather new interpretations of an art-practice using today’s technology. Rule systems can be in place to various degrees of strictness and complexity in both of these universes. To move from a conceptual idea to an “aesthetic event” in generative art, a generative engine has to be designed, tested, and implemented, for which mathematics is indispensable. It is the design of such engines that provides insights, fascination, and pleasure.

the Fibonacci numbers. The resulting images are plotted on a pen-plotter or digitally enhanced and printed on paper. The experiments use a mathematically based starting point, and continue with intuitive judgments. Strong graphic figures related to each other are expected. Image fib_13_w shows a typical result of the process: algorithmic run, digital enhancement, and print to paper.

pen-plotter drawings aesthetic events digital enhancement

Hans Dehlinger // University of Kassel, Germany.

Dehlinger was born 1939 in South Germany and studied architecture at the University of Stuttgart. He worked as an architect and was a chief designer in the design teams for the Olympic-Game-Buildings in Munich. He continued studies and received an M. Arch. and a Ph.D. from the University of California, Berkeley. As planning scientist, he worked for “Studiengruppe für Systemforschung” in Heidelberg, Germany and as a freelance architect. In 1980, he was appointed Professor for “Foundations of Industrial Design” at the University of Kassel, Germany, where he founded the “Institut für Rechnergestuetztes Darstellen und Entwerfen”. In the early 80s, he started to explore computers artistically with a focus on algorithmically generated line drawings executed on pen plotters.

The interest in this work is on algorithmically generated aesthetic events. Programs (in Python) deliver the code for line drawings. Random variations on parameter sets contaminate the outcome in a distinct manner. Sequences of drawings are the result. I am not a mathematician, but the strictness of mathematics, and the inherent structure and order of data often received from a mathematical process, seem to become visual in the drawings. They show a distinct quality difficult (or not at all) achievable by hand. It is difficult to prove this observation objectively, but in my judgment it is valid. This observation is in line with a basic hypothesis I subscribe to: Some kind of order is a necessary condition for any aesthetic event.

www.generativeart.de

Image fib_13_w is one of a series of generative-fine-artimages using the Fibonacci sequence as a rigid system of order. The generative approach is mathematically simple, because this sequence is well known. A Python program sets and manipulates number and spacing of horizontal sections, slant of lines towards horizontal, number of lines in sections, and generation of random parallels. Section-width increases per line according to 11

Melancholia (2011)

by Brian Evans Snap to grid version 25” x 40” Originally 17” x 23” Digital Drawing

connectionism networks algorithmic art generative art

Parsing a network from source to target, is all about finding our way—from problem to solution, from person to person, from here to home. We find our way through a small world, a network of incestuous links, and a little randomness. It’s pathfinding through myriad maps. And as behavior follows structure, it’s not surprising that the intricacies of our lives mirror the filigreed arbors of our neural forests.

Brian Evans // University of Alabama. Evans is a digital artist and composer. For over thirty years, he has been experimenting with the integration of image and sound.

His artwork and music animations are exhibited and screened internationally, including recent showings at the Disney Music Hall in Los Angeles, the High Museum in Atlanta, the New York Hall of Science in Brooklyn, and the Galleria della Biblioteca Angelica in Rome, Italy.

Thoughts move through our neural networks as little spikes of chemistry-induced electricity. Like pinballs bouncing from bumper to bumper, these spikes connect the most subtle of patterns, memories that traverse the small world linkages of our brain, axon to dendrite, axon to dendrite. We hear the buzz of a bee on a dry summer day and feel sad. Why is that? This work is computational, exploring and visualizing topographies of networks that model the structure of our brains and the structure of our culture. Final images are algorithmically generated drawings, edited in Adobe Illustrator and manifested as inkjet prints.

Evans holds a DMA from the University of Illinois and an MFA from CalArts. He is Professor Emeritus from the University of Alabama, where he directed the program in digital media in the Department of Art and Art History. He currently lives in Nashville, Tennessee. www.brianevans.net

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small world networks linking mapping

Szechuan Crystals (2008-2014)

by Richard Hassell and Patrick Bingham-Hall Snap to grid version 25” x 25” Originally 25” x 25” Digital Photography of Architectural Façade

Ammann tiling aperiodic tiling substitution tiling architecture façade

Art, architecture, and tiling are overlapping fields, but despite this, the mathematical developments in tiling over the last 50 years, and our understanding of the complex structure of our world, only rarely appear in the constructed environment. My ongoing artistic and geometric research in complex tilings is being incorporated into WOHA’s designs.

Richard Hassell // WOHA Architects, Singapore.

Patrick Bingham-Hall // Pesaro Publishing, United Kingdom. Hassell is a founding director of the architectural firm WOHA, an artist, and a geometer, who has been developing aperiodic, quasicrystal, and fractal tilings for the last 10 years for both artworks and for building projects. Richard is based in Singapore.

Bingham-Hall is a photographer, author, and publisher, based in Oxford in the United Kingdom. Patrick’s publishing company, Pesaro Publishing, specializes in books on architecture and urbanism.

This project uses Ammann A4 set of tiles as a basis for a façade system. Ammann tilings are useful for architecture as they are based on a right-angled system, which in real world construction makes them simpler to fabricate and frame up. The Ammann bars form the vertical support structures. The two basic tiles are divided into triangles of perforated metal powder coated in various colors, with some left as voids. Each Ammann tile is the same, so is easy to fabricate. The aperiodic arrangement, combined with the triangles, creates a façade that has a great complexity, like the rocks it is inspired by.

www.woha.net

The A4 set had been the subject of an artistic investigation, and then further applied research into its potential as a building facade system. When this project came along, a particular pattern was developed drawing on the rock formations of the mountains around Chengdu, the location of the project. The design was made in Singapore, using AutoCad to test out various patterns.

Using the block command in AutoCad, the design could be refined many times to get the right combination of colors and shapes. The design was fabricated in powder-coated aluminum in China, with further rounds of refinement first through fabrication drawings, and then with life-size prototypes and samples. Once approved, the design went into full-scale production for the building project. After completion, Patrick Bingham-Hall photographed the building.

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screen natural inspiration inspiration photography

Chrome 163 (2002-2005)

by John Arden Hiigli Snap to grid version 25” x 25” Originally 56” x 64” Transparent Oil on Canvas

interaction transformation isotropic vector matrix system

Early in the development of my artistic life, I discovered two extraordinary objects: the Geodesic Dome and the Isotropic Vector Matrix of Synergetic Geometry.

These encounters led me to the study of elementary mathematics and the development of strategies to comprehend, organize, and translate theory into a comprehensive system. These studies culminated in a patent on a geometrical block system in which a few elementary structures may be used to build up complex spatial systems (United States Patent #5,249,966). The transformations inherent in these systems became the subject matter of experiments documented in my abstract geometric paintings, including Chrome 163.

the IVM. The polyhedrons inherent in these two interrelated systems form a family-of-relationships united by a common edge length and this system is intertransformable. It projects, in the very same moment, a cube-octahedron phase and a duo-tetrahedron phase.

These two phases can cycle back and forth freely. This is the “miracle of space” that R.B. Fuller, and of course many others, only led us… to discover for ourselves!

phase proportion polyhedron synergetic geometry transparency

John Arden Hiigli // Jardin Galerie. Hiigli is an Indiana artist based in New York. In his formative years, he attended the New York Studio School of Drawing, Painting and Sculpture. He earned a Bachelor’s Degree from Empire State College and a Master’s Degree at Bank Street Graduate School of Education, both in New York City. He was active in 4-H and school athletics and attended Indiana University for several years. In the early 70’s, he met Richard Buckminster Fuller. With his second wife, Dominique Bordereaux-Hiigli, he created the French-American Pre-school (Le Jardin a l’Ouest) and Jardin Galerie, the NYC Children’s Art Gallery. Since 2000, he has worked with the International Symmetry Association and Bridges Mathematics and Art.

The key that unlocked the mystery of this dual system, characterized by everywhere the same edge-length, was proportion. In Chrome 163 the proportion of height to width is 8 units to 7. In contradistinction to which the proportion of height to width in the front view is 7 units of height to 8 units of width. This discovery allowed me to draw the two views of the IVM with great precision and control. Inter-diagonalizing vertices and mid-face points of the cube locates other structures which have a common edge length: cube-octahedron volume 20, duo-tetrahedron volume 12, dodecahedron volume 6, octahedron volume 4, the regular tetrahedron with a volume of 1, and a smaller octahedron in the very center with a volume of .5 or one-half of the regular tetrahedron.

The octahedron of four tetrahedrons and the octahedron of .5 tetrahedrons is an instance of scale change, an important feature of my Transparent Geometric Paintings.

johnahiigli.com

My other goal was to use transparent oil paint as a vehicle for creating the brilliant light of nature, or what I call “the light of the heavens”. It is no coincidence that transparency also allowed the viewer an insight into the complex interactions of the dual systems characteristic of 17

Angel II (2010)

by So Yoon Lym Snap to grid version 25” x 25” Originally 22” x 30” Acrylic on Paper

cornrows hair braiding paintings

Dr. Ron Eglash’s website on cornrow hair-braiding best details the mathematical content behind my hair and braid paintings (see http://www.ccd.rpi.edu/Eglash/csdt/ african/CORNROW_CURVES). Professor Eglash’s website, called “Transformational geometry and iteration in cornrow hairstyles”, outlines one aspect of his research in ethno-mathematics and cybernetics. Ethnomathematics “aims to study the diverse relationship between math and culture.”

So Yoon Lym // Lym (born 1967 in Seoul, Korea) moved to Uganda in 1967 shortly after her birth until the age of 7. She came to live in northern New Jersey in 1974, where she has resided since. She pursued her studies as a Painting Major at the Rhode Island School of Design, where she received her Bachelors in Fine Arts in Painting in 1989 and then at Columbia University, where she received her Masters in Fine Arts in Painting in 1991.

Since then, she has exhibited her work at the United States Embassy in Djibouti, Studio Museum of Harlem, International Print Center New York, Paterson Museum, and the Newark Museum, among many other places.

The Newark Museum acquired two paintings from “The Dreamtime” series on May 5, 2015. She was awarded an Artist Residency, sponsored by Winsor and Newton, at ISCP in Brooklyn, New York, July 1-December 31, 2015.

I recognized the geometrical aspect and symmetry of the hair pattern on Angel II, but did not see the deeper implications of mathematics and science in my painting until I became more knowledgeable in Ron Eglash’s research and practice. The Dreamtime is inspired by the Aboriginal stories and visions of creation. Each braided pattern, carried by the students, is a map of the ancient universe, a topographical palimpsest of the world in pattern: valleys, mountains, forests, oceans, rivers, streams. The painter and the hair-braider lay down their marks like their predecessor creator beings, carving and inscribing, creating and being, in turn, created by their labor. These braid patterns are the language for the new aboriginal, the transplanted and de-territorialized nomad.

In the age of GPS cell phones tracking movement and satellite surveillance with biometric scanning recognition, the modern day aboriginal wears his location like an image-text on his head.

www.soyoonlym.com

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symmetry geometric pattern design

Irregular Hyperbolic Disc as Lampshade (2014)

by Gabriel Meyer Snap to grid version 25” x 25” Originally 30” x 30” x 16” Digital Photography of Yarn and Shaped Line

hyperbolic surface application of geometry topology

I have always been fascinated by smooth curves and surfaces, both in nature (shells, leaves) and in mathematics (graphs of real functions of two variables, surface geometries, topology). Visiting Cornell in 2008, Daina Taimina showed me her crocheted surfaces.

I wanted mine to curve in three dimensions and experimented with willow branches and clothesline before I hit upon shaped line. This was the start of my curved, hyperbolic surfaces. Since then, my surfaces have realized various views of the hyperbolic plane, the disk model for the ball-shaped surfaces, and also the half-plane model for the long algae. More recently, there are lamps (egg shaped, bead shaped), with attached hyperbolic axes.

Gabriel Meyer // University of Wisconsin, Madison.

Meyer was born in Tubingen, Germany. She received an M.S. degree in Computer Science from Cornell University, followed by a Ph.D. in Topology, also from Cornell.

She has been a lecturer in computer science and/or mathematics at Brown University, Princeton University, the University of Buffalo, and the University of Wisconsin, Madison. She is currently a lecturer in computer science at the University of Wisconsin, Madison. Since 2012, she has been a participant in mathematical art exhibitions at Bridges and Joint Math Meetings, as well as at various art galleries. www.math.wisc.edu/~meyer

The curvature of a flat piece of paper is 0, that of a round ball is a positive number, that of a saddle a negative number. This surface is flat in the center and looks locally like a saddle for all the points sufficiently far away from the center. Mathematically, this means that in the flat part at the center the curvature is 0, which is the largest curvature of the surface. In all other places, the curvature is a negative number. The areas with tightest warp have the smallest curvature.

This piece started out as a large flat disk. Then, around the perimeter I started the hyperbolic crochet, i.e., more stitches than are necessary to keep the surface flat and expanding outward. This introduces waviness around the perimeter. Not increasing the number of stitches in a regular pattern causes the surface to warp more in some regions than in others. This makes the result artistically more interesting.

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lamp shade crochet

Gradient0119C (2012)

by Robert M. Spann Snap to grid version 25” x 25” Originally 16” x 20” Digital Print

abstract mathart

I am intrigued by the analogs between the compositional rules and color theory principles that artists use and the statistical properties of images. For example, the compositional principle that an image be balanced horizontally and vertically is equivalent to stating that the first horizontal and vertical geometric moments are zero. A color theory principle that tones in an image be balanced around a middle tone is equivalent to stating that the distribution of color intensities has zero skewness. One can then think about inverting this process. That is, start with a given, desirable set of statistical or mathematical properties and use equations to compose the image. The mathematics yields candidate images for further digital manipulation based on my own aesthetics.

images for further consideration. I then choose one of these candidate images for further digital manipulation to produce the final image.

Robert M. Spann // Spann is a retired economist/ statistician. He holds a Ph.D. in economics and statistics from North Carolina State University and has taken graduate mathematics courses at George Washington University. Prior to entering the economic consulting business in Washington, DC, he held academic appointments at Virginia Tech, the University of Chicago, Montana State University, and George Washington University. His current research interests include computer graphics, iterated function systems, and the application of mathematical and statistical tools to the analysis of art images, as well as the use of those techniques to produce digital images. He has exhibited his work at the Joint Mathematics Meetings, Mary Washington University, ISAMA, and at Bridges MathArt Conferences.

This image illustrates the use of equations as a compositional tool. One can think of a digital image as a map from the unit square into a three-dimensional space (one dimension for each color channel). Compositional and color theory rules are constraints on the form of this map. The mathematical properties of this map determine the visual properties of the image. By finding maps that have “desirable” properties–such as balance, symmetry, etc.–one produces images that have those same visual properties. Conceptually, the resulting image is a visualization of an equation.

I started working on this image by specifying a series of constraints on the composition and color distribution.

These constraints include specific values for the first four moments of the distribution of pixel values for the three color channels; specific values for the image’s geometric moments up to order three; a positive horizontal and diagonal correlation; as well as other constraints. The conjugate gradient method is used to solve this system of equations. Since there are more unknowns than constraints, this process produces several candidate 23

Curatorial Team

Tim Korb is the former Assistant Head in the Department of Computer Sciences at Purdue University, where he was responsible for a number of departmental programs, including the computing facilities, K-12 outreach, corporate and alumni relations, and undergraduate scholarships and awards. He has been involved in a number of faculty research projects, most recently in computer science education. Korb has been active in bringing art exhibits to the Lawson Computer Science Building and in encouraging students to explore the intersection of art and computer science.

Petronio Bendito is an Associate Professor of Visual Communications Design at the Patti and Rusty Rueff School of Visual and Performing Arts at Purdue University. He has served on the editorial board of Media-N: Journal of the New Media Caucus. Currently, he serves on the editorial board of the Journal of Visual Literacy. Bendito’s primary research and creative endeavor interests include computational color design, color theory, algorithmic art, and visual literacy. In 2005, he co-curated the exhibition Digital Concentrate: Art and Technology for Purdue Galleries. He has exhibited his work nationally and internationally, including the 2014 Joint Mathematics Meetings Art Exhibition.

Acknowledgments There are many people who have helped and inspired us to put this exhibit together. Dr. Sunil Prabhakar, Head of Computer Science, encouraged the creation of this exhibit—and provided funds from the Departmental Corporate Partners Program. Jean Jackson, the former manager of corporate relations for Computer Science, was a consistent advocate for public works of art to provide an inspirational setting. Marilyn Forsythe and Nan Fullerton have been both encouraging and generous in their support of art in the Lawson Building.

We thank Dr. Harry Bulow, Head of the Patti and Rusty Rueff School of Visual and Performing Arts, for his continued support for the integration of technology in the arts and interdisciplinary collaborations.

Finally, we thank the ten artists, scientists, and mathematicians who allowed us to display their inspiring works in this exhibition.

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