Applying Helical Triangle Tessellations in Folded Light Art (Bridges Conference Paper)

Citation:

Wu, J. (2017). Applying Helical Triangle Tessellation in Folded Light Art. In D. Swart, C Séquin. & K. Fenyvesi (Eds.), Proceedings of Bridges 2017: Mathematical Connections in Art, Music, and Science (pp. 383-386), Phoenix, Arizona: Tessellation Publishing

Abstract:

This article describes how I created a collection of lamps made of folded sheets of material using helical triangle tessellations, which are also called Nojima patterns. I started by working with a periodic helical triangle pattern to fold a piece of light art that is shaped in a hexagonal column. I continued by modifying the periodic pattern into a semi-periodic design by adding variations so that the tessellation could be folded into a light art that is shaped in a twisted column. I further developed tessellations that consisted of self-similar helical triangles by using a geometric construction method. These self-similar helical triangles form algorithmic spirals. I folded the tessellation design into a work of light art that is shaped in a conical hexagonal form.

External Links:

http://archive.bridgesmathart.org/2017/bridges2017-383.html

Link to PDF

 

Kaleidoscope 5 at Culver City, California

Ruga Lumina at 3labs, Culver City, California

I was invited to participate at Kaleidoscope 5 in 3Labs in Culver City, California, in May of 2017. The exhibition featured seven engaging installations from nine artists:  Alex Beim, Ben Jones, Kate Parsons and Ben Vance, Ara Peterson and Jim Drain, James Turrell, Akiko Yamashita, and myself. I installed the Ruga Lumina and the Anemoi Light Art.

About seven hundred or more guests attended the Kaleidoscope 5. According to the event organizer, the groups of artists’ “transcendent efforts harness the complex properties of light, skillfully manipulate real and virtual space, and utilize experimental forms of materiality to produce intriguing atmospheres that provoke unique physical and emotional responses.”

Artist Akiko Yamashita posts in front of Into the Light and Folded Light Art (Stefanie Keenan / Getty Images for Harper Sloane Productions)
Honorees Alexandra and Sean Parker post in front of Ruga Lumina and Folded Light Art. (Stefanie Keenan / Getty Images for Harper Sloane Productions)

Ruga Lumina at Detroit Center for Design + Technology, Detroit, Michigan

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Ruga Lumina, 2017, Coroplast, Video Projection, Digital Sensor, Detroit Center for Design + Technology, Detroit, Michigan. Photography by Kyle Overton

Ruga Lumina, an ongoing design research project, is part of my solo show, Jiangmei Wu: Folding into Rhythm and Algorithm, that was on display From January 10, 2017, to February 10, 2017, at Detroit Center for Design + Technology in Detroit, Michigan. There was a closing on February 10, 2017. As part of the solo exhibition, I spoke at School of Architecture and Planning at Lawrence Technological University in Southfield, Michigan on January 12, 2017, at 4:00 pm.

In Ruga Lumina, the latest iteration of  Ruga Interior Skin, interactive digital projection techniques are used to actively engage body-space relationship. As the viewers move in the space, their movements are captured by the Kinect Sensors and the information is translated into color changing information in the digital projections to be projected onto the translucent interior skin that is fabricated from 4 mm Coroplast sheets. A scaffolding that was made of cardboard and wooden rods was used to frame the somewhat flexible topology of the interior skin to facilitate the positioning and connecting of over seventy individual panels. Since the folding mechanism in each of the Coroplast panel is a flexible hinge joint, the edges of the interior skin are reinforced with fixed braces to give rigidity to this otherwise flexible topology.  Both flexible and rigid,  the interactive interior skin draws the connection between the body and the interior space, placing the dichotomy of permanent vs. ephemeral, solid vs. light, and materiality vs. digital fabrication at the center of the concept.

Acknowledgment: This project is supported by New Frontier of Creativity and Scholarship and Center of Arts and Humanities Institute Fellowship, Indiana University. The artist will also like to credit Kyle Overton for his work on interaction technology.

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Ruga Lumina 2017, Detroit Center for Design + Technolgy. Photography by Kyle Overton
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Ruga Lumina, 2017, Detroit Center for Design + Technology. Photography by Kyle Overton
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Ruga Lumina, 2017, Detroit Center for Design + Technology. Photography by Kyle Overton
Ruga Lumina, 2017, Detroit Center for Design and Technology. Photography by ManziYang

Video of Ruga Lumina deconstruction made of still photography. Photography by Joseph Caputo

Paper Folding Workshop at College of Architecture and Design, Lawrence Technological University

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Folding a piece of paper can be simple and doesn’t require any sophisticated tools. I often tell the students who participate my workshop that paper folding can do a lot more than computer CAD modeling. Since paper folding is unstable and flexible, manipulation of the paper surface to achieve depth and volume is dynamic. The fold stores kinetic energy, which allows the folded form to contract and unfurl. It can then be balanced, connected, hinged, suspended, pulled and popped up to alternate states of disequilibrium and equilibrium. Paper folding is unforgiving and honest. A folded form embeds the memory of a series of actions of scoring, creasing, twisting, wrapping, pressing, bending and folding. Unfolding folded paper reveals a patterned map of creating and generating. Paper folding is generative and evolving. It is difficult to describe an abstract folded form through its visual characteristics. Paper folding is improvisational and unpredictable. A simple fold has many possibilities and can generate many visual results, and it can only be discovered by folding.

About twenty students from the College of Architecture and Design at Lawrence Technological University participated the workshop. The workshop was conducted in the gallery The students are from Interior Design, Architecture and other programs.

I often begin my process using a step-by-step procedure, or algorithm, first by hand only. I demonstrated this technique to the students.  They started by folding smaller pieces of square paper into simple designs, and they then repeated the same steps for a multiple of times to create repetitions of these simple designs. And finally, they worked on connecting the folded pieces to create a larger form. The students learned that small seeds can be compounded and aggregated to create something that is a lot of complex than the original simple design.

 

2017 Mathemacal Art Exhibition Awards

light_torus_night_1.jpgThe 2017 Mathematical Art Exhibition Awards were made at the Joint Mathematics Meetings last week “for aesthetically pleasing works that combine mathematics and art.” The three chosen works were selected from the exhibition of juried works in various media by 73 mathematicians and artists from around the world.

“Torus,” one of my folded light art, was awarded Best textile, sculpture, or other medium. I’m interested in how paper folding can be expressed mathematically, physically, and aesthetically. Torus is folded from one single sheet of uncut paper. Gauss’s Theorema Egregium states that the Gaussian curvature of a surface doesn’t change if one bends the surface without stretching it. Therefore, the isometric embedding from a flat square or rectangle to a torus is impossible. The famous Hévéa Torus is the first computerized visualization of Nash Problem: isometric embedding of a flat square to a torus of C1 continuity without cutting and stretching. Interestingly, the solution presented in Hévéa Torus uses the fractal hierarchy of corrugations that are similar to pleats in fabric and folds in origami. In my Torus, isometric embedding of a flat rectangle to a torus of C0 continuity is obtained by using periodic waterbomb tessellation.

The work is made of Hi-tec Kozo Paper and measures 45 x 45 x 20 cm.

Folded Light in Beginning Interior Architecture Studio

fullsizerender-1_editedIn my Beginning Interior Architecture Studio in Fall 2016, co-taught with Jei Kim and Jon Racek, the first year design students were asked to use paper folding design methodology to understand basic design principles, such as unity, repetition, symmetry, contrast, etc. They were also requested to use the assembly and construction process in paper folding to produce a small scale light sculpture. The project was divided into three cohesive small parts that serve as scaffolds for the students. Before this project, the majority of students had never folded before and had never made any design objects. Therefore learning scaffolds were necessary.

In the first part, the students were asked to create small units of paper folds from pieces of small square paper based on simple line draws they made using straight edges and compasses. They were asked to explore these patterns in both bilateral and quadrant symmetries. They were given a couple of examples learn about how to assign mountain and valley folds to the lines patterns and then they were asked to turn their own line patterns into crease patterns by exploring various ways of folding and cutting by hand. The students were intimated at first as they were not comfortable working with their hands. They soon gained confidence when they observed how flat pieces of square paper changed into something that had sculptural depths.

In the second part, the students were asked to connect at least eight units of their paper folds. The goal was to generate somewhat seamless designs. Students were taught to connect the units by using ways to make the symmetric pattern in a plane, such as translation, rotation, reflection, glide-reflection. They were also taught to use polyhedron geometry to connect the units into spherical volumes. They studied platonic solids such as icosahedron and dodecahedron, Archimedean solids such as cuboctahedron and rhombicuboctahedrons, as well as Catalan solids such as rhombic dodecahedron and rhombic triacontahedron.

In the last part, the students were asked to add more units to create a volumetric paper sculpture. They were graded on the craftsmanship and the final lighted presentation. Many of the students turned in interesting works. Most students did a good job creating their units design. However, they had more difficulty connecting the units to generate structure volumes.

Special thanks to Noelle Zeichner, Abigail Stawick, Julia Gilstrap and Yuning Ding for providing some of the pictures shown on this blog. For my Folded Light Art brand, please visit www.foldedlightart.com.

Engaging body-space relationship: making of an interactive interior skin

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A prototype of To Feel the Space. Photo courtesy of Kyle Overton

Citation: Wu, J. (2016). Engaging body-spacer relationship: Making of an interactive interior skin, IDEC Exchange: A Forum for Interior Design Education, Fall 2016

Link to PDF

There is an increasing interest in interior design theory that focuses on understanding interior spaces as both the specifics of objects and environments within the interior and the subjects who experience them through their bodily presence. If a theory of interiority cannot simply be characterized by reference to qualities such as walls, ceilings and floors in a Cartesian space and by the objects and finishing contained in it, and we wish to engage physical and psychological body-space relationships as well, then what are some new spatial expressions that can affect our perception of space? What is our perception of a space? What does it mean to feel a space? According to Gestalt psychology, when we enter an interior space, what is first and immediately perceived is neither the subjective sensation nor shapes, colors, or objects, but rather, atmosphere. German philosopher, Gernot Böhme, in his seminal work, Atmosphere as The Fundamental Concept of a New Aesthetics, articulated the interrelationship between the subjects and objects in atmospheric space. According to Böhme, atmospheres are neither something object nor something subject. Instead, atmospheres are both object-like, articulating their presence through qualities, and at the same time subject-like, presenting a bodily state of being of subjects in space.

Human skin is the interface between the body and world: it is our outermost organ that protects our physical bodies, it is sensuous to touch and constantly gives us information about our surroundings. In design history the concept of ‘skin’ has been used as a site for rich metaphors referring to the clothing that wraps around the body or the building walls that enclose and protect our body. In fact, ‘second skin’ is often used as a metaphor for clothing or fashion while ‘third skin’ is often used as a metaphor for architectural cladding and surface interiority. An architectural skin, referred to generically as the boundary between indoor and outdoor, has to negotiate with both exterior and interior presences. In contrast, interior skin, mediated by the architectural skin, can be understood as a series of layers demarcating various interior enclosures: inside and outside demarcation is erased and dichotomy becomes relevant only to the presence of the body.

Directly borrowing from the metaphor of human skin, this art installation To Feel the Space, is a full scale interactive interior skin that is produced by using folded plastic corrugation boards and digital technologies. It attempts to explore the potential object-like and subject-like expression of interior atmosphere by focusing on the ephemeral status between subject and object and capturing the fleeting moments of body-space experience. Situated within a large public space, for example, an exhibition hall, the form of the interior skin, digitally fabricated from folded plates is not the result of the design generated from a specific program, but the result of parameterizing the dome-like structure to the bodily dimensions and movement. The interior skin, as the object in space, actively engages with the subjects as they walk into the exhibition space. Digital cameras capture the colors palettes from the clothing people wear in space and add the live color information to a database to be live project-mapped onto the interior skin. As the people move closer to and within the interior skin, the additional digital cameras will capture people’s movements in space and allow for the interactive plays between the bodies and the space. When people move outside of the interior skin and the exhibition hall, they will leave their color information behind in the space and therefore the space is present with the traces of bodies even if the bodies are absent in space. As a result, the atmosphere is neither objective nor subjective, but infused with the fleeting interplay between the object and the subject that is felt through the body and met with the eyes.

Acknowledgement: This project is supported by New Frontier of Creativity and Scholarship and Center of Arts and Humanities Institute Fellowship, Indiana University. The author would like to thank Kyle Overton for working on aspects of the interactive technology.

Upcoming Exhibition: Light Harvest

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A photograph of one of the three chains of Light Harvesting Complex. Photo courtesy of Kyle Overton

Light Harvest will be part of a group exhibit, (Re)imagining Science at Grunwald Gallery at Indiana University. It is also part of Themester 2016 exhibitions that are centered on the theme of Beauty. The show opens on Oct 14th, 2016.

This project is inspired by D’Arcy Wentworth Thompson’s work on form and growth and the structural biology. In 1917, Thompson first published his magnum opus “On Growth and Form,” with a second edition appeared in 1942. Thompson studied the system of forms and structures found in all species of nature. He was the first bio-mathematician who used mathematical and geometric analysis to study the myriad living forms as a product of dynamics at work at cellular and tissue level within all organisms. For Thompson, the beautiful world we live in can be understood as an ethereal palpitation of waves of energy making up all things. Thompson’s book has inspired generations of artists and designs in search of beauty found in natural structures that reach into vastness and smallness beyond our human sensory range.

Proteins are essential to all forms of life on earth. Without proteins, there would be no life as we know it. Proteins are small molecular machines with unique folding structures. Their various functions rely on their proper structural architecture; this is called the structure-functional relationship. Protein structures cannot be seen with the naked eye. Therefore structural biologists use X-ray Crystallography to determine the structure of proteins, which can be visualized in 3D. This allows not just analyzing the folding structure to understand a protein’s function; it also reveals the beauty of nature’s design on the atomic level.

The particular protein that is presented in Light Harvest is called Light-Harvesting Complex (LHC), which is the solar sail of the photosynthesis components in plants and some micro-organisms that uses bundled sunlight and together with water to create sugar and oxygen, thus providing the basis for life on this planet. It is made of three amino acid chains with 207 amino acids in each of the chains. Computer algorithm-based program Grasshopper was used to create the scaffolding of the three-dimensional protein chain. 642 pieces of rollout patterns, of which 207 were unique, were laser-cut and etched at Noblitt Fabricating in Columbus Indiana and were hand-folded and assembled at my studio at Smith Research Center. The material is high-tech Kozo, a type of Japanese-made paper that comes from renewable mulberry trees.

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Layout of three canopies of Light Harvest at Smith Research Center

Video projection mapping technologies will be used to bring the light, colors, and the interactivity to live. For the artistic meanings and the science behind Light Harvest, please come to the show on Oct 14th and make sure to check out www.foldedlightart.com for more information.

Acknowledgement: This project is supported by New Frontier of Creativity and Scholarship and the Grunwald Gallery of Art at Indiana University, Bloomington, Indiana.

Project Credits: 

  • Science: Susanne Ressl (Assistant Professor, Structural Biology, Indiana University)
  • Technology: Kyle Overton (Ph.D. student, HCID, Indiana University)
  • Fabrication: Steve Dixon (Noblitt Fabricating, Columbus, Indiana)
  • Production: Siqiao Gao (Undergraduate student, Interior Design, Indiana University)

 

Gold and Silver Foil Painting with Mikako Suzuki

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Gold and silver foiling painting is a very special traditional Japanese art form. One of the masters in foil painting is Mikako Suzuki. A graduate of Aichi University of Arts, Ms Suzuki has been practicing foil painting in her studio in Nagoya for almost of a decade. I was very fortunate again to learn the technique from her during my visit to Aichi University of Arts in the summer of 2016.

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Detail of Mikako Suzuki’s gold foil painting

Before I arrived at Aichi, I designed a set of abstract and generative diagrams for the making foil prints on hand-made Washi paper. The first step of gold and silver foil painting was to use silk printing technique to print a very thin layer of Nori, or Japanese paper glue, to the Washi paper. A small amount of yellow oil paint was added to the Nori so that the original pattern would be visible after silk screen printing. The next step involved transferring a foil sheet and layering it on top of the silk screen printed sheet, a process turned out to be a lot more difficult than I imagined.

A pack of silver foil of 50 pieces usually costs over $100. Comparing to silver foils, gold foils are a lot more expensive and precious, often costing twice as much. Separating a single piece of foil sheet and picking it up without breaking or tearing it required very special tools and very soft and steady hands. Ms Suzuki uses sets of bamboo tweezers. She first burnished one of the corners of foil stack to separate sheets of the foil and then picked a single sheet up using the bamboo tweezers. She then moved gracefully and laid the foil on the top of the silk screen printed patterns. Since this process needed to be accomplished before the Nori dried, Ms Suzuki, Professor Shibazaki and I had to work simultaneously together. As we worked on the foiling, several of Shibazaki’s assistants were working on the silk screening simultaneously. Since the foil was so delicate and could break easily, I learned never to directly touch the foil using my hands. I learned to blow on the foil slightly so that the foil would stick with the Nori glue patterns.

The next day we were ready to brush off the part of the foil that were not glued to the Nori pattern. By doing this, the initial patterns with the design were revealed as the foil painting. We then pieced together hundreds of the foil painted Washi to make large tapestries to be shown at Ozu Washi gallery in Tokyo.