Punica: folding Miura-ori with divots

Punica, 2019. 22″ W by 22″ D by 26″ Hi-tec Kozo paper, stainless steel

Free access at https://www.tandfonline.com/toc/tmaa20/current till the end of 2020.

Citation: Wu, J. (2020). Punica: Folding Miura-ori with divots, Journal of Mathematics and the Arts, Volume 14, Issue 1-2, pp. 170-172. doi: https://doi.org/10.1080/17513472.2020.1733914

The transformation of a flat sheet of paper to a three-dimensional form through folding is easy and yet complex. Conceptually, folding is always in-between, bringing together two edges and the inside and outside. As a material operation, folding is always unstable. A fold stores kinetic energy, which allows the folded form to contract and unfurl. I am fascinated by folding as a tactile process of working with material – for instance, paper, or other rigid sheet materials. I am drawn to these naturally occurring folds and working on understanding how they can be analysed in order to understand the material tectonics. I use balancing, connecting, hinging, suspending, pulling and popping in my works. I often fold intuitively and tactually using small pieces of paper first, oscillating between states of disequilibrium and equilibrium.

Unfolding a folded design reveals a patterned map of creating and generating. And this map, also called a ‘crease pattern’, is often the result of counterintuitive deliberation and calculation based on mathematical understanding. While it is difficult to describe the folded form through the visual characteristics of the folds on this map, it is even more difficult to reverse engineer and come up with logical patterns of folds that can then be folded into desirable forms – in other words, even though one can think of or see what one wants to fold, it is still very difficult to come up with a crease pattern. I often explore mathematical understanding and computational algorithms in generating a map of folds. These final outcomes of patterns of folds are often etched and cut on very large sheets of paper using an industrial-scale laser cutter. These large sheets of paper, sometimes as wide as 5′ and as long as 10′, are then hand creased and folded in my studio.

A simple fold has many possibilities and can generate many visual results, and it can be discovered only by folding. Only through the act of folding that is grounded in material reality, one can find out what the folds want or need to become visually. To bring folds and folding together, I alternate between intuition and calculation, imagination and logic. An accidental crimp or crinkle in the small pieces of paper may reveal an internal logic to organizing and abstracting the fold. When all the folds are organized and folded in a large sheet of paper, the folding in the material may behave in a self-organized way. When this happens, I stop folding. I observe how the material self-folds and self-assembles.

Punica is the Latin name for pomegranate. I named the work shown below Punica as it reminded me of the silhouette of the pomegranate flowers that I saw while growing up in Southeast China. Punica is folded based on flat-foldable Miura-ori tessellation with divots. Miura-ori tessellation, credited to Japanese astrophysicist Koryo Miura, has become well-known for its application in deployable structures, such as the solar array deployed in a 1995 mission for JAXA, the Japanese space agency (Miura, 2009). It is made of repeated parallelograms arranged in a zigzag formation and has only one type of vertices: a 4-degree of vertex. A key feature of the Miura-ori is its ability to fold and unfold rigidly with a single degree of freedom with no deformation of its parallelogram facets. Robert Lang, who wrote several books on origami and mathematics, described a method to semi-generalize the Miura-ori in order to generate any arbitrary target profile for surface with rotational symmetry without almost no mathematics involved (Lang, 2018).

In general, to fold Miura-ori into smooth curvature is materially impossible – the width of paper corrugation will be too small to fold physically. So, in order to generate folded surfaces with smooth and gentle curves, Miura-ori is altered by adding divots. Using linear algebra, I work with algorithm-based design tools such as Grasshopper and Rhino in order to study parametric changes of the folding angles and their relationships to the target smooth curved profiles. In the work shown here, an approximation of the target profile of a sine curve is generated first. And this profile curve is then arrayed and stretched into a rotational double-curved surface with both a positive Gaussian curvature value and a negative Gaussian curvature value.

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Punica, 2019. Top figure shows the sine wave profile when Punica is flat folded, while the bottom figure shows the layered effect with the light.

Light Harvest: Interactive Sculptural Installation based on Folding and Mapping Proteins

Installation views at the CODA musueum

Citation: Wu, J., Ressl, S. & Overton, K (2018). Light Harvest: Interactive Sculptural Installation based on Folding and Mapping Proteins, Digital Creativity, doi: 10.1080/14626268.2018.1533871.

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Light Harvest is an interactive sculptural installation that explores a protein called Light-Harvesting Complex II (LHCII) in the realm of materials, digital fabrication, projection mapping and interaction design. This article gives an account of the making of Light Harvest, a collaboration between an artist/designer, a structural biologist, and an interaction design technologist. The artistic concepts in material construction and digital techniques are drawn from protein folding, sophisticated mapping processes in protein X-ray crystallography, and the remarkable abilities of LHCI proteins to convert full-spectrum visible sunlight to useful energy for life. Through its interactive installation, Light Harvest engages us in an appreciation and understanding of the biological processes studied and the scientific techniques used to study them.

Ruga Lumina: Folding Interior Skin with Dynamic Light

Citation: Wu, J. (2018). Ruga Lumina: Folding Interior Skin with Dynamic Light, Journal of Interior Design, Volume 43, Issue 2, pp. TBD. doi: 10.1111/joid.12123

Link to full paper in PDF


Ruga Lumina investigates body–space relationships by leveraging digital fabrication and interactive technologies. Ruga Lumina is a spatial construct in the form of a smart luminous “skin” made of thin sheets of folded material that respond to the movement of live bodies within and surrounding its interior space. Spatial occupancy is registered through the use of smart technology; sensor information activates illumination and lighting effects, which, in turn, prompts perceptual and expressive aesthetic qualities as affects. This visual essay gives an account of the construction of Ruga Lumina at two exhibition sites: Detroit Center for Design and Technology (DCDT) in Detroit, Michigan, and 3Labs in Culver City, California. This account describes how bodies can be read and registered upon a spatial surface that points to a potential to re‐envision fundamental notions of surface interiority.

Folding Helical Triangle Tessellations into Light Art

Citation: Wu, J. (2018). Folding Helical Triangle Tessellations into Light Art, Journal of Mathematics and Arts, Volume 12, Issue 1, pp. 19-33.

Link to full paper in PDF

Abstract: This article concerns the artistic and perceptual quality of translucent light transmitted by an origami-inspired paper surface when a light source is placed behind it. It describes my geometric strategies in origami design to create light art through the luminous effect of gradations of light. I first present historical background and related work on origami-inspired paper light art and origami tessellation designs. Case studies follow, focusing on geometric strategies for helical triangle tessellations, considering specific design requirements for creating functional folded light art.

Ruga Interior Skin (RIS): Concept, Topology, Material and Making


Wu, J. (2015). Ruga Interior Skin (RIS): Concept, Topology, Material and Making. Proceedings of the Interior Design Educators Council Annual Meeting, Fortworth, Texas

In design history, the concept of ‘skin’ has been used to refer to the outermost tissue that encloses a physical body. Lois Weinthal writes that our skin is the first layer that we inhabit and it is the foundation of concepts that have influenced architects, designers, and decorators in creating various forms and surfaces in our interior space (Weinthal, 2013). The second layer we inhabit is sometimes said to be clothing, the third layer is furniture and objects, the fourth layer is colors and surfaces, and so on and so forth until we reach the last layer where the interior starts to merge into the exterior. According to Weinthal, interior architecture can be understood as a series of layers of enclosures where the body is placed at the center (Weinthal, 2011).  If ‘second skin’ is used as a metaphor for clothing, ‘third skin,’ or ‘interior skin,’ can be used as a metaphor for all layers of interior surfaces, as found in furniture, finishes, and curtains, that brush up against architecture and the body, but do not necessarily have to mimic either(Weinthal, 2011).

The relationship between fashion, architecture, and interior design have been explored by many modernist architects, either through making and designing clothing, or through theoretical writings. For at least ten years, Frank Lloyd Wright not only designed houses, but he also sometimes designed clothing for the owners of the houses he was the architect for, aiming to achieve total unity in a built environment(Gorman, 1996). Aldof Loos, who wrote extensively on fashion, style, and architecture, argued that the cut of an Englishman’s suit could be seen as a paradigmatic model for the construction of modern architecture (Loos & Opel, 1998). In fact, the intersection between fashion, architecture, interior design, and between surface skin and structural depth, reaches back as early as the nineteenth century.  In 1845, Charles Baudelaire, called the black frock coat “the outer skin of the modern hero,” thus allowing the word skin to first take on a literal role in reference to fashion (Baudelaire & Charvet, 1972). German architect Gottfried Semper, in the nineteenth century, argued that the origin of the architectural concept of skin came from the hanging of textile and cloth, and that the German word Wand (wall), had the same root and basic meaning as Gewand (garment) (Semper, 1989). For Semper, walls and interior surfaces gave shape to space as much as garments enclosed and defined the contours of the body. The form and the movement of clothing—the second skin—mimics the body through the materiality of textile and the apparel construction techniques. Similarly, interior skin, from the sheets we sleep between to the curtain we draw on the window, require active and flexible engagement from the body (Weinthal, 2013). From early modernist architecture to contemporary art, architects, designers and artists who draw the connections between fashion, interior and architecture often visibly connect and blur boundaries between the spaces wrapping around the body and the spaces formed within the rigid architecture frame. For example, the avant-garde artists Christo and Jeanne-Claude, created large scale installation by wrapping architectural structures and other large structures such as bridges and fences in vinyl fabrics. By changing the bodily scale of the drapes, folds and pleats to the scale of buildings and landscapes, the artists not only created new visual forms, but also challenged the viewers to see ordinary structures in the new contexts of wrapping and dressing.

So, if the concept of ‘interior skin’ can be understood as a generator of ideas for interiors that lie in between the flexible spaces around the body and the rigid spaces within the building, what new form and context can an interior skin take? Can this interior skin be made of non-structural sheet material and be semi-rigid while fulfilling an important spatial function? Can it be configurable, and can it move and interact with its occupants at the human scale? What are some design considerations, tools, techniques, material selection for making an interior skin? And how can a new approach to developing an innovative interior skin contribute to our ongoing search for sustainable design that places the human body at its center? This paper investigates Ruga Interior Skin (RIS) in an ongoing research project that explores new approaches to these interior skins. RIS explores ways to cross the boundaries between the clothing making and interior surface making by the use of patterning, pleating or folding.

Ruga Swan at Clay Center for Arts and Sciences, Charleston, VA
Ruga Swan at Clay Center for Arts and Sciences, Charleston, VA

Folding into Light: Sustainability, Making, and Materials


Wu, J. (2015). Folding into Light: Material, Form, and Making, International Journal of Design Objects, Volume 9, Issue 4, pp. 34-45, 2015

Environmental issues (such as pollution, climate change, and natural resource depletion) are increasingly becoming the core factors in consumer manufacturing industries.  Designers, manufacturers and marketing strategists are more conscious of taking account of sustainable product development in their design strategies (Kloepffer, 2003). Today, more and more products are designed by reducing the amount of materials and energy used, and by increasing the recyclable content and its potentiality for reuse. This trend has resulted in sustainable product designs that incorporate the use of green materials. One such green material is paper, due to its high level of recyclable contents. Paper is often thrown away or recycled after one-time or short-term use because of its fragility and commonality. Due to recent advances in the material science of paper development, paper has started to be used for technical components and for three dimensional products (Schmidt, 2009). According to Schmidt, technical paper is a new type of material that is manufactured in a similar way to conventional paper and consists of similar raw materials. It is processed and shaped using the same technologies or processes as conventional paper and possesses qualities similar to conventional paper, such as its feel, weight, and format. Technical paper that is water- and weather-proof, tear-proof, and chemical resistant, is now being used for the manufacturing of light-weight and long lasting products. Product designers have begun to turn their attention to this cheap and common material and have started to recognize the sustainable value in it. For example, renowned architects such as Frank Gehry and Shigeru Ban and renowned designer Issey Miyaki have used paper to produce their furniture, buildings, and even fashion.

Paper may be cut, scored, torn, rolled, or folded. In particular, folded paper design, using techniques that are similar to traditional origami, have inspired designers to come up with innovative design products. One of the early design explorations through paper folding was found in Josef Albers’ preliminary design class in the Bauhaus (Wingler & Stein, 1969). When a flat piece of paper is folded, the stiffness of the paper is significantly increased. When paper is folded in certain tessellation patterns, the mechanical behavior of the paper is altered as it becomes deployable and kinetic. Origami-inspired paper designs have been the subjects of many scientific research projects.  For example, mathematical theorems concerning geometric properties in folded paper have been studied (Demaine & O’Rourke, 2008). Computer algorithms have been developed to help fold desirable objects and to understand the best ways to fold tray cartons (Mullineux, 2010). Finite element analysis has been used to study the behavior of paper during the folding process (Beex & Peerlings, 2009). Curved folding and creasing have been investigated. Many more research projects focus on understanding the computational complexity and geometric algorithms of paper folding and unfolding. While research into paper folding has been conducted in computer science, mathematics, engineering and material science, little research has been conducted on paper folding in the field of design practice. This article is an attempt to fill this gap by systemically exploring practical means of using paper folding in product design in order to understand the making process and the materiality of paper in product design.

The goal of this paper is to understand the overlapping issues of sustainability, making techniques, and material choices by applying the art of paper folding in product design and the development of light sheds. Geometric tessellated patterns that can produce flat-foldable and rigid-foldable designs are focused, and variations of these crease patterns are explored to generate a variety of folded designs that can be used toward light sheds. A wide variety of durable conventional paper and technical paper materials that are appropriate for light sheds are compared and tested in terms of their material properties, functionalities and sustainability attributes. In order to investigate such issues, we will examine a lighting brand, Folded Light Art. Currently technical production processes for cutting and etching sheet materials, such as digital cutting or laser cutting, as well as traditional hand folding, are used to produce the scale paper models and 1:1 scale prototypes for the works of Folded Light Art. Luminary hardware is fabricated at local sheet metal shops. Potential CNC technologies of creasing and folding sheet materials are further explored in this article.


Ruga Architectural Skin (RAS): Towards Building Smart Self-Folding Topology


Wu, J., Anwar, S. (2016). Ruga Interior Skin (RIS): Towards Building Smart Self-Deployable Structures,” International Journal of the Constructed Environment, Volume 7, Issue 3, pp. 17-30, 2016

In architectural design, skin is a familiar metaphor for building envelopes that provide flexible layers of protection and are often dependent upon rigid structural supports. With advances in material technology and sustainable development, architectural skins are changing, creating new topological forms, providing new visual and tactile experiences, and becoming the conceptual bridge between our body and our environment. Can a three-dimensional architectural skin be self-assembled or self-folded from two-dimensional sheet material? Can this architectural skin be made of non-rigid material and yet provide semi-rigid structural support? What are the design considerations, tools, techniques, methods and processes of building such an architectural skin? And how can a new approach to developing an innovative architectural skin contribute to our ongoing search for energy-efficient building design, self-assembling deployable shelter, as well as sustainable construction techniques? This paper will introduce Ruga Architectural Skin (RAS), an ongoing research project exploring the potentiality of a new type of architectural skin.

“Ruga” is a Latin word for making winkles, creases, and folds, and the word has been recently used by material scientists to describe the various physical qualities of these various folded states. RAS is inspired by the use of folding to create complex topological forms from flat thin sheet material with simple and low cost tools. Folded forms have inherently rigid properties and at the same time are flexible. In comparison to other fabrication techniques, folding or bending allows for complex and innovative structures formed with simple and low cost tools at the point of assembly. From flat sheet material, folded designs can be easily deployed into a three-dimensional volume and then can be collapsed back to a two-dimensional flat shape that is much smaller for ease shipping and storage.

Many folded designs are inspired by origami, the Japanese art of paper folding. The original purpose of origami is to obtain various shapes, ranging from animals figures to objects, both abstract and figurative, by folding a flat sheet of uncut paper. Constructing a three-dimensional surface from two-dimensional sheet material in origami has inspired designers and engineers to come up with novel ways to fabricate, assemble, store and morph structures that are safe, efficient and energy saving (Edwin, Hartl, Malak, & Lagoudas, 2014), from collapsible medical stents for hearts (Kuribayashi et al., 2006) to airbags for cars. In architectural design, one of the earliest examples of exploration of paper folding and topological design of architectural system was conducted by Ron Resch (Ronald D Resch, 1973). In the last two decades, folding, both as a theoretical idea and as a means for form generation in architecture, has inspired a new generation of architects and designers to create morphogenesis architectural volumes with continuous variations and interpolations that overlaps gaps and avoid fracture (Lynn, 2004). Morphological architectural structures are starting to make use of one of the main characteristics of folding design – the kinetic ability to deploy and collapse in three-dimensional space (Liapi, 2002; Motro, 2009). More recently, researchers have been looking into using active materials that can convert various form of energy into mechanical work for folding to create self-folding (Edwin et al., 2014). However, low cost architectural skins that are deployable, configurable and that are in large scales, continue to be very challenging for architects and designers.

This architectural skin comes from two-dimensional sheet materials that can be pre-fabricated off-site and then shipped flat to the site, thus tremendously reducing the required amount of energy and resources in comparison to conventional structures. Once arriving on the site, it can be self-assembled or self-folded, suspended and reconfigured differently into various semi-structural surfaces. Although this architectural skin has roots in a paper folding art form, it proposes not only to significantly advance the technology of the art form, but also to transform this technology to the self-assembling structures that can potentially shift the paradigm in building temporary architecture.

This paper starts with a discussion of the application of origami in self-assemble and deployable architectural topologies. While objective of this paper is towards building smart self-folding architectural topology, this paper currently focuses on identifying the design considerations, tools, techniques, methods and processes of making and installing of several 1:1 scale mock-ups in corrugated cardboard, testing of varies materials, and surveying of the self-folding mechanism design and remote micro-processor control system design. Pending funding opportunity will allow us to build a 1:1 scale smart architectural skin prototype.

This research is a collaboration between Jiangmei Wu and Sohel Anwar.