Punica: folding Miura-ori with divots

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

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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.

Double-layered Weaving of Infinite Bi-foldable Polyhedral Complexes

Weaving of Miura Weave surface using Mi Teintes paper: (a) Front view, (b)&(c) in deployed and folded stages in the first direction, (d) (e) in deployed and folded stages in the second direction.

Citation: Wu, J., Weber, M. (2019). Double-layered Weaving of Infinite Bi-foldable Polyhedral Complexes, Proceedings of Bridges 2019: Mathematical Connections in Art, Music, and Science, Johannes Kepler University, Linz, Austria.

Link to full paper in PDF here

Abstract: We present various weaving constructions, as applied to our previous work on infinite bi-foldable polyhedral complexes. These enable one to build doubly or triply periodic structures that mimic certain origami patterns.

Folding Yoshimura Pattern into Large-scale Art Installations

Various spatial expressions of Ruga Swan. (a) Ruga Swan at the Juliet Art Museum in Clay Center of Arts and Sciences in 2016, Charleston, West Virginia. Photo Courtesy: Robert J. Lang. (b) Ruga Swan at the Allentown Art Museum in 2017, Allentown, Pennsylvania. Photo Courtesy: Harry Fisher. (c) Ruga Swan at the Hermitage Museum and Garden in 2016, Norfolk, Virginia.

Citation: Wu, J., (2018). Folding Yoshimura Pattern into Large-scale Art Installations. Lang, R., Bolitho, M. & You, Z. (Eds.), Proceedings of the 7th International Meeting on Origami in Science, Mathematics and Education (7OSME), Volume One, pp. 1-14, St. Albans, United Kingdom: Tarquin Publications.

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Abstract: recent years, origami art has developed from a traditional paper craft to a contemporary art practice that is capable of intricate and complex expressions. Focusing specifically on the Yoshimura pattern, this article explores its potential for being used at an architectural scale to create spatial expressions that blur the boundaries between a human body, where it dwells, and what it wears. Various form finding, material choices, fabrication tools, assembly details, and installation techniques are experimented upon in order to transform the Yoshimura pattern from scale paper origami to full-scale folded ‘skins’ that allow the human body to move within and through.

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.

Folding Space-filling Bisymmetric Hendecahedron for a Large-scale Art Installation

Synergia at night, installed at the North Christian Church, Columbus, Indiana

Citation: Wu, J., Inchbald, G. (2018). Folding Space Filling Bisymmetric Hendecahedrons for Large Scale Art Installation. Torrence, E., Torrence, B., Séquin, C. & Fenyvesi, K. (Eds.), Proceedings of Bridges 2018: Mathematical Connections in Art, Music, and Science, pp. 483-486, Phoenix, Arizona: Tessellation Publishing.

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This article discusses the bisymmetric hendecahedron, a space-filling polyhedron that was used to create a large-scale art installation at the site of the famous North Christian Church by Eero Saarinen in Columbus, Indiana. The article focuses on the geometric construction of the bisymmetric hendecahedron as well as its transformation into a large-scale art installation. The focus is on the artistic design, the material construction, and the assembly techniques. 

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

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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.

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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.

Method for Folding Flat, Non-rigid Materials to Create Rigid, Three-dimensional Structure

Citation: Wu. J. (October 31, 2017). Method for Folding Flat, Non-rigid Materials to Create Rigid, Three-dimensional Structures. Patent No: US 9,803,826 B2. Washington DC: The United States Patent and Trademark Office

Published_Patent in PDF

Priority Claim: The present application claims priority to U.S. Provisional Patent App. No. 61/893,519, filed Oct. 21, 2013, the entire disclosure of which is hereby expressly incorporated herein by reference.

Field: The present disclosure relates generally to creating rigid three-dimensional structures by folding flat, non-rigid materials. More particularly, the present disclosure relates to a method of folding a non-rigid material with a score or crease pattern into a three-dimensional structure for covering a light source.

Body, Form, Material and Surface Making of Ruga Interior Skin

Citation: Wu, J. (2017). Body, Form, Material and Surface Making of Ruga Interior Skin, Interiors: Design/Architecture/Culture, Volume 8, Issue 3, pp. 73-87. 2017

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Abstract: In design history, the concept of ‘skin’ has been used to refer to the outermost tissue that encloses a physical body. So, if the concept of ‘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 in adding to the contemporary interiority? Borrowing from the metaphor of ‘skin’ in fashion, interior design and architecture, Ruga Interior Skin (RIS) explores the ambiguous and conceptual realm connecting the act of wearing, inhabiting and its relationship between body, form, material, and surface-making of a novel interior semi-structural wall and partition. ‘Ruga’ is the Latin word for making wrinkles, creases, pleats, and folds. RIS is inspired by the use of wrinkling and folding to create flexible frameless topological forms that can be suspended in a way that is similar to a piece of cloth or textile. Both flexible and rigid, RIS draws the connection between the body and the interior surface, placing the dichotomy of permanent vs. ephemeral, solid vs. light, and material vs. digital at the center of the concept.

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

Applying Helical Triangle Tessellations in Folded Light Art

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

Link to full paper in PDF

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.