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On the aesthetics of folding and technology: Scale, dimensionality, and materiality

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On the Aesthetics of Folding and Technology:
Scale, Dimensionality, and Materiality
Matthew Gardiner
1. Introduction
The question “What is a fold?” produces simple and complex answers. Origami pro-
vides a simple answer that we can demonstrate; make a crease in a sheet of paper and there
it is, done. However, this answer does not address the infinite possibilities of folding that
origami artists, scientists, mathematicians, and educators know and relish, nor does it even
begin to explain folds in Deoxyribonucleic Acid (DNA) chains [Rothemund 05], pleats
embedded in haute couture fashion [Van Herpen 14, Miyake 15], creases in the façades
of new architectural icons [Delugan Meissl Associated Architects 12], or analogies for the
shape of dark matter [Abel et al. 12].
As a result of these artistic and scientific advances, the meaning of origami is shifting
from its association as an art and craft. This is evident in the title of OSME, that origami
is a science as well as an art form. The term origami is used in the fields of computation,
biology, soft-matter, design, and fabrication to describe folding operations, functions, and
stylistic approaches. Origami is often used as a metaphor, as very few cases literally in-
volve the folding of a sheet of paper: DNA origami [Rothemund 05], for example. The
term origami is being borrowed for its culturally associated image of a complex of folds,
from which the materiality of paper is no longer necessary, but rather for the functional
aesthetic of folding. Rather than contest or try to compartmentalize the term origami into
its literal meaning, this paper investigates this shift through the proposition of three inter-
dependent aesthetic and functional characteristics: dimensionality, scale, and materiality.
2. Background and Related Works
The philosophy of thought surrounding the universality and complexity of folding be-
gan in earnest with Gilles Deleuze in The Fold: Leibniz and the Baroque [Deleuze 06].
Treatments prior to this were principally engineering and design approaches, focused on
developing systems and equations, constructed as tools for solving the mathematical prob-
lems of folding. The impact of computation in architecture and design shifted to a more
theoretical landscape when Deleuze’s article was reprinted in Folding in Architecture
[Lynn 93] alongside a set of essays and example projects that evoked a more ephemeral
architectural theory to address the Free For m or Digital Baroque [Eekhout 02]. These
theories enveloped space structures: folded plate structures, shell structures, space frames
and tensegrity structures; once inventions of the latter half of the 20th century, they are
©2015 Matthew Gardiner
Figure 1. Concrete Dürer tiles with subtle fold patterning on the upper surface.
now matured design systems. Architecture was not the only beneficiary of these theoreti-
cal advances; the structural language of origami informing theory in construction also in-
formed tinier design targets—in materials other than paper, other than concrete, glass, and
steel, but and rather in DNA or in silicon as Micro Electro Mechanical Systems (MEMS)
[Pickett 09].
My eorts here are to reflect on the broad diversity of origami as the “science of
matter” [Deleuze 06] and to use the process of artistic research—including speculation,
computational design, and fabrication—as part of a process to address the question, “What
is a fold?”
3. Dimensionality
At the beginning of my practice-led research, my intentions were focused on develop-
ing an understanding of the visual aesthetics of folds. Origami has many diering visual
aesthetics, ranging from the artistic-organic “Akira Yoshizawa” style to the geometric-
faceted “Tomoko Fuse” style of models. Style is a topic loaded with opinion in the broader
origami community, and in my view these two artist’s works bookend the stylistic extremes
of origami language: one is figurative, emotive, and defined by approximations; the other
is abstract, pristine (equally emotive to some), and informed by strict mathematical rules.
Trends in fashion, architecture, and design have adopted folding as a stylistic language and
tend toward the unit-style, geometric-faceted, aesthetic of folding, such as the Bao Bao bag
by Issey Miyake [Miyake 15].
The aesthetic of origami and technology combines the futuristic abstracted style of
mathematic–organic intersections, the wireframe and polygon views of three-dimensional
modeling, and the attraction of the techno-organic in catwalk fashion [Van Herpen 14].
My examination of these stylistic shifts began with the consideration of two-dimensional
tessellations, the tiling patterns, and the history of complex interlocking polygons. This
research led to the idea of designing a concrete tile with a subtle folded surface. While
making the drawings for a tiling design (Figure 1) of interlocking concrete blocks, I real-
ized that the lines on the page were one-dimensional, constrained to the two dimensions
of the page, and the corners were folds. My vision extended to the realisation that a fold
separated each additional step toward a higher dimension (Figure 2): the fourth dimen-
sion being expansion and contraction (folding and unfolding) of all lower dimensions. The
folds form the structure of each dimension.
Figure 2. Folds define dimension, each dimensional is created by the
folding/unfolding of a new dimension.
The criteria of dimensionality is used in mathematical models of origami. For DNA
origami, the model is a one-dimensional string. Sheet fabrication consists mostly of two-
dimensional models of crease patterns and their influence on three- and four-dimensional
geometries. Several research projects have also investigated four-dimensional printing
[Tibbits 14]—a fabrication process using three-dimensional printing to produce larger prod-
ucts in the small volume of three-dimensional printers. An object is designed and then
pre-folded, using a tessellation of the surface, so that it fits into the build dimensions. The
resulting three-dimensional print can then be unfolded to a larger form outside the three-
dimensional printer. Research into rigid origami [Tachi 09] is an investigation into the
four-dimensional (time-based morphology) and requires computational assessment of the
three-dimensional folded model. In addition, the notion of architecture as manifestation of
the folded surface intersects with Deleuzian architectural notions of The Fold [Deleuze 06],
as the angular variations at the intersection of two or more planes in a building’s surface is
visually interpreted as “folded.”
4. Scale
In the natural world, folds can be found at all scales, from the nanoscopic scale of
DNA origami and protein folding [Rothemund 05] all the way up to an analogy for the dark
matter sheet at the cosmological scale [Abel et al. 12]. We find folds, buckling in structural
geology [Hunt 10], in Earth’s topography: One can the perceive folds of landscapes (in the
language of origami, the terms mountain and valley evoke such landscapes) formed by
tectonic movements, a mountain range with ragged peaks, and the worn-down folds of
rolling hills. Depending on the scale of magnification, a fold can appear soft and curved
close up, while far away it appears sharp and pointed.
The introductory essay for my publication on the topic of origami design and mate-
rials, Designer Origami [Gardiner 13], attempted to position origami across scales with
a diagram illustrating the scales of origami as follows: nano, origami, interior, exterior,
and space. (See Figure 3.) This diagram and concept was intended for a nontechnical
audience. Miyamoto’s Origami Powers of Ten [Miyamoto 12] takes this concept even fur-
ther, tabulating the scale in meters, materials, hinges, and actuators from 10611 m up to
1020 m, covering DNA, proteins, MEMS, art/crafts (origami), furniture, machines, build-
ings, Earth, and the Solar System. This concept, based on Eames’ famous Pow ers of Ten
video, clearly illustrates the idea that scale is indeed an important factor in understanding
what is a fold.
Scale is not simply a matter of size; it shares interdependence to the amount of force
required to program a given material with a fold and the force that binds the material.
Figure 3. The scale of folds, from the nanoscale of DNA to the
macroscale of the cosmos.
Scale also determines the structural stability of the material to resist gravity and maintain
its structural integrity. For example, paper functions reliably as a material for folding from
as small as 104m up to around the 1 m scale. Any smaller or larger and the fibrous
structure and the bonds between them become compromised, being either too small to fold
or too large to cope with the forces of gravity.
5. Materiality
In the case of the materiality for origami scales, qualities like strength, thickness, elas-
ticity, and plasticity equate to what we can call foldability. A series of paper reviews pub-
lished in The Fold [Garibi and Vishne 10] detail qualities relevant for expert paper folding.
The materiality concerns in folding and technology include foldability, but the attention
in contemporary scientific circles is on the actuation and programming of kinetic mate-
rial properties: the focus is on materials and material hybrids that oer actuation through
shape memory, elasticity, or chemical or mechanical hinging and that allow self-folding,
programmable shape-changing. Hybrid material solutions such as Elastomeric Origami
[Martinez et al. 12] in fields like soft matter show how simple material combinations aord
new possibilities for soft robotics and mechanism design. The use of traditional methods of
pleating can be applied to woven materials such as polyester fabric in artistic contexts, such
as Oribotics [Gardiner 11]. Shape-memory actuators hinging a tessellated plate structure
aords the reprogrammabilty of folded sheet structures [Hawkes et al. 10], and the use of
shape-memory polymer/paper composite allows self-folding by heating [Felton et al. 13].
In these applications, it is the bonding of rigid and flexible materials with diering rates of
change to stimuli, such as chemistry and temperature, that aords actuation. The combi-
nation of rigid and flexible materials is exemplified by the quality of production, such as
the variety of shapes aorded by the design of Issey Miyake’s Bao Bao [Miyake 15] series
of bags. This materiality can be seen as either giving “life” as movement or extending the
life of the living hinge. The knowledge required for fabricating these material composites
is process-based and requires experimentation and significant expertise for high-quality
results. The materiality of these origami mechanisms can be generalised as material hy-
brids that aord the following properties: structural rigidity across the planar faces, hinged
flexibility along the fold lines, and, where present, embedded actuation between adjacent
folded planes.
6. Folding =Force +Matter
Folds are formed when the material and dimensional natures of an object are influ-
enced by a force. We can categorize the intent of these forces as being either chaotic or
6.1. By-chance folding. Chaotic or chance processes are produced as the result of
buckling and bifurcation when a sheet is compressed by a force. Miura established a
mathematical basis for studying the nature of folding by showing a set of patterns that can
be found through compression [Miura 97]. The easiest kind of buckling to imagine, though
dicult to predict, is the crushing of a sheet of paper into a ball. When the crumpled sheet
is flattened out, we see folds made by chance and the surface has a topographical aesthetic,
as if the crumpled sheet were a tiny landscape. Despite the chaotic appearance of such
folds, when taken as a source of inspiration, studies of crushing and buckling have aided
the discovery and generalization of well-known origami patterns such as the Yoshimura
[Yoshimura 51] and Miura [Miura 70] patterns.
6.2. By-hand folding and by-code folding. Designed processes in origami are forces
applied with specific intent, such as the pinching actions of fingers in shaping a sheet of
paper. Artists and designers use the origami axioms to reliably make the same sequence
of folds, often resulting in symmetrical geometric aesthetics, which Engel attributes to the
perfection of the square and its latent symmetries [Engel 97]. Figure 4 illustrates a simple
diagram of three possible approaches to making folds: by-chance,by-hand,andby-code.
The latter example, by-code, has been derived and expanded upon in several directions
depending on the design problem: specific software tools such as Treemaker [Lang 98],
Origamizer [Demaine and Tachi 10,Tachi 10b], and Freeform Origami [Tachi 10a], among
others allow a user to tackle specific design problems, while bespoke software applica-
tions like Grasshopper for Rhino allow a user to construct their own parametric solu-
tions using an extensible set of components. The aesthetic of these forms dates back to
the pre-computational works of Ron Resch [Resch 73] and earlier to the Bauhaus school
[Wingler et al. 69]. More recent contemporary research such as Tomohiro Tachi’s rigid
Figure 4. From left to right, by-chance folding (a crumpled sheet), by-
hand folding (Ananas (waterbomb) base), and by-code folding (felt wall
Figure 5. A lightweight “wireframe” fold mapped around a toroid,
printed in silver.
origami works, Gregory Epps’ works at Robofold [Tachi and Epps 11], Daniel Piker’s de-
velopment of Kangaroo for Grasshopper [Piker 13], and the works of Erik and Martin
Demaine—for example, Computational Origami as part of the exhibition “Design and the
Elastic Mind” at the Museum of Modern Art [Antonelli 08]—have been pushing the defi-
nitions of what is foldable.
The aesthetic of folding and technology is by-code, infinite, developable approxima-
tions of continuous sculpted surfaces, reminiscent of tectonic topography. We find algo-
rithmically iterated, faceted, asymmetric, dynamic forms that evoke the organic origins of
buckling patterns and the undeniable precision of calculated order.
7. Fold Mapping By-Code
My recent aesthetic experiments (see Figures 5, 6, 7, 8, and 9) apply design by-code.
The experiments are based on mapping discrete folding units, such as open corrugations
(like the Yoshimura, Miura, and Ananas patterns), onto designed surfaces. The units can
Figure 6. The mapping of a folded pattern around a twisted cylinder:
Queen of Diamonds 5.24.42, mesh and wireframe versions.
Figure 7. A folded surface in felt-resin composite. The base surface is a
flat plane, sculpted with curved valleys and mountains of expansion and
be either designed by-hand with a specific aesthetic or functional intent, or adopted from
by-chance studies of buckling. The results are continuums of discrete folded elements that
form an approximation of the surface.
Figure 8. This crease pattern is a near approximation of a developable
pattern of the folded surface in Figure 7 generated using the developable
constraint in Freeform Origami.
Figure 9. Stills Fallen Future, a giant origanic leaf falls backward
through time into Ho Chi Minh City, researchers mine the the artifact
for future technologies.
These works dier from existing folding processes, such as those enabled by Freeform
Origami [Tachi 10a], that involve interactive manipulation of a folded surface, and they
begin with the design of the object and retrospectively map the folds across the design. The
process takes advantage of the modeling of surfaces in Rhino, and it is combined with the
PanelingTools plug-in. “PanelingTools plug-in helps generate two- and three-dimensional
Figure 10. This spiral blossom explores the idea of recursive infinity
through by-code fold-mapping across an algorithmically generated spi-
cellular patterns and populate them over rectangular grids” [Issa 14]. The folding units
are defined by a sets of vertices to make up the edges and faces of the folded unit in an
open state. To overcome limitations in the software and to ensure the vertices of adjacent
units are aligned, the folded unit is generalized such that the vertices are positioned only
on positive integer (x,y,z) coordinates. The pattern mapped onto Figures 5–10 was defined
as shown in Figure 11. These figures are indicative of my artistic response to the notions
explored above. They explore dimensionality, materiality, and scale, and they were created
with the by-code design method. Further work will involve exploration of the kinetic
functions through material experimentation and fabrication.
8. Conclusion
These aesthetic experiments and theoretical statements will form the basis for further
investigation. The criteria of scale, dimensionality, and materiality are shown to be relevant
Figure 11. Set of faces defined by a string of (x,y,z) vertex coordinates
(top left). The open folded pattern with annotated vertex points (center).
Side and top views showing vertices constrained to a grid (bottom right).
in understanding the aesthetics of folding and technology. In addition, the aesthetics of
folding and technology are deeply informed by the methods of fold programming: by-
chance, by-hand, and by-code. These criteria and methods continue to be a rich field for
studies in new aesthetics for the artist, researcher, engineer, and scientist alike.
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Ars Electronica Futurelab,Linz,Austria and School of Creative Arts,University of Newcastle,New-
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A trained architect, who works with the Specialist Modelling Group (SMG) at Foster + Partners, Daniel Piker is also the developer of the Kangaroo plug-in for Rhinoceros® and Grasshopper®. He explains how Kangaroo has been devised to simulate aspects of the behaviour of real-world materials and objects in order to modify designs in response to engineering analyses, engendering an intuitive sense of the material world.
How might 4D printing overcome the obstacles that are hampering the rolling out and scaling up of 3D printing? Skylar Tibbits, Director of the Self-Assembly Lab at the Massachusetts Institute of Technology (MIT), describes how the Lab has partnered up with Stratasys Ltd, an industry leader in the development of 4D Printing, and is making the development of self-assembly programmable materials and adaptive technologies for industrial application in building design and construction its focus.
Structural designers are confronted in the last decade with architectural spatial schemes that greatly benefited from the aid of computer-operated design and modelling programs like Maya, Rhino and 3D-Studio Max. These architectural designs are referred to as 'Fluid or Liquid Designs' or 'Blob Designs'. They contain sculptural building forms in an arbitrary geometrical form which is not developable mathematically or to be generated easily, even by computer. These building forms do not have a systematic and recognisable repetitive structure, either. The gap between architects and structural engineers seems to open wide at first in each project and an even larger gap appears between architects, technical designers on the one hand and co-engineers, producers, co-makers, sub-contractors and builders a little later in the same project. In the structural glass building parts, with its tight tolerances and high degree of prefabrication an enormous effort is necessary in the engineering phase to define accurately all individually shaped building components. This will definitely transform 'production' into 'co- engineering & production'. What is the most appropriate approach for structural design of components in these 'Liquid Design' concepts? What agreements and working discipline have to be developed for applying the existing knowledge of industrially produced components into highly individualised components 'produced in lots of one' that together form these highly irregular sculptural 'Liquid Design' building envelopes? The introduction of this new view on architecture is more or less a revolution in the world of structural designers. th century has witnessed the development of a number of spatial and systemised lightweight structures: shell structures, space frames, tensile structures, cable net structures, pneumatic structures, folded plate structures and 'tensegrity' structures. Most of these structures were developed by dedicated pioneers in the 1950-ies who designed, analysed and built impressive amounts of ever new concepts: Felix Candela, Frei Otto, Max Mengeringhausen, Richard Buckminster Fuller, Zygmunt Makowski, Walter Bird, Peter Rice et all (Ref. 1). The common basic idea was to minimize the amount of material consumed, and in order to attain this, extensive intellectual investments in man hours were necessary. Computer analysis programs assisted the accurate analysis of complex geometries of the components in these three-dimensional though - in our current view - highly regular 3D-structures. Thanks to the further development of accurate analysis programmes based on non-linear structural behaviour these 3D-structures can now be designed by structural engineers all over the world. They reached a status of accepted and mature technology. Peter Rice (or rather: R.F.R) introduced the intricate use of structural glass in buildings in the 1980-ies, based on regularity and systemization in the Serres of La Vilette, Paris in 1986 (Ref. 2). In the meantime the ratio material / labour has been changed dramatically. For cost effective structures not longer the minimal amount of material counts, but the minimal amount of totally invested manpower. The post-war adage of 'minimal material' became an intellectual goal for architects and structural engineers only. It is not an item for the building industry, nor for clients. This greatly influenced the choice of building technologies over the last decades. It differs of course from country to country. With increasing wealth also buildings were realised in a fashion more elaborate than the very minimalist results of the early Modern Movement. Local colouring on an international scale could not be suppressed. But the development of architecture appeared to be more capricious. The Modern Movement with her world-wide innovation of concrete technology over local building technologies was caught up by other approaches of later generations of architects, wanting to express themselves over the built results of previous generations. The subsequent changes in
The primordial velocity dispersion of dark matter is small compared to the velocities attained during structure formation. The initial density distribution is close to uniform and it occupies an initial sheet in phase space that is single valued in velocity space. Because of gravitational forces this three dimensional manifold evolves in phase space without ever tearing, conserving phase-space volume and preserving the connectivity of nearby points. N-body simulations already follow the motion of this sheet in phase space. This fact can be used to extract full fine-grained phase-space-structure information from existing cosmological N-body simulations. Particles are considered as the vertices of an unstructured three dimensional mesh, moving in six dimensional phase-space. On this mesh, mass density and momentum are uniquely defined. We show how to obtain the space density of the fluid, detect caustics, and count the number of streams as well as their individual contributions to any point in configuration-space. We calculate the bulk velocity, local velocity dispersions, and densities from the sheet - all without averaging over control volumes. This gives a wealth of new information about dark matter fluid flow which had previously been thought of as inaccessible to N-body simulations. We outline how this mapping may be used to create new accurate collisionless fluid simulation codes that may be able to overcome the sparse sampling and unphysical two-body effects that plague current N-body techniques.