On the Aesthetics of Folding and Technology:
Scale, Dimensionality, and Materiality
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
636 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)
My eﬀorts 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?”
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 diﬀering 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.
ON THE AESTHETICS OF FOLDING AND TECHNOLOGY 637
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.”
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 106−11 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.
638 MATTHEW GARDINER
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 10−4m 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.
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 oﬀer actuation through
shape memory, elasticity, or chemical or mechanical hinging and that allow self-folding,
ON THE AESTHETICS OF FOLDING AND TECHNOLOGY 639
programmable shape-changing. Hybrid material solutions such as Elastomeric Origami
[Martinez et al. 12] in ﬁelds like soft matter show how simple material combinations aﬀord
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
aﬀords 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 diﬀering rates of
change to stimuli, such as chemistry and temperature, that aﬀords actuation. The combi-
nation of rigid and ﬂexible materials is exempliﬁed by the quality of production, such as
the variety of shapes aﬀorded 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 aﬀord the following properties: structural rigidity across the planar faces, hinged
ﬂexibility along the fold lines, and, where present, embedded actuation between adjacent
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
diﬃcult 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
640 MATTHEW GARDINER
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
ON THE AESTHETICS OF FOLDING AND TECHNOLOGY 641
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.
642 MATTHEW GARDINER
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 diﬀer 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
ON THE AESTHETICS OF FOLDING AND TECHNOLOGY 643
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.
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
644 MATTHEW GARDINER
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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E-mail address:firstname.lastname@example.org http://matthewgardiner.net