the arts and architecture of italy

“A man who has not been in Italy is always conscious of an inferiority, from his not having seen what it is expected a man should see.” -Samuel Johnson

The New School of Making, situated in Piazza Mentana in Florence, seeks to create a place of study that connects students and masters across all levels and disciplines. The design and layout of its studios, classrooms, and offices provides visual connections that facilitate an apprenticeship model of learning. The existing historical statue is moved to a place of importance, inviting both students and the public inward along major sight lines. Prominent gallery spaces display student work for all to enjoy. The main C-shaped wall serves to both protect and welcome, wrapping the building in functional 3’ x 3’ block units that undulate in response to the

needs of the spaces within.

The new St. Petersburg Pier is designed to become a new icon for the city. Its organic shape is derived from the surrounding water and existing land, utilizing curves that flow and connect more readily to the environment than the current pier’s rigid geometry. The same organic nature that lends it fluidity allows for a variety of paths to the same end point, transforming a walk that was previously an unpleasant necessity to exciting exploration. Landscaping and a large water feature serve to further soften the connection between land and pier. An outdoor amphitheater, large-scale aquarium wall, restaurants, shops, and children’s play areas become distinct destinations along the way, with the addition of many areas for informal gathering. Above all, the pier will become an exciting destination for the city, both during the day and at night.

The USF Undergraduate Classroom and Support building occupies the end of the Leroy Collins axis, situated just in front of the existing Administration Building. This new building would serve the needs of both students and faculty. It features naturally lit offices, department suites, auditoriums, multiple classroom sizes, educational laboratories, and numerous support spaces. Connecting all major areas is a multi-tiered walkway ribbon that serves as both a linking corridor and study space, providing the campus with a central point of identity.

Approach and MethodologyThe project seeks to develop a series of networks that begin to address the major needs of Havana in such a way that preserves and enhances the strengths of what is existing by stitching together the strong context with the idea of the street as a catalyst for social interaction.

District ScaleContinuing the green corridor along the waterfront and linking with the existing open space network connects interventions with the context. Creating a connection between those two corridors along the subtle grid shift of crespo street helps to celebrate that connection.

Neighborhood ScalePlacing a strip of higher density mixed use one block behind a historic urban edge begins to draw some of the energy of the waterfront into the site. This combines with a landmark building and a new language for open space to bring identity to the neighborhood.

Block ScaleWater retainage and disposal are major issues affecting the area. Creating a network of paths connecting a series of watergardens begins to celebrate the journey of water.

With no glue necessary and cut from a single sheet of plywood, this coffee table is held sturdy by interlocking pieces and four strategic keystones that allow for easy assembly and disassembly.

A redesign of the SACD entry features three bench units flexibly arranged along a painted floor pattern, seeming to melt into and emerge from the ground. Their amorphous shapes are possible through foam construction, coated with a durable hard finish.

Primarily an investigation in paper, the use of digital modeling programs and a laser cutter allowed for unusual explorations in bending, folding, and cutting. This culminated in a paper dress made of individually folded crane units. A newly installed CNC router allowed for the final project to be designed digitally and translated to plywood, resulting in an undulating form that can be utilized in multiple orientations.

Spiral Fantasia — A Child’s Dream An 80-foot glass mosaic designed by Mari Gardner for the Glazer Children’s Museum. Creating this large scale piece of public artwork ultimately comes down to the cutting and installation of thousands of individual glass shapes on a piece-by-piece basis.

“What we call the beginning is often the end. And to make an end is to make a beginning. The end is

where we start from.”

-T.S. Eliot

Ashley GarrettThesis 2012

Origami: A Generative Design Process

1. A Short History of Origami

Origami is, first and foremost, an art form, an expression of creativity, and it

is the nature of creativity that it cannot be taught directly.

- Robert J. Lang

Origami, from the Japanese words ori meaning “folding”, and kami

meaning “paper”, is simply defined as the art and process of just that—

paper folding. Though historically associated with Japan, it is actually an art

of mixed origins. In Japan, the earliest record of what might be attributed

to origami is noshi, a ceremonial wrapper folded around a strip of dried

abalone meat and exchanged among samurai for good luck. In the West,

baptismal certificates were popularly folded into “double blintzes” as early

as the 17th century. However, the style of these two types of origami was

considerably different. European models typically used square sheets with

few to no cuts, with folds based on a square or diagonal grid. Japanese

origami, on the other hand, was often made with different sized sheets and

cuts, complicated angles, and was often painted. This suggests that origami

may have evolved independently in both regions and is not a true “Japanese

art”. Regardless, the influx of European educational models in Japan during

the 1860’s and 70’s soon merged European styles with Japan’s existing

traditions to become what we currently recognize as origami. Japanese noshi

Double blintz (circa 1741)

Though old in origin, it wasn’t until the twentieth century that origami

really began its evolution to a modern form. There are only two types of

origami folds—the mountain fold and the valley fold—but until the 1950’s,

there was no clear system of depicting these in a model diagram. The first

origami book, “Hiden Senbazuru Orikata” (“Secret to Folding One-Thousand

Cranes”) was published in 1797, but showed only the result of the folding

processes with very unclear diagrams. As such, there was little way to

determine how each model was created. Japanese origami master Akira

Yoshizawa is credited with creating the first modern system of diagramming

origami in 1954 with his first published monograph, “Atarashi Origami

Geijutsu” (“New Origami Art”). He employed two varieties of dotted lines

to represent mountain and valley folds, as well as a few symbols to indicate

more complex actions of folding. Two early Western origami authors, Samuel

Randlett and Robert Harbin, added a few additional symbols and adopted

it as the standard in origami diagramming. Now known as the Yoshizawa—

Randlett system, it is the most generally used system today.

At the time of its adoption, there were so few origami models in

existence that they could have been catalogued on a single sheet of paper.

Few had more than twenty steps and most could be folded in a few minutes

by even a novice. However, that changed dramatically once it became

easier to record and share models on an international level. The past fifty

years have been a renaissance in the world of origami with huge leaps in

complexity. Thousands of models have been published in books, journals,

and archives. Some now consist of hundreds of steps that would take an

advanced folder many hours to produce. Most importantly, origami is now

gaining attention from fields outside of the realm of art.

Pages from Hiden Senbazuru Orikata

2. Precedent Studies

There seems to be no limit on the range of artistic expression possible within

origami. But there are absolute limits on the physical structures foldable with

origami. Those limits are defined by the underlying mathematics of origami.

By exploring, elucidating, and describing those mathematical laws, modern

origami artists have found ways to push the art to undreamed-of heights,

and to begin to develop computational tools that augment the capabilities

of the human artist in order to more fully realize their artistic visions.

- Robert J. Lang

For hundreds of years, origami has been designed by “feel”. Design

is now evolving to be more systematic—no longer just about aesthetics,

origami has made strides in math, physics, and engineering. It has been

used in the design of compact car airbags, collapsible heart stents, panel

cores for aircraft fuselages, shock absorbing devices, and collapsible space

telescopes, just to name a few. The potential applications of origami are

nearly limitless, and architecture is no exception.

Heart stent prototypeGreen Waterfall

by Erik and Martin Demaine

Beginning research into current applications of origami in the field

yields several conclusions. The first is that while origami has influenced

numerous commercial and residential designs, it is often used in a primarily

visual manner. Folding becomes the signature mark of the design, but does

not lend to it much more than an aesthetic component—the act of folding

is unseen. One such example is the Klein Bottle house designed by Rob

McBride and Debbie Lyn Ryan. Its experimental geometry, developed by

topological mathematicians, creates visually exciting multi-faceted surfaces

with opportunities for new spatial relationships. The influence of origami is

apparent; however, on a functional level it does little more than lend it a means

for theoretical design expression. Design by folding still directly influences

the end result, but fails to take full advantage of origami’s potential.

A second approach to origami architecture takes advantage of

origami’s modularity. Some origami models, such as those of complex

polyhedrons, use simple modules to assemble more complex arrangements.

Kepler’s Star, for example, is assembled from eight pyramidal units—half as

joining units and half as slot units. The result is a structural figure that is

more efficient than its equivalent folded from a single sheet. Architectural

applications can be approached the manner. Laboratory for Visionary

Architecture [LAVA] created an origami window installation for La Rinascente

in Milan using 3500 recycled and recyclable cardboard molecules of two

different shapes. The assumption made was that the intelligence of the whole

is dictated by that of the smallest elements of design. Origami provided a

way to create these modules simply, efficiently, and of a lightweight material.

Though it remains a primarily sculptural installation, it does begin to explore

a potential strength of origami.

Klein Bottle House

Digital Origami Installation

A third category can be derived by grouping those that use the

structural functionality of origami as a starting point. San Francisco-based

IwamotoScott Architecture has produced two installation-type designs that

explore different aspects of this approach. The first, Voussoir Cloud, was

designed for the California Institute of Architecture gallery, Los Angeles. The

installation combines a structural system of pure compression with an ultra-

light material system of thin wood laminate. Like the previous example, the

overall structure is made of individual units that work together to form the

whole. Each “petal” unit is formed by folding the laminate along curved

seams, resulting in a form that relies on an intrinsic internal surface tension

to hold its shape.

Their second project utilizes this structural nature of origami in a

different manner. IN-OUT Curtain was designed as a prototype combining

modular origami and digital production, resulting in a flexible, user responsive

operable screen. Pieces are folded to create volumes that can change shape

both individually and in concert with one another. The material resistance

results in modules that can hold two distinct shapes—concave and convex—

relying on internal tension and elasticity to both hold them in shape and allow

for switching back and forth. This example of an operable surface structure

begins to truly explore the potential of origami on a transformative level.

Voussoir Cloud IN-OUT Curtain units

The last approach—and the most relevant—is also the least

developed, remaining on a purely conceptual level Tomohiro Tachi has

a special interest in a type of origami dubbed “rigid origami”, in which

flat rigid sheets are connected through a hinging mechanism to create

large, structural designs that often remain flat foldable. Tachi designed a

hypothetical structure to connect two existing buildings. When deployed,

it acts as a gallery space; when not in use, it can be neatly flat-folded onto

the façade of one of the buildings. Its rigid-foldable quadrilateral mesh

is designed so as to connect along a predetermined path without risk of

deviation. In this exploration, origami begins to stand for itself as a structural

space maker of both efficiency and beauty, limited not by its lightweight

materiality, but by the objectives of the designer.

Gallery deployment

IN-OUT Curtain

3. Crane Studies

Folding by hand is as low-tech as any making activity can be. You are making

something directly with your body (your hands) without the intervention of

a third-party tool such as a pencil, mouse or needle. It is an almost unique

making experience and perhaps unfamiliarly primal.

- Paul Jackson

Before I could truly learn from these precedents and begin to

think as an architectural designer, I had to first understand the techniques I

was working with. As with any other art or skill, comprehension of origami

begins at its most basic level. All models generate from two types of folds—

mountain and valley. Various combinations thereof can create reverse folds,

inside reverse folds, rabbit-ear folds, squash folds, swivel folds, petal folds,

sink folds, pleats and crimps. Realistically however, the step-by-step nature

of modern origami diagrams eliminates the need for a casual folder to know

anything beyond how to follow instructions. For a designer, though, the

strengths and weaknesses of each fold become vital in understanding the

art.

Traditional origami models became the starting point of my

exploration. The most popular model is without a doubt the Japanese paper

crane, with many children learning to fold one at some point in their lives. It

is a model of relatively few steps and low difficulty, yet it has persisted for

quite some time as the unofficial mascot of origami.

In Japanese legend, the crane is known as the tancho and said to

live for a thousand years. Also referred to as “Honorable Lord Crane” and

“the bird of happiness”, the crane is frequently used to represent long life,

prosperity, and good health. This symbolism carries over to origami most

clearly in the tradition of Senbazuru—thousand origami cranes. An ancient

Japanese legend promises that anyone who folds a thousand paper cranes

will be granted a wish by a crane, such as long life, recovery from illness,

or luck. The cranes would be folded and strung together on strings joined

to hang from a single point—hanging them in the home is thought to be a

powerfully benevolent charm.

The practice gained popularity in modern times through the story

of Sadako Sasaki. Sadako was only two years old when the atomic bomb

dropped a mile from her home in Hiroshima. She survived the initial

explosion, but at age twelve was diagnosed with leukemia and given only a

year to live. Her best friend came to visit her in the hospital and folded for

her a single paper crane out of golden paper in reference to the Japanese

legend. Sadako soon set out to fold one thousand paper cranes before her

death so as to wish for her recovery, using any paper she could find around

the hospital. Unfortunately, on October 25, 1955, Sadako Sasaki passed

away after only completing 644 cranes. Her friends and classmates folded

the remaining cranes and buried them with her, continuing to honor her after

her death by raising funds for a memorial to her and all children that had

died as a result of the atom bomb. In 1958, a statue of Sadako holding a

golden crane was unveiled as part of the Children’s Peace Monument in

Hiroshima Peace Park.

Sadako’s statue at the Children’s Peace Monument

Groups of senbazuru

I set out to fold one thousand cranes. There were two main intentions

behind the project. The first was to begin my approach to origami in a

modular sense. Typical origami models are small enough to be held in the

hand, but the same model repeated to an extreme soon becomes an entirely

different organism. The idea was to manipulate space using this theory. Each

crane could be appreciated on its own as a single entity, but it would be the

amalgamantion of all thousand together that would connect the idea of the

unit to the whole. The second intention was to commit the mechanisms and

actions of origami to a nearly subconscious level—understanding through

repetition. The act of folding became a study in itself, forcing a change of

focus from result to an awareness of the process. To think like a folder is

far different from simply following a diagram, and folding each crane soon

become an almost instinctual response separate from conscious thought.

While the process of folding each paper crane was simple enough,

it was painstaking and time intensive. I chose to work with 5 7/8” square

sheets of origami paper manufactured by Suisai Origami. Each sheet has

a “dyed” pattern effect along the red to yellow color spectrum, and was

folded inside-out into each crane. This was to create a more subtle color

transition along thered to yellow color spectrum, and was folded inside-out

into each crane. This was to create a more subtle color transition along the

installation, and also to introduce light variation. Each crane remains a pale

pastel when lit normally, but when backlit, glows with the color intensity of its

interior. In the beginning, each crane took approximately five to six minutes

to fold completely—by the end, that time was halved.

Assembling the cranes into an installation brought new challenges.

In Japan, senbazuru are typically assembled 20 to 40 per strand and then

gathered into a bunch. This creates an object—but does not accomplish

anything spatially. My goal was to use the “flock” of cranes to manipulate

space by creating a fluid overhead plane. This would require each crane to

be strung and hung individually, an extremely tedious task. To accomplish

this, ten lightweight squares of fiberglass screen and wooden frames

were created, in reference to the square sheets that each origami model

inevitably starts as. These were hung at various heights and angles to

create a spiraling, descending motion. Each crane was then threaded onto

a length of fishing line with a knot at its base. The other end of the line was

then looped through the screen and secured with silver crimp bead. One

thousand knots, crimps, and adjustments later, it was complete.

A Japanese-style paper lantern serves as a

focal point at the center of the cranes. The

flock circle around it, as if it were the sun.

4. Pleating

Folding, or pleating, allows new spaces and territories to emerge without

losing the native characteristics of what is being folded. It is already well

understood that an architectural aspiration for the fold lies in its potential for

manifesting cohesion and a continuity of competing spatial, cultural, social,

programmatic, and contextual conditions within a single language.

- Lisa Iwamoto

The next step in my research was to begin folding origami in a

fashion that was more directly translatable to architecture. Without a fixed

result in mind, I began to explore different types of folding in relation to

materiality and scale, beginning with a focus on pleated origami. A pleat in

origami is the same as pleating in fabric; the material is simply doubled back

upon itself. While there are four main types of origami pleats—accordion,

knife, box, and incremental—I chose to focus primarily on the knife pleat.

In the simplest type of pleating, accordion pleating, the fold progression is

an evenly spaced mountain-valley-mountain-valley and so on. The result is

much the same as a folded paper fan. Knife pleating, on the other hand, has

different spacing between mountain-valley pairings than valley-mountain.

The result is a surface with directionality, where the pleats appear to creating

a pile that moves in one direction or another.quite some time as the unofficial

mascot of origami.

Accordian pleating

Knife pleating

An interesting phenomenon occurs when knife pleating is used

in two directions simultaneously, for example, pleats that are alternated

between the bottom edge and the left edge of the paper. The intersection of

the pleats will create a ridge that travels upward diagonally from the bottom

left corner. This ridge both locks the pleats in place and begins to sculpt

the paper three-dimensionally, forcing curvature through the interaction of

various pleat layers. The result is a wide variety of shapes that emerge from

identical crease patterns; final form is dictated by the order the pleats are

folded.

I initially started with one foot square sheets of 50 lb art paper,

folding relatively simple pleat orders in order to begin to understand the

results. It was design by exploration—there is a certain feeling that the

paper is dictating its own shape, rather than being told by the folder what it

is to be. Intuition and an understanding of material behavior were the only

reliable indicators of shape. As I moved up in size from one foot to two

foot squares, I began introducing other materials, finding that the degree of

curvature was dictated by the thickness of the surface and material memory.

A model made from 98 lb paper had more dramatic curvature and a higher

degree of stiffness than those created with 50 lb paper. The same extreme

curvature was seen in a model made from metalized film; this was enhanced

further by a low degree of material memory that caused all folds to remain

slightly open. Curvature could be further enhanced and controlled by pulling

selected folds apart, essentially sculpting the piece through deconstruction.

The biggest drawback of pleating became apparent when I moved

up to a four foot square. Folding became difficult; I needed to sit on top

of the paper in order to fold it. The 50 lb paper also proved too thin at that

size, leading to tears and a lack of rigidity. More critical, however, was that

pleating had caused a reduction in size by one half. Some size could be

regained by pulling folds apart, but only minimally, and with a reduction of

structural integrity. This type of pleating was not only materially inefficient, but

also made any further increase in size implausible. Though the remarkably

organic shapes and complex textures that pleating can produce have an

appealing quality, it is unlikely to be well-suited for architectural applications.

New curvatures are introduced as pleats are deconstructed, adding structure to the flexible material.

This material has a different kind of material memory than paper. Pleats tend to stay partially open, but creases remain sharp.

5. Rigid Origami

Paperfolds are manipulable: bendable, flexile, versatile and retractable.

Some are able to deploy themselves, expanding and contracting. Some

achieve a number of equilibrium states upon a plane, balancing in different

positions. Some retrieve several shapes, adjusting to their context. The

versatile and polymorphic nature of paperfolds increases their potential to

generate design prototypes.

- Sophia Vyzoviti

I soon moved from pleated origami to the mathematically-oriented

rigid origami. Best summarized by Tomohiro Tachi,

“Rigid-foldable origami (or rigid origami) is a piecewise linear

origami that is continuously transformable along its folds without

deformation by bending or folding of any facet. Therefore, rigid

origami can realize a deployment mechanism using stiff panels and

hinges, which has advantages for various engineering purposes,

especially for designs of kinetic architecture.”

Because of the necessary precision required, technology also became

key. I began utilizing a laser cutter to precisely inscribe patterns onto paper

with just enough power to produce a slight score mark. The goal was to

understand the type of folding mechanisms that rigid origami presented

so as to be able to manipulate and design my own. As a result, I initially

designed models in AutoCAD by referencing existing patterns.

My initial studies led to several conclusions. The first was that

as opposed to traditional origami model making, rigid origami produced

models that had the added element of “play”. Rather than just being a static

sculpture, these pieces had numerous forms and configurations that they

could exist in. Some were stable, some not—most could be bent, twisted,

gathered, stretched, and compressed. One side was often drastically

different than the other. Most importantly, they could be manipulated almost

infinitely; the only limit was material failure. The heavy weight drawing

paper that I primarily worked with had a good degree of durability and tore

infrequently. However, as I explored other materials, including those with a

more plastic nature, material failure became more common. Whereas paper

seemed to have a degree of flexibility, in plastics the joints between creases

would often become holes or sever completely. This made achieving true

transparency with a single material quite difficult.

Ron Resch pattern

I also found that certain models held an inherent shape when

folded. Though each pattern was primarily a simple repeated geometry,

some folding patterns always resulted in curvature of the overall piece. The

waterbomb pattern is a good example of this. The pattern itself consists of

only vertical, horizontal, and 45 degree folds. However, once folded, the

entire piece begins to curve around itself to form a cylindrical shape. It

can still be manipulated by hand into a flat plane, but its only stable state

is in curvature. This quality becomes especially relevant in designing any

origami-based structure at a larger scale, where maximizing stability requires

understanding innate structural behavior.

The most interesting quality that emerged was that of flat-foldability—

simply stated, the pattern will collapse completely to a two-dimensional

plane. To accomplish this mathematically, it must follow Kawasaki’s

Theorem for Flat-Foldability. It states that in order for a crease pattern to be

flat-foldable, the alternating sum and difference of its angles around a vertex

must add to zero. Equivalently, the sum of alternate angles must total 180

degrees. This quality is only involved in a few of the basic rigid folds—for

example, the miura ori, waterbomb, and yoshimura patterns. In larger scale,

flat foldable patterns have the advantage of being more easily transportable

and storable; Tomohiro Tachi’s theoretical art gallery could collapse flat on

a building façade. These types of folds also have the greatest range of

motion, but tend to stay stable in a halfway state, midway between each

extreme. This gives these models more dimension than a non- flat foldable

model, which is more open in its stable state.

Stable waterbomb pattern

Ron Resch 90º pattern

Tomohiro Tachi, aside from designing uses for rigid origami

structures, also designed software that allows users to interact with origami

forms while altering the crease pattern of the model, titled Freeform Origami.

The software can maintain multiple parameters, including developability, flat-

foldability, planarity of facets, point coordinate coincidence, and paper size.

Models can be exported as a 3D wireframe model or as a crease pattern in

a .dxf format for further editing in programs such as AutoCAD. This makes

the software incredibly useful to a designer interested in origami structures.

I used Freeform Origami to begin to modify select flat-foldable

patterns into new designs, focusing first on small changes and increasing

manipulations to push patterns into chaos. This was the first step to

beginning to truly design through origami. I studied how much deformation

could occur before losing integrity, how changes to crease patterns affected

the various folded states of a model, and how to control these modifications

to produce a desired result. These folding pattern studies became the

foundational tools for the eventual creation of full-sized installations.

Original miura-ori, waterbomb,and

yoshimura patterns.

Freeform Origami program Modified miura ori Modified waterbomb

Modified waterbomb, leftYoshimura, right

Modified waterbomb, leftYoshimura, right

Modified waterbomb, leftWaterbomb, right

6. Dance

Much of the beauty that arises in art comes from the struggle an artist

wages with his limited medium.

- Henri Matisse

Rigid origami studies had provided the building blocks, but not a

framework to guide their usage. I had a site for an installation—the office

of the School of Architecture and Community Design—but the near infinite

combinations and scale potentials proved daunting. As I had since the

beginning, I turned to Henri Matisse’s quote for inspiration and decided to

look further into Matisse as an artist.

La Gerbe, 1953

Born in 1869, Henri Matisse was a French artist best known for

his expressive use of bold color and form. A draftsman, printmaker, and

sculptor, he is most widely recognized for his paintings and his work with

paper cut-outs. It was Henri Matisse’s approach to design that makes him

an exceptional source of inspiration across all fields of art, including origami.

As John Hallmark Neff explains,

“He always insisted that Nature was the source of his art, stressed

the importance of working from Nature, and studied it in order

to “possess” and make it his own: to identify with his subject so

completely that he was free in his knowledge to improvise, to distort

its appearance without losing its fundamental character, its “rhythm”

or “timbre”. Matisse continually refined his technical skills to enable

himself to create his images with a minimum of conscious control—

the better to intuit its essence or “sign”. That visual symbol which

was the simplest, most evocative record of its character. Only by

going far beyond the specific details of visual appearance could it

evoke his subject in its entirety, through all the senses: touch, taste,

smell, even sound.”

Dance, a painting completed in 1910 for Russian businessman

Sergei Shchukin, is widely regarding as a key point in Matisse’s career and

development. It is bold, rhythmical, beautiful, and savage—its saturated

color palette outlines five dancers in perpetual motion, simultaneously

depicted as both hopelessly crude and utterly refined. The simplicity of it

contrasts with the primal intensity of its portrayal of hedonistic rituals and

Hellenic grace.

Blue Nude, 1906

La Gerbe, 1907

Dance (8.5 ft x 12.8 ft), completed in 1910.Painted with a companion piece, Music, for the Russian businessman and art collector Sergei Shchukin. Until the October Revolution of 1917, they hung together on the staircase of Shchukin’s Moscow mansion. Today they reside in the Hermitage Museum in St. Petersburg, Russia.

I turned to this painting as my framework for design. I hoped to

understand it in the same way that Matisse had painted it, on an evocative

level beyond just visual shapes and colors. I wanted to capture its

fundamental character, its essence. I endeavored to dissect it into base

energies, to capture the spirit of each dancer individually and in the act

of dancing itself. I produced three studies analyzing shape, energy, and

movement, attempting to recall the third dimension from a painter who had

willfully compressed it down to two.

I pulled from these studies fundamental ideas of shape, movement,

and energy. It became important that my intervention should touch the

ground lightly but definitively, just as his dancers seemed to. There was

an enveloping quality and level of intensity that needed to translate into the

choice of my origami folds. There was also the issue of color; the palette

choice made by Matisse is as inseparable from the spirit of the painting as

the subjects themselves, and my use of color and light needed to also be

intrinsic to the overall spirit of the installation. I needed to translate the soul

of the Dance.

7. Installation

Folding as a generative process in architectural design is essentially

experimental: agnostic, non-linear, and bottoms up.

- Sophia Vyzoviti

The origami installation grew from many differing sources of

inspiration, brought together by ideas from Matisse’s Dance into one unified

design. Once I had established the qualities I intended to portray, it became

only a matter of production. Each piece was to be based on a different

crease pattern that would be abstracted into a representational model. I

used a combination of Tomohiro Tachi’s program Freeform Origami and

AutoCAD to design new patterns that would fall into the category of rigid

origami and maintain Kawasaki’s Theorem for flat-foldability. The reasoning

for this was two-fold: to take full advantage of the positional possibilities of

each structure, and to maximize potential developability on an architectural

scale, where transportation and assembly become critical to efficiency.

Due to the size of each planned piece, it quickly became obvious

that no commercially available paper-like material would be sufficient. The

tendency of folded models to reduce in size by up to one-half meant that

when flat, most patterns would be over twenty feet in length. The alternative

was to join much smaller sheets of paper together to form to correct size

sheet. I chose to use 18” by 24” 80-lb Strathmore Drawing paper. The sheet

size would fit into the laser cutter bed to accurately score designs, the weight

of the paper was sufficiently strong, and the cream color would allow lighting

to provide the greatest effect. Each sheet would be scored, numbered, pre-

folded, and then joined along its edges with transparent tape.

Design 1: Yoshimura

The first piece to be constructed would form an archway across the

right side of the room, partitioning it off by creating an overhead threshold.

The choice of pattern origin was simple for this piece—the Yoshimura crease

pattern naturally forms a structural arc. The inflection of the curve can be

controlled by changing the angles of the diamonds within the pattern; a

sharper angle creates a flatter area in the bend, whereas an obtuse angle

will create a sharper curve. By modifying the vertices of the crease pattern,

I was able to create a model that when folded would precisely span the

eight foot space while remaining structurally stable. Drawing inspiration

from Dance, the crease pattern transforms from symmetrical diamonds,

modulates in waves across the middle of the span, and finally ends in

disorder. The overall pattern was laser-scored onto 22 sheets with total

unfolded dimensions of 16’2” by 4’.

As the first prototype, problems were bound to emerge. When

initially assembled the arch remained structural and stood without

assistance, however, it was susceptible to lateral forces. To counteract this,

the model was hooked to the ceiling by a single point. This soon proved to

be the simplest issue to solve; within a few days, the tape had failed and the

structure had fallen down and torn apart at its seams. It was reassembled

by reinforcing the joints between each panel with heavy duty packaging tape

and securing each end in place with pins. It was clearly necessary to use a

combination of transparent tape and packing tape on further models.

Design 2: Miura-Ori

The second piece was the largest endeavor of the installation. The

intention was to create a model that could gather at one point to gently

touch the ground, while also growing upwards and sweeping out in rotation

to become an overhead plane. This required a great deal of flexibility in the

design. Because of this, I chose to base it on the miura-ori fold. Invented

in 1995 by Japanese astrophysicist Koryo Miura, the fold was originally

designed for large solar panel arrays on space satellites. The crease pattern

mirrors a series of rhombuses to create a simple but efficient collapsible

model that can be twisted with ease.

The design allows the crease pattern to shrink and grow according

to density needs. Areas of density tend to have more stability, and so key

areas were “pinched” to form smaller quadrilaterals. The overall effect is one

of growing and stretching with a decidedly horizontal flow. The flexibility of

the pattern allowed more alteration post-assembly; in exchange, this model

required more points of support in order to maintain its shape. The overall

pattern required 46 sheets and measured 12 ‘by 20’ in a flat state.

Design 3: Waterbomb The final iteration came in the form of a waterbomb, but only after

two separate attempts. The waterbomb pattern has a fairly unique quality

of being entirely different from one side to the other—the side typically on

the exterior features offset quadrilateral depressions, while the opposite side

spikes outwards in a layout that seems to weave around itself. Because of

this fact, I initially planned to use it to create a folded division between the

waiting area of the office and the hallway that would be visible on both sides.

Alternating triangles of material would be removed from the model to allow a

variation of visibility where needed. However, the model began to fail soon

after assembly due to a number of different problems. Though viable in

theory, the strength of the paper did not readily support removal of material

without deformation. Due to difficulty in assemblage, collapse of the model

into a flat-folded occurred after joining panels rather than simultaneously.

This created a series of tears along heavily used seams. After transporting

it to location and attempting to unfold it, it was deemed too damaged to be

successful.

Returning to the design phase allowed me to reexamine the

strengths of the waterbomb fold. While there is interest in its dual-natured

sides, the structural strength in the pattern is more apparent in its natural

state of circular curvature. This makes it more suitable for a cylindrical shape

over a flattened one. The decision was made to relocate the installation

and to redesign it as a column. To contrast with the more heavily modified

crease patterns of the other installations as well as to fully take advantage

of its shape behavior, I chose to leave the pattern relatively unchanged. The

result was a twisting column of 17 sheets, 11’2” by 3’11” in its flattened state.

Failed waterbomb pattern

8. Final Impression

If there is a single effect produced in the architecture of folding, it will be the

ability to integrate unrelated elements within a new continuous mixture.

- Greg Lynn

The final installation features the original one thousand

cranes, three unique large-scale rigid folds, and a number of enlarged

macro photographs of origami studies. These abstractions create a

flattened backdrop of three-dimensional imagery, collapsing the volumes of

the room back to the flat state of the paper they originated from. The soft

warm colors of the cranes are amplified in the illumination of the rigid origami

structures; red, orange, and yellow spotlights blend to create dramatic lights

and shadows on an otherwise neutral surface. The overall strength of the

installation stems from this union of elements into an overall impression of

place.

9. Conclusions

All designers fold. That is, all designers crease, pleat, bend hem, gather,

knot, hinge, corrugate, drape, twist, furl, crumple, collapse, wrinkle, facet,

curve or wrap two-dimensional sheets of material, and by these processes

of folding, create three-dimensional objects. These objects will perhaps not

be origami-like in appearance, or the folding may only be a detail, but most

will nevertheless have been folded—wholly or in part—in some way. Since

almost all objects are made from sheet materials (such as fabric, plastic,

sheet metal or cardboard), or are fabricated from components used to make

sheet forms (such as bricks—a brick wall is a sheet form), folding can be

considered one of the most common of all design techniques.

- Paul Jackson

However spatially pleasing an installation such as this might be, there

is admittedly still a gap between folded paper and real-world application. I

argue that it is not a very large one. As seen in precedent studies, architects

are recognizing the potential in origami-like structures; in reality, the action

of folding has always played a role. Folded plate structures, thin-shell

concrete, and wrapped volumes all share elements of folding—their three

dimensional forms are developed from two-dimensional templates. Folding

as a generative design tool is also making strides in digital processes,

bridging the gap between an old craft-based art and modern technology.

US Air Force Academy Cadet Chapel - Walter Netsch

Yokohama Ferry Terminal - Foreign Office Architects

Valencia Oceanographique - Felix Candela

As said by Lisa Iwamoto,

“When folds are introduced into otherwise planar materials, those

materials gain stiffness and rigidity, can span distance, and can often

be self-supporting. Folding is materially economical, visually

appealing, and effective at multiple scales. It is not surprising that

architects have expanded its use in the digital age.”

In the realm of rigid origami, developability is being pushed from

two-dimensional states into the reality of material thickness. Rigid origami

is truly the motion of mechanisms, regardless of the nature of the hinge.

As paper structures, material intersections are rarely an issue; in actuality

however, unplanned intersections can cause the design of rigid origami to

fail. This has already been addressed in a number of ways, including axis-

shift—locating hinges on edges of axes rather than center line—and the

trimming and tapering of bisecting planes. As Tomohiro Tachi states, “we

need structures composed of thick panels or composite three-dimensional

structures that have finite (nonzero) volume in order to cope with gravity,

bear loads, and to insulate heat, radiation, sound, etc”.

From an engineering standpoint, origami has multiple applications

that can be simplified into three categories. Deployable structures, such as

solar sails, heart stents, and emergency shelters, take their inspiration from

the folding mechanisms themselves. Things like lightweight panel-cores

and folded plate roofs take advantage of stiffness at a minimum expense

of weight. Shock absorbing devices, like car crash boxes and packaging

materials combine these elements—structure and collapsibility are used

conjunctively.

Tachi’s rigid origami hinge studies

I believe that recognizing the validity of origami as a creative tool will

encourage a different way of viewing design—as a generative process, as

a mathematical resolution, as an object of flexibility and change. Origami

bridges the worlds of precision and intuition, discovery and failure. It makes

material choice intrinsic to results rather than a subsequent decision.

Material fluctuations, limitations, and constraints become part of the art

itself. Most importantly, origami becomes the event—an infinite series of

variability containing neither answers nor limits, defined in nature only by the

imaginative limits of the designer.

Ming Tang’s temporary shelters

10. Works CitedBuri, Hani and Yves Weinand. “Origami: Folded Plate Structures, Architecture”. 10th

World Conference on Timber Engineering. 2008, Miyazaki, Japan. n.p.

Print.

Chen, Yan and Kunfeng Wang. “Folding a Patterned Cylinder by Rigid Origami”.

Origami5: Fifth International Meeting of Origami Science, Mathematics,

and Education. Eds. Patsy Wang-Iverson, Robert J. Lang, Mark Yim.

Boca Raton: A K Peters/CRC Press, 2011. 265-276. Print.

Cowart, Jack, et al. Henri Matisse: Paper Cut-Outs. St. Louis: St. Louis Art

Museum, 1977. Print.

Gangal, Sanjay. “Digital Origami by LAVA”. AECCafé Blogs. AEC Café, 27

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Hatori, Koshiro. “History of Origami in the East and the West before Interfusion”.

Origami5:Fifth International Meeting of Origami Science, Mathematics,

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Yim. Boca Raton: A K Peters/CRC Press, 2011. 3-11. Print.

IwamotoScott Architecture. Office vs Office, 2012. Web. 19 Apr. 2012.

Iwamoto, Lisa. Digital Fabrications: Architectural and Material Techniques.

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Jackson, Paul. Folding Techniques for Designers: From Sheet to Form.

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Jones, Jonathon. “Why this is the Most Beautiful Modern Painting in the World”.

The Guardian. The Guardian News, 19 Jan. 2008. Web. 4 Apr. 2012.

Kasahara, Kunihiko. Origami Omnibus: Paper Folding for Everybody. Tokyo: Japan

Publications Inc., 1988. Print.

Lang, Robert J. “Front Matter”. Origami4: Fourth International Meeting of

Origami Science, Mathematics, and Education. Ed. Robert J. Lang. Boca

Raton: A K Peters/CRC Press, 2009. i-xi. Print.

Lang, Robert J. “Front Matter”. Origami4: Fourth International Meeting of Origami

Science, Mathematics, and Education. Ed. Robert J. Lang. Boca Raton: A K Peters/

CRC Press, 2009. i-xi. Print.

Lang, Robert J. Origami Design Secrets: Mathematical Methods for an Ancient Art.

Natick: A K Peters Ltd., 2003. Print.

Schenk, Mark and Simon D. Guest. “Origami Folding: A Structural

Engineering Approach”. Origami5: Fifth International Meeting of

Origami Science, Mathematics, and Education. Eds. Patsy Wang-

Iverson, Robert J. Lang, Mark Yim. Boca Raton: A K Peters/CRC

Press, 2011. 293-305. Print.

“Studying the Crane”. Arts of Asia in Reach. Oberlin College & Conservatory, n.d.

Web. 20 Apr. 2012.

Tachi, Tomohiro. “Designing One-DOF Mechanisms for Architecture by

Rationalizing Curved Folding”. Proceedings of the International

Symposium on Algorithmic Design for Architecture and

Urban Design. 14-16 Mar. 2011, Tokyo. ALGODE TOKYO: 2011. Print.

Tachi, Tomohiro. “Simulation of Rigid Origami”. Origami4: Fourth International

Meeting of Origami Science, Mathematics, and

Education. Ed. Robert J. Lang. Boca Raton: A K Peters/CRC Press, 2009. 175-

187. Print.

Tachi, Tomohiro. “Rigid-Foldable Thick Origami”. Origami5: Fifth International

Meeting of Origami Science, Mathematics, and Education. Eds. Patsy

Wang-Iverson, Robert J. Lang, Mark Yim. Boca Raton: A K Peters/CRC

Press, 2011. 253-263. Print.

Vyzoviti, Sophia. Folding Architecture: Spatial, Structural and Organizational

Diagrams. Amsterdam: BIS Publishers, 2003. Print.

Vyzoviti, Sophia. Supersurfaces: Folding as a Method of Generating Forms for

Architecture, Products and Fashion. Amsterdam: BIS Publishers, 2006.

Print.

Special thanks toDavid Hendryx, Jackie Faulk, and everyone

else who facilitated my insanity.