Peel Masters Research Book 042011 by Jacob Peel

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MASTERS RESEARCH PROJECT

ACTUATING GEOMETRIC PRIMITIVES

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Term:

Spring 2011

Principal Investigator:

Jacob Peel

Committee:

1st

Bradley Walters

2nd

Mark McGlothlin

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CONTENTS

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ABSTRACT

INTRODUCTION

INTERACTIVE SYSTEMS

1.1

OVERVIEW

3.1

KINETIC ARCHITECTURE

1.2

PLATO’S TIMEAUS

3.2

RESPONSIVE ARCHITECTURE

1.3

TOY

3.3

REACTIVE AND INTERACTIVE

PRECEDENTS

3.4

ROBOTIC ECOLOGY

2.1

3.5

TASK DISTRIBUTION

2010

3.6

USER INPUT

2.2

LIVING GLASS // The Living // 2006

CONSTRUCTION OF

2.3

WHOWHATWHENAIR // Philip Block, Axel

TRANFORMABLE GEOMETRIC SYSTEMS

Killian, Peter Schmitt and John Snavely // 2006

4.1

GEOMETRIC PRIMITIVES

2.4

4.2

REGULAR POLYHEDRONS

bv // 2003

4.3

SCHLAFLI SYMBOL

2.5

CHEMBOT // iRobot // 2009

4.4

BEHAVIOR OF GEOMETRIC SYSTEMS

2.6

HYPOSURFACE // Mark Goulthorpe // 2002

4.5

INITIAL STUDIES

2.7

DESERT HOUSE // Future Cities Lab // 2008

4.6

EUCLID’S ELEMENTS

2.8

XEROMAX // Future Cities Lab // 2010

4.7

MOTION TYPOLOGY

2.9

AURORA // Future Cities Lab // 2009

4.8

CASES OF CONTROL

2.10

EXPANDING DOME // Hoberman Associates

4.9

GEOMETRIC CONSTRUCTION

// 1997

4.10

CONFIGURATIONS OF

2.11

DEFENSIBLE DRESS // MY Studio // 2001

GEOMETRIC CONSTRUCTIONS

2.12

SELF-ASSEMBLY UNIT // Skylar Tibbits //

100

MODULUS MACHINES

2008

112

MACHINE CONFIGURATIONS

2.13

DECIBOT // Skylar Tibbits // 2009

144

REFERENCES

2.14

DIVERTIMENTO // ORAMBRA // 2005

HYLOZOIC GROUND // Philip Beesley //

MUSCLE NSA // ONL [Oosterhuis_Lénárd]

RESEARCH ON ADAPTABLE AND

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ABSTRACT

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Max Bill, 1949

The long held, but timidly executed, modernist mantra of â&#x20AC;&#x153;form follows functionâ&#x20AC;? has been more appropriately demonstrated outside of the discipline from which the precept originated. An understanding of form as a mechanical property of an object or space has been more certainly adopted by many engineering industries. However, with data increasingly being incorporated into the design process, architecture is recovering this objective in shaping the built environment. But is the data being used to its full potential? How might this data be extended to further inform form? In the 1970s, Nicholas Negroponte advanced the notion that, by coupling the industries of cybernetics and architecture, a novel building system could be developed that could optimize the performance of a space or form by becoming dynamically reconfigurable. This topic of

responsive architectural systems has been

included in the discourse of the discipline for nearly half a century following. There have been a number of proposals that have suggested the value offered by endowing a building with this faculty, but it has only been in recent years that a small collection of projects have actually been produced.

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In every work of art the basis of its composition is geometryâ&#x20AC;Ś Thus, just as mathematics provides us with a primary method of cognition, so too some of its basic elements will furnish us with the laws to appraise the interactions of separate objects, or groups of objects, one to another.

It has been suggested that this slow uptake is owing to a theoretical and practical deficit in architectural design, and that this has left dynamic structures and systems unsupported by architectural methodologies (Sterk, 2006). However, we are currently experiencing a shift in the industry that is beginning to prepare the foundation for this to be propelled.

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produced static forms, and this has limited the scope of data considered viable for inclusion. In most cases, the information at work in a project is limited to the most predictable or persistent -- even as this data may not necessarily be owing to the most critical forces and events. Outside of this defined range of input lay those transient forces and events that could be equally, if not more so, valuable to incorporate. However, to make use of this type of information might require immediate reactions. The suggestion is that the relationships being setup in the design approach between the forces, function and form be extended into physical construction through the use of actuated structures.

geometries and the dynamic coordination of motions by which responsive compositions would be allowed to emerge. The focus has remained trained on the development of a method of conception; a method by which the answers to more typical architectural issues might only need to be supplied at the latest stages of the design process -- perhaps not even by the designer but by the end-users. In this way, the design process might be left not only open-ended, but never-ending. Building on initial research at the scale of the singular unit, the current work investigates the possibilities of larger assemblages of responsive and interactive units.

This being the aim, the resonant question is how to set up an approach that is â&#x20AC;&#x153;minimal enough to index force yet maximal enough to allow emergent organization to arise?â&#x20AC;? (Reiser and Umemoto, 2006) To do this, I began by stripping away from the investigation notions that are more typical in architecture -- such as scale and materiality-- and ultimately was left with trying to understand the geometry necessary to allow for movement to occur and track the interaction within a structure. The objective of the research has been primarily concerned with interrelated configurations of

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INTRODUCTION

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To extend the notion above, the most important part of the creative process is the introduction of something new. It can be a new thing, a new idea or a new problem. It can also be a new experience, a new environment or a new outlook. What is important to the creative process is to discover and keep clear pathways in which the new and novel can easily flow. At its core and most transmissible, this

research has been about discovering and opening such pathways, and understanding how an architectural design process can benefit from the inclusion of the tools and ideas of other disciplines. There as been a trend in computer science and electrical engineering, rumored to have originated out of MIT, in which the contents and knowledge within those industries are being made public and accessible to any who wish to view it. With technology becoming more pervasive, a general inclination is being encouraged to understand and engage it. Communities are developing in which people build, test and share their endeavors and experiences in deploying this technology. This community is made up of people from various backgrounds, each applying this knowledge to their relative crafts. As a result, a veritable open field of possibilities is being realized, and a layer of information and intelligent is being installed.

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As the proverb proposes, “necessity is the mother of invention”. An appropriate twist on this original idea was rendered by the social philosopher Thorstein Veblen as “invention is the mother of necessity”. The latter was not put forward to displace the former. These statements do not run counter to one another. They are not mutually exclusive nor are they diachronically opposed. Instead, the assertions, as a set, illustrate a long standing and very essential dialog that has provided the most basic motor driving the creative process. Among the variety of creative endeavors, architectural design is involved with and depends on this process.

Given how the adoption and use of computation, and its peripheral technologies, has provided incredible benefits on varying industries and scales, it would seem reasonable to think

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it possible that it become more and more embedded into social and industrial processes as pathways are discovered that lead to more discreet applications. What benefits could be expected if this becomes incorporated into the built environment? In what way could it be applied, and to what end? There are many possibilities and examples of just such a development; however, this research has chosen to focus the above questions on the formal, and consequently spatial, attributes of Architecture. Even in the most simplified instances of building, form is recognized as a central factor in the design of a building. The form in which a project takes should come from an obedient analysis of a location and the forces acting on it. From this, the form of the project will dictate many subsequent design decisions. But what might be possible if the form is allowed to change dynamically and in response to changes in contextual forces?

1.1 OVERVIEW In the 1970s, Nicholas Negroponte advanced the notion that, by coupling the industries of cybernetics and architecture, a novel building system could be developed that could optimize the performance of a space or form by becoming dynamically reconfigurable. This topic of

responsive architectural systems has been included in the discourse of the discipline for nearly half a century following. There have been a number of proposals that have suggested the value offered by endowing a building with this faculty, but it has only been in recent years that a small collection of projects have actually been produced. It has been suggested that this slow uptake is owing to a theoretical and practical deficit in architectural design, and that this has left dynamic structures and systems unsupported by architectural methodologies (Sterk, 2006). However, we are currently experiencing a shift in the industry that is beginning to prepare the foundation for this to be propelled.

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immediate reactions. The suggestion is that the relationships being setup in the design approach between the forces, function and form be extended into physical construction through the use of actuated structures.

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With data is being integrated into the design process to inform a project, it has imparted on the process the ability to respond to a multiplicity of forces or events that act on a given location, and properly associate materials and compositions with these forces to allow for the potential to optimize the performance of the space. In this way, architecture is beginning to reaffirm its role in shaping the built environment by demonstrating the inextricable relationship between form and function. Yet, given the results of such an approach, the utilization of this information is tempered by having produced static forms, and this has limited the scope of data considered viable for inclusion. In most cases, the information at work in a project is limited to the most predictable or persistent -- even as this data may not necessarily be owing to the most critical forces and events. Outside of this defined range of input lay those transient forces and events that could be equally, if not more so, valuable to incorporate. However, to make use of this type of information might require

This being the aim, the resonant question is how to set up an approach that is â&#x20AC;&#x153;minimal enough to index force yet maximal enough to allow emergent organization to arise?â&#x20AC;? (Reiser and Umemoto, 2006) To do this, I began by stripping away from the investigation notions that are more typical in architecture -- such as scale and materiality-- and ultimately was left with trying to understand the geometry necessary to allow for movement to occur and track the interaction within a structure. The first half of the semester began by suggesting and developing a base unit that might be used to assemble a responsive structural system. The potential and limits encountered in this study provoked an investigation into the possibilities of propagating movement, and building and testing systems that might be capable of such dynamic interactions.

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Based on the understanding gained from these efforts, the latter half of the semester was used to employ a single method of conception that led to the development of a series of actuated base units. These units were then tested in larger assemblies according to different configurations to produce a catalog of effects. 1.2 PLATO’S TIMEAUS Before proceeding, the impetus of this research should be explained. It was Plato who provoked the initial line of thinking that eventually gave way to this research. In Timaeus, Plato explains the organization of the universe as following along a continued geometric pattern. “In finding the visible universe in a state not of rest but of inharmonious and disorderly motion, [God] reduced it to order from disorder.” In this way, an infinite geometric proportion was established which stretches out into infinity. Of this system, all corporeal things are a part, either individually or generically. Plato

explains that these sensible things come into existence being the result of disturbances within this pattern, and that these disturbances are owing to some cause. As an extension of the above idea, Plato relays the allegory of a Goldsmith who could be found molding and remolding gold into various geometric shapes. What this story was intended to point out is that “if anyone were to point to one of [these shapes] and ask what it was, it would be safest… to say that it was gold and not speak of the… figures as being real things.” The gold, in this case, was the Receptacle by which the Model, or Idea, within the head of that Goldsmith would be imprinted upon. The gold was the vehicle to render something intangible tangible. This material’s function is not unlike the proposed pattern. The pattern is imagined to be as malleable as that lump of gold. It is simply a substrate upon which all things are imprinted. With this, Plato goes on to argue that the elements that compose anything sensible

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It is not the intention of this research to advance Platonic ideals, nor strictly work within their bounds. This description of the sensible world is included here to provide the instigation behind initial thoughts about what potentials exists in formal manipulation, and

about what qualities could result if granted the capacity. This line of thinking lead to an idea that an object’s form should be thought of as a mechanical property rather than simple being an inconsequential result, a secondary interest or developed from an aesthetic proclivity.

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– fire, air, water and earth – should be understood as having a quality and that this quality is a function of these disturbances in or impressions upon the substrate pattern. Because the knowledge or language to describe accurately such a process did not exist at the inception of this text, Plato must rely on using a geometric analogy to describe the relationships and mechanisms in play. As such, he describes these component elements as being bound by planes and are constructed as regular geometric solids. He uses the equilateral triangle as the basic planar component in the constructions. With this description of the universe and its underlying logic, Plato is able to advance the idea of transmigration. He painted a vivid picture of the universe not as a static model, but as a sheet hosting turbulent events.

1.3 TOY The creation of something new is not accomplished by the intellect but by the play instinct acting from inner necessity. The creative mind plays with the objects...

Carl Jung

In the Spring 2010 semester, I was a student in Professor Hui Zou’s Phenomenology and Architecture seminar. Throughout this course, we would read a number of texts and essays that had been curated by the instructor, and discuss their contents during our meeting times. As a part of the course’s requirements, the students were asked to select one of the texts that had been read and discussed, and to use it to generate a project that synthesized

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the notions being proposed therein. Having gravitated toward Platoâ&#x20AC;&#x2122;s Timaeus, I had chosen it to guide the development of what ultimately resulted in a toy. In the text, Plato employs the metaphor described above to go into further detail on the concepts of Being, Becoming and how this Receptacle enables movement between these realms. He describes the world as being made up of random bits that can be constructed into something -- something we might be able to sense and interact with -- and can be dismantled into nothing. As mentioned, he employs a system of geometric proportioning to explain these things; the base unit of this system being the triangle. My final project for this seminar was an attempt to represent this idea. In a sense, the project developed into something similar to the House of Cards designed by Charles and Ray Eames, except instead of a uniformly sized set of interlocking rectangular plates, they were interlocking triangular plates of varying sizes. I set my first prototype out in the studio

with a sign that said â&#x20AC;&#x153;Please play with meâ&#x20AC;?. And so people did. It was interesting to see what they would make. Some constructions were very regular, rational and symmetrical. Others were very organic. The idea that this employed was that a single system of some sort could be deployed to allow for a multitude of constructions and configurations. By taking a small set of elements in which only a single feature varies from one to another, and designing them so that they can interlock, any basic shape or form can be created. We have seen this idea demonstrated with Legos and Erector sets. These toys provide a collection of different pieces that can be joined together to produce different constructions and configurations. However, what I became interested in was not necessarily to design a bunch of different pieces, but one component that could be linked with other like components to create a structure. I was interested in this component being able to assume different simple geometric proportions by itself, and as similar components come together, the

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construction would be able to take more and more sophisticated forms and postures. It is in this sense that I became interested in making a sort of Volumetric Pixel, and that differing forms would results not only from locating a module within different patterns, but also controlling the variables specific to the individual modules. Where the variables of a Graphic Pixel are Red, Green and Blue, the variables of a Volumetric Pixel would be Length, Width and Height. Just as the Graphic Pixel is used in an orchestrated array to provide the system by which any image can be rendered, the Volumetric Pixel could be organized in a structure and used to render any form. It was in this way that the line of thinking eventually lead to an investigation into kinetic architecture. However, it was the opinion that the movement being sought after be of some value, and in effect, should be associated with responsive and interactive systems

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PRECEDENTS

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Hylozoic Soil was an interactive environment that was first exhibited at the Montreal Museum of Fine Arts in 2007. The idea behind this installation was initiated by ongoing research into the relationship between the biological and artificial, and attempts to blur the boundary that separates them. The installation has moved through various iterations and manifestations. Most recently, the work was exhibited under the name Hylozoic Ground as a part of the Canadian Pavilion at the 2010 Venice Biennale. Occupants move within the structure as they would a dense thicket within a forest. Microprocessor controlled sensors embedded within the environment signal the presence of occupants, and motion ripples through the system in response. Dozens of microprocessors, each controlling a series of sensors and actuators, create emergent reactions akin to the composite motion of a crowd. Visitors move freely amidst hundreds of kinetic devices within this environment, tracked by many dozens of sensors organized in groups that exchange

signals in chains of reflexive responsive. The installation is designed as flexible, accretive kit of interlinking parts organized by basic geometries and connections. Variations are created by numerous individuals assembling the work. The result is a turbulent chorus of motion.

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2.1 HYLOZOIC GROUND // Philip Beesley // 2010

The structural core of Hylozoic Ground is a flexible meshwork assembled from small acrylic chevron-shaped tiles that clip together in tetrahedral forms. These units are arrayed in a resilient, self-bracing and diagonally-organized truss. Curving and expanding this truss work creates the flexible grid-shell topography. Columnar elements extend out from this membrane, reaching upward and downward to create tapering suspension and mounting points. Fitted into this flexible structure are hundreds of small mechanisms that function in ways similar to pores and hair follicles in the skin of an organism. The Hylozoic Ground includes three kinds of actuators elements: breathing pore mechanisms, actuated by shape-memory alloy wires; whisker elements, driven by small direct-current motors; and miniature LED lights.

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Hylozoic Grove // Philip Beesley // 2010

Philip Beesley, Hylozoic Grove. 2009. Ars Electronica Archives (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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Beginning with the premise that architectural elements might move in response to their environments, Living Glass developed as a kinetic system that would lend itself to the overall well being of an occupant. Living Glass collects input through an array of sensors and processes the input through a microcontroller that triggers local movement. Like gills, this movement is meant to allow air to flow through a surface as required. The movement is contained in the surface. This is done by embedding shape-memory alloy

wires in a silicon sheet.

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2.2 LIVING GLASS // The Living // 2006

The material actuators used in this system are thin, light weight and silent. Their movement occurs without mechanical parts or motors, but rather through the contraction and expansion of the material itself. Using SMA wires attached to a surface, the surface could be made to move and open when electricity is applied to the wire. This movement was set to occur when triggered by infrared sensors. The result is a polymer glass that responds to the presence of an occupant. Chemical sensors are also tied into the system to allow the â&#x20AC;&#x153;glassâ&#x20AC;? to react to pollutants. The resulting movement is a function of both inputs.

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Living Glass // The Living // 2006

The Living, Living Glass. 2006. http://www.thelivingnewyork.com/ lg.htm (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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WhoWhatWhenAIR was the winning entry in a mini skyscraper competition sponsored by MITâ&#x20AC;&#x2122;s School of Architecture. The project was chosen among ten entries submitted by teams of students from both MIT and Harvard. With a $7000 budget allotted to them, and a time frame limited to sixteen weeks, the winning team was able to realize their tower

proposal.

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2.3 WHOWHATWHENAIR // Philip Block, Axel Killian, Peter Schmitt and John Snavely // 2006

WhoWhatWhenAIR is a 40 foot tall structure that was built in front of MITâ&#x20AC;&#x2122;s student center. It is able to bend and sway up to eight feet in either direction. This movement is accomplished through the use of pneumatic actuators that had been donated to them by the German actuator company, Festo. The tower stood in its location for a period of four weeks, and drew much attention.

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WhoWhatWhenAIR // Philip Block, Axel Killian, Peter Schmitt and John Snavely // 2006

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Philip Block, Axel Killian, Peter Schmitt and John Snavely, WhoWhatWhenAIR. 2006. http://musclesfrombrussels.blogspot.com/ (accessed December 2010).

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For the exhibition Non-Standard Architecture, ONL realized a working prototype of the Trans-ports Project called the Muscle. The Muscle is a pressurized soft volume wrapped in a mesh of tensile Festo muscles, which can change their own length. Orchestrated motions of the individual muscles can changes the length, the height, the width and the overall shape of the Muscle prototype by varying pressure pumped into the 94 swarming pneumatic actuators. The balanced pressuretension combination bends and tapers in all directions. The public connects to the Muscle prototype by sensors and inputs through sliders on a computer screen. The sensors are attached to the reference points of the construction, and when a visitor moves closer to the sensors it

triggers a reaction of the Muscle prototype. “The public will discover within some minutes how the prototype reacts to their actions, and soon the public starts to find a goal in the play.” (Oosterhuis, 2003)

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2.4 MUSCLE NSA // ONL [Oosterhuis_ Lénárd] bv // 2003

Another way to communicate with the Muscle prototype is to operate the sliders on a computer screen. Bringing the sliders to the right probably means that the selected area should move to the right. But ONL has programmed the Muscle to have its own will. The Muscle may not want to follow commands from this port and may try to crawl back or resist. Then a true interaction starts, and the outcome of the transaction process may become unpredictable. The Muscle is a prototype for an environment that is slightly out of control. Muscle is a prototype for a building which is pro-active rather than reactive and obedient to the user.

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Muscle NSA // ONL [Oosterhuis_Lénárd] bv // 2003

ONL, Muscle NSA. 2003. http://www.oosterhuis.nl/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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Chembot is a robot whose motion is a result of jamming-skin enabled locomotion. Jamming is a process that involves using granular materials packed into an enclosure and controlling the amount of the medium in which the grains are suspended. The medium can be either air or water, and when either medium is removed, the granular material becomes seemingly solid and the overall form contracts. In this way, Chembot is a soft prototype which can morph its shape to move along a horizontal surface. In this prototype, the granular material fills the cells of the robots elastic membrane.

Using a single pneumatic actuator capable of volumetric variation, the cells can be inflated of deflated. Through proper sequencing of this action, locomotion begins to occur.

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2.5 CHEMBOT // iRobot // 2009

In addition to simply providing a novel mode of movement, the Chembot was also intended to use this ability to change shape and rigidity to grant passage into previously inaccessible spaces. By being able to squeeze through small openings and transverse complex terrain, Chembot is imagined to find some use in military applications and disaster scenarios. This jamming method of shapeshifting is also being developed to create a more adaptable robotic grip.

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ChemBot // iRobot // 2009

iRobot, ChemBot. 2009. http://www.technovelgy.com/ct/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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Hyposurface is a three-dimensional display system. Information and form are linked to produce a new media technology. The surface behaves like a precisely controlled liquid to create waves and patterns, and display logos and text upon a dynamic surface. Hyposurface uses powerful information bus technology to control many thousands of linear actuators that deform a pliable surface

and allows for the high-speed movement on the screen. Linking this capacity to an input offers some interactivity with the audience. In early installations, a microphone was used to detect sound, which was translated into sound waves rippling across the Hyposurface. As a marketing tool, this sort of interaction and scale of physical movement gives Hyposurface a basic advantage over other display systems.

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2.6 HYPOSURFACE // Mark Goulthorpe // 2002

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Hyposurface // Mark Goulthorpe // 2002

Mark Goulthorpe, Hyposurface. 2002. http://hyposurface.org/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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The Desert House was an initial proposal in the development of the Xeromax envelop. In this application, it was specifically designed as a prototype for desert living; calibrated, tuned and responsive to its desert habitat. It is adaptable, mutable and variable desert ecology. Contrary to current trends in desert suburban development, Xeromax is a porous, permeable and evolving habitat in synchrony with its surroundings â&#x20AC;&#x201C; hyper situated, indigenous and local. Xeromax responds to the conditions of the desert; this includes wind direction, solar orientation, temperature and sand. The synthetic recombination of extreme conditions was used to produce a new hybrid

of desert living machine.

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2.7 DESERT HOUSE // Future Cities Lab // 2008

Out of this study, the Xeromax Robot (XR) was produced to study and exhibit the possible behaviors and interactions being proposed. XR is a working prototype for a responsive architectural system and interface. The XR model weaves ultra-thin shape-memory alloy wires to activated truss modules that receive direction from processed signals from an array of infrared sensors. A customized LCD screen displays status and states. It is part kinetic structure, part experimental interface and part analytical drawing instrument. In addition to adapting in real-time to shifting conditions in the gallery, X also gains intelligence, spatial complexity and richness over time.

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Desert House // Future Cities Lab // 2008

Future Cities Lab, Desert House. 2008. http://www.future-cities-lab. net/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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The Xeromax Envelope prototype is a proposal for a responsive membrane whose intricate geometric surface plays host to clusters of tiny energy-harvesting robotic parasites. Part biological formation, part symbiotic machine, and part micro-climatic instrument, Xeromax proposes to envelope and augment Americaâ&#x20AC;&#x2122;s growing stock of iconic yet energy inefficient modernist buildings. The suspended model was fabricated from

hundreds of small interlocking geometric parts made of folded, notched and sewn PET-G plastic and synthetic paper modules. Networks of embedded sensors track the proximity of gallery visitors and trigger tiny air-cleaning blades and small auroras of amber LED lights.

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2.8 XEROMAX // Future Cities Lab // 2010

The suspended Xeromax model was first presented in 2010 at the BiodiverCity Exhibition in Washington DC. This developed into a more intricate structure that was displayed later that same year at the Pratt Gallery in New York.

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Xeromax // Future Cities Lab // 2010

Future Cities Lab, Xeromax. 2010. http://www.future-cities-lab.net/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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The Aurora Project is an index of shifting territorial resources in the Arctic and a speculative vision for a massive new energy infrastructure and settlement pattern. Aurora suggests an alternative approach to the exploration, exploitation and eventual colonization of the region. It is simultaneously a projection of an imminent environmental condition, and the materialization of how

contemporary political, social and ecological trends might be channeled towards a more productive future.

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2.9 AURORA // Future Cities Lab // 2009

The Aurora installation on view in the Van Alen Institute gallery superimposes the ephemeral qualities of the Arctic ice field with the dynamic behavior of visitors, translating the shifting dimensions of the ice into an immersive system of flickering auroras and responsive luminescent skins.

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Aurora // Future Cities Lab // 2009

Future Cities Lab, Aurora. 2009. http://www.future-cities-lab.net/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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The Expanding Geodesic Dome opens from a 14 inch cluster to a 48 inch dome when pulled from its base. This is made possible through the repetition of a scissor mechanism. This same mechanism has been deployed to

make various forms that can operate at many different scales ranging from architectural applications to childrenâ&#x20AC;&#x2122;s toys, and has even been used in the medical industries to open clotted or collapsed veins.

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2.10 EXPANDING DOME // Hoberman Associates // 1997

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Expanding Dome // Hoberman Associates // 1997

Hoberman Associates, Expanding Dome. 1997. http://www. hoberman.com/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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such space. Personal space is increasingly violated by external pressures.

The Defensible Dress is a response to the increasing breakdown and encroachment on personal space in everyday life. Historically, each culture and generation has had varying definitions on personal boundaries. Globalization and urbanization have diminished an understanding and respect for

Inspired by the porcupine and the blow fish, the Defensible Dress marks the wearerâ&#x20AC;&#x2122;s personal space by activating a space-defining physical projection around the body. When infrared sensors detect a body entering a personal space, a series of mechanical quills are activated, bristling to prevent encroachment.

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2.11 DEFENSIBLE DRESS // MY Studio // 2001

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Defensible Dress // MY Studio // 2001

Meejin Yoon and Eric Howeler, Defensible Dress. 2001. http://www. mystudio.us (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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Each component includes a servo and an electromagnet per edge. The servo motor rotates the electromagnet on edge, and loops this panning as it tries to find similar devices.

When found, the electromagnet will activate and lock two components together. The components continue to rotate and climb over one another to find more secure positions with respect to neighboring components. Through this simple repetitive process, a structurally sound system will develop.

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2.12 SELF-ASSEMBLY UNIT // Skylar Tibbits // 2008

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Self-Assembly Units // Skylar Tibbits // 2008

Skylar Tibbits, Self-Assembly Units. 2008. http://www.sjet.us/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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As collaboration with Neil Gershenfeld’s Center for Bits and Atoms, the Decibot was developed along side a family of other like robots that differ in scale. The Decibot is the largest in the family. It measures 144 inches long when straight, and 36 inches

cubed when folded completely. This robotic system was the product of an investigation into systems of programmable “matter” that uses one-dimensional folding chains. The Decibot, as well as other robots in the family, use electromechanical folding actions.

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2.13 DECIBOT // Skylar Tibbits // 2009

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Decibot // Skylar Tibbits // 2009

Skylar Tibbits, Decibot. 2009. http://www.sjet.us/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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The Divertimento prototype structure uses pneumatic muscles that pull opposing structural elements together, causing the skin to become rigid and change shape. By controlling the activity of each actuator, different regions of the structure can be shaped in response to

local stimuli or as a pre-programmed activity. With an understanding that stiffness can be increased through differing configurations, this system can also control the integrity of the structure. The structural pattern used is developed from Buckminster Fullerâ&#x20AC;&#x2122;s tensegrity structures.

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2.14 DIVERTIMENTO // ORAMBRA // 2005

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Divertimento // ORAMBRA // 2009

Tristen dâ&#x20AC;&#x2122;Estree Sterk & ORAMBRA, Divertimento. 2005. http:// www.orambra.com/ (accessed December 2010). seam MASTERS RESEARCH PROJECT - SPRING 2011 - PEEL, JACOB

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RESEARCH ON ADAPTABLE AND INTERACTIVE SYSTEMS

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For what we can call, for the time being, a Volumetric Pixel to be able to alter its dimensions, it must become animated. In terms of an architectural application, for this animation to prove to be valuable, it should be responsive. Responsive devices, or in this case we can say Responsive Architecture, should be understood to be a subset of a larger industry of design and production. In a more general sense, the term â&#x20AC;&#x153;kineticâ&#x20AC;? refers to works that are simply able to move. Kinetic Architecture has been defined as buildings or building components with variable mobility, location and/or geometry (Kronnenburg, 2003). The reasons for this movement do not necessarily have to be owing to any external stimuli or input. The Prima Tower in Singapore is an example of a space that moves, but not according to any transient forces or internal logic. It is simply a restaurant that revolves, offering patrons sweeping views of the surrounding city. The Prima Tower is an extraordinary project to

say the least; however, the value of Kinetic Architecture might be better based on its ability to adapt to the dynamics of any given context and the flexibility to accommodate a multitude of purposes.

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3.1 KINETIC ARCHITECTURE

Although the tendency may be to think of Kinetic Architecture as being the result of endowing a building with a magnificent mechanical system that provides for such monumental motions, with the given definition above, we may understand that there have been numerous examples of Kinetic Architecture extending as far back in time as the very beginning of building shelters for ourselves. There is some benefit to understanding the definition in this way in order to expand the scope of examples beyond those actualized using only the most modern systems. Given the nature of the materials used and the techniques by which they were composed, primitive huts could be considered some form of Kinetic Architecture given its temporal nature. In this sense, we may include any such deployable structure under the heading

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of Kinetic Architecture. Focusing on indigenous building traditions, some of the more interesting examples of adaptive building can be found in Northern Ghana, in which the inhabitants build with mud. How they make use of the mud is done in a way that eventually causes it to fail under normal stresses. It should be noted that these people do possess the ability to build more durable and lasting structures; this they reserve for religious monuments and granaries. As for their dwellings, they build small circular huts made from the available material. Each year, after the harvesting season has ended, the community engages in a vigorous period of rebuilding. This reoccurring event allows the homes to be appropriately tailored to the needs of the occupants. Within each hut lives a single family. How that family expands and contracts is reflected in the form of the house during this time. If a child has been born, the hut expands. As that child moves into adolescence, they may require their own room to be added to the

home. When the child moves into adulthood, they may marry or move away. In the case of the former, the room previously belonging to the family hut will serve as the beginning of a new hut. This leads to a development of nucleated clusters. In the case of the latter, the room is left to fall back into the earth. As a result of this method, what may seem to an outsider as a purely local activity manifests as a very clear community plan that reflects accurately the villageâ&#x20AC;&#x2122;s genealogy. This method, as well as other similar methods, can be found in many places across the globe, and it has been the adaptability of these structures that have greatly contributed to the success of a society living in harsh conditions and arid climates. Bernard Rudofsky has collected and presented a number of such examples in his book Architecture Without Architects. Also, Rudofsky provides an image that places the individual in control of the design of their homes and buildings (this topic is expanded on in the section â&#x20AC;&#x153;User Inputâ&#x20AC;?). In this

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It may be of some use to consider how a building could become more economical and effective if given the faculty to enact responsive variable mobility. As mentioned, this has enabled some communities to persist in quite inhospitable regions. Even in modest examples, the potential of this development is easily identifiable. For example, Gary Chang is an architect in Hong Kong, where space is at a premium due to the city’s enormous

population. Apartments here are typically small, and this includes Chang’s. However, by devising a kinetic system of partitions, he is able to layer various programs within the 330 square foot space. In this Domestic Transformer, he lives with both his sister and mother, and is still able to rent out a space to a fourth person. This optimization would not have been possible without the use of the kinetic partitioning system.

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situation, building types are constrained by the availability of the materials and climatic conditions, and therefore provide a unifying conventions and traditions that define its particular “vernacular”. With the introduction of mechanical systems and taking advantage of modern logistics, buildings are able to avoiding having to confront and manage such external and internal forces. However, in recent years this unnatural approach to building has been reproached while there has been a reuptake in sensitive and responsible methods brought on by issues of over population, resource deficiencies and polluted environments.

3.2 RESPONSIVE ARCHITECTURE Being granted the ability to reconfigure itself, reallocate its resources or respond in someway to forces acting on it, a space may be able to play a more active role in the happenings within and surrounding it. In this way, a project could be able to optimize such activities and augment the performance of a space. Kinetic applications could also optimize the performance of the material used in a project. The notion has been put forward, most notably by Guy Nordenson, that “if architects designed a building like a

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body, it would have a system of bones and muscles and tendons and a brain that knows how to respond. If a building could change its posture, tighten its muscles and brace itself against the wind, its structural mass could literally be cut in half.” A building in which it would be possible to reallocate its materials and resources in response to some stimuli could allow a project the ability to use more economically the materials embedded. The key to realizing this possibility is “the brain” that Nordenson mentions, which is also the main feature that delineates the subset, Responsive Architecture. Nicholas Negroponte was one of the first practitioners to begin speculating on the potential benefits of endowing a project with the ability to be responsive. Through the coupling of Cybernetics and Architecture, he proposed that a building could be granted an ability to perceive and understand its given location, as well as be designed with a set of operations it may employ in order to mitigate, mediate or magnify what was being sensed. In Soft Architecture Machine, he defines this

industry related to Responsive Architecture and its scope. In terms of operations that a building could be capable of, Negroponte suggests there being only two classes; Reflexive and Simulated. Reflexive responses would include those that “take place as a part of space, reflecting a purpose” and would be capable of physical alterations and translations. Simulated responses would include those that intend to render an imitation of a condition. This brand of behavior is often seen in entertainment industries. Where as the first type of behavior results in a physical response, the second results in a visual, or virtual, response. Negroponte also describes two general classes in which the purpose driving a response can be classified; Operational and Informational. In working toward an Operational goal, a system would be programmed with more pragmatic concerns. In working toward an Informational goal, a responsive system would be programmed with the intention of sending and receiving signals from a variety

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3.3 REACTIVE AND INTERACTIVE Within the industry of Responsive Architecture, there are two major categories that can be established based on the quality of dialog between the user and the system. Usman Haque, an architect and artist, has very clearly stated the difference between the two categories; or rather, has identified the features that define the gradient between and beyond these categories. In short, the major differences are owing to the pattern of transactions between a user and the system, the intelligence that is embedded in the system and the robustness of the overall interaction. Haque argues that if a system is given the ability to account for or accommodate a single transient force or event, and does so in a predetermined and singular manner, it is not an interactive system, but a reactive system. As an example, Haque describes a system of louvers that are able to change their angles

with respect to the changes in the sunâ&#x20AC;&#x2122;s position through out the day and through out the year. This is a purely reactive system. It is linear in nature and requires only a single loop of coding in order to function. In addition, the changes registered on the louvers do not influence the environmental factors by which it is being influenced. In effect, it is not in a dialogue with its context, but rather subject to the context.

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of sources, and monitoring and filtering these lines of communication.

This same louver system can begin to enter into the interactive category as it becomes more robust and more intelligent. This same system of louvers can be granted the ability to mediate the sunâ&#x20AC;&#x2122;s position with other contextual cues if sensors are added that can detect occupancy. Additional sensors can be added to allow an occupant to make known their desires. These efforts would foster various options that a system could engage, assuming it might have some overall effect or goal (such as to light a space by using as little energy as possible). In this way, we might be able to imagine a darkened room, shielded from the sun by these louvers. We

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enter and register the need for light by turning a switch to some level. The louvers adjust not just to allow light in but to bounce light in accordingly. In this example, the angles of the louvers are a function of both need and the sunâ&#x20AC;&#x2122;s position. Occupancy in this example does not trigger anything, but as the system is used, it could log a history of actions and begin to draw upon the experiences to make more accurate and automated decisions about what and when it might need to enact a certain position or response. This is perhaps a very simplified example of how such system can develop, but as more sensors and actuator are embedded into the processing, the more opportunities are allowed for the system to take advantage of and process. The entire building can be layered with sensors monitoring the environment and collecting contextual data. The sensors should be networked together and supplying the data for processing. With a system of actuators, working in concert to achieve some ultimate goal, the building should become able to attain some level of performance not

otherwise possible. 3.4 ROBOTIC ECOLOGY Robotic Ecology refers to compositions of many different devices, each able to perform a specific task in response to environmental cues. Robotic Ecology could be considered a subset of Kinetic Architecture, but the endeavor originated in the fields of Computer Science and Robotics. The unique quality of these systems is that it employs a diverse range of device; individually, they are able to sense and respond, but are also able to share the data with neighboring devices within the network, process it and produce coordinated responses. In this way, the devices interact with the context in which they are situated, as well as with each other. This results in an ambient processing of contextual inputs. The value here is that a myriad of responses aggregate. The simplicity of the individual task, and the distribution of computing, results in a responsive system in which the quality and resolution of the reactions are made fluid

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Robotic Ecology is relevant in this research, in which the ultimate goal is to produce a system in which input is able to happen locally and responses require a coordinated effort. For the purposes of this research, the responses are intended to be manifested in spatial and formal manipulations. The transformations should take place in order to accommodate various programs, optimize some activity or resource, and mediate contextual forces. Christopher Alexander recognizes need as being the main drive behind form. Though this may be correct, he does not recognize how this need is capable of shifting, and in some cases, can shift quite quickly. Michael A. Fox improves upon this sentiment by describing formal origins as pressures -cultural, sociological, meteorological, and so on. To adopt this line of thinking allows for an understanding that pressure gradients occur, and that these forces at play are dynamic; changing though out the day, through out the year and through out a projectâ&#x20AC;&#x2122;s life-span.

Fox argues that being able to respond and adapt to these pressure may add many years to the usefulness of a structure and add value through out its life-span.

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and fine.

The conception of a responsive system, with regard to the pressures that exist, must address the notion of cause and effect in the most precise manner. In this sense, a survey of a site in which a formally dynamic architecture would be situated would indeed benefit from deigning with the data that can be gleaned or simulated. It is in this sense that the responsive architectural project might install the first sensorial layer of the system before even schematic design even commences. It could even be the case that this layer is installed prior to acquisition. Robust Field Systems are being deployed in the city as a means to collect data that can offer insight that is useful when drafting planning strategies. The data being collected from private sensors are also becoming available through websites such as Usman Haqueâ&#x20AC;&#x2122;s initiative Pachuba.com.

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3.5 TASK DISTRIBUTION As mentioned in the above, Robotic Ecology has its roots in the field of Computer Science and Robotics. Initial experiments were inspired by the idea of biological aggregation and the swarm behaviors as seen in the natural world. In the mid 1900s, many scientists and mathematicians began studying and describing these happenings. Through observations of large populations of organisms such as slime molds, ant colonies and bird flocks, cumulative behavior models began to appear. During the 1970s and on, various computer programs started to show up that had been developed from these models. Notable figures on the science side of this development are Evelyn Fox Keller and Lee Segel. Among many others, on the computer side of this development is Craig Reynolds. In 1969, Keller and Segel published a paper that marked what could be considered the beginning of a certain shift in awareness and interest in emergent and self-organized systems. In their paper, they presented their

observations of slime molds and argued that the behavior and growth of the slime molds took place according to an aggregation of responses to the local environmental conditions. At the center of their study was a chemical called acresin, which was used by the organism as a mode of communication within the community. When a single cell found their local conditions to be favorable, it produce acresin, and in effect would be calling to other like cells and inform them of its discovery. To this, other slime molds would move in. From here, the more cells that accumulated in a location, the stronger the signal was broadcasted and the farther it could reach. Keller and Segel wrote several key algorithms that described this occurrence, which in turn would become the basis of a number of computer programs that would apply the ability to self-organize. One of these is a simple and straight forward program called StarLogo, written much later by Mitch Resnick, a faculty member at MIT. One of the most well-known computer programs was written by Craig Reynolds in

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Deborah Gordon, a professor of Biology at Stanford University, has been studying ant colonies since the 1980s, and has been able to identify some key features that lead to successful aggregate behaviors. These key features have been translated into tenets that can be easily applied in disciplines outside of biology, and used to structure an understanding and approach in developing similarly behaving artificial systems. The first of Gordon’s tenets would state that

“ignorance is useful”. An ant, by itself, has no conception regarding the state of the whole colony. However, it does have an image of its immediate surroundings and is able to respond locally. Through an amalgamation of individual responses, the colony as a whole is activated. Though the majority of cues gleaned from environmental conditions, one mode of input is the interaction between ants. The second tenet places an importance on these interactions. It is in this way that ants communicate through chemical signals and antennal contact. However, as Gordon points out, “the signal is not in the contact… the signal is in the pattern of contact.”

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1986, call Boids; the name being a portmanteau of the Bird and Droids. In this program, individual agents were given only three instructions that described the relationship they should maintain with each other during the simulation; these being referred to as separation, alignment and cohesion. With groups of such agents, Reynolds would supply a goal to achieve, marks to meet and objects to avoid. The success of these tests was encouraging, and the application of such modeling has extended in many different endeavors including video games and urban planning.

In larger ant colonies, with populations exceeding ten thousand, tasks are performed at a high level of efficiency and with a significant amount of endurance. This is owing to a redundancy of signals that can saturate any stray communication. If a negative signal were presented, the signal could be passed very quickly through the colony. However, if that negative stimuli does not receive any concurring signals, it will be lost in those

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that differ and not cause any major effect. In smaller ant colonies, numbering less than two thousand, the same temperament is not present. Nearly any signal being passed around will cause some effect to ripple across a small ant colony. It is because of this situation that Gordon proposes her third tenet that “more is better”; or at least more stable and able to supply appropriate responses. The overarching idea draws attention to the fact that the global operations of an organism can be, and often are, determined by the local activity and the flow of information. Application of these idea require, above all else, individual components that are able to receive, send and process this information. The importance of distributed pathways for communication is perhaps one of the most basic notions in the development of emergent systems. 3.6 USER INPUT With respect to the above section entitle “Kinetic Architecture,” what is a much more

interesting item about indigenous building methods is the participation of the occupant in the design of the space and building. At the time in which Rudofsky’s text was published, it was in the company of many other books and essays that had risen from the direct rejection of the Modernist idea of the Hero Architect. When Pruitt-Igoe, a modernist housing project in St. Louis, was demolished, architectural historian Charles Jencks wrote “Happily, we can date the death of Modern Architecture to a precise moment in time.” As an effect of this shift, user participation became an idea of note and practitioners began to explore the potentials of introducing a method by which the eventual occupant can influence the design. The main trouble in developing these methods had been to protect the position of the architect while allowing for some control to slip into the hands of those who have little or no training. In the 1960s, Archigram suggested a method of construction by which a client might be able to literally make a space of their own. By

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Another interesting, and more recent, method of inclusion is one that seems to side step a clientâ&#x20AC;&#x2122;s direct control over architectural design while still gleaning valuable input. Chris Travis is an architect who has his clients submit to fairly intense psychological evaluations that begin to distill specific emotional connections. Travis uses this information to put together an idea about what

a client might really desire in their home. His projects have been able to demonstrate the value of this approach by having met and consistently exceed the clientâ&#x20AC;&#x2122;s expectations.

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filling a hollow block with foam, the client and their family could burrow in and carve out various spaces that they might like to have in their home. The parents can go in and shape the master suite, kitchen and so on, while the children can fashion their playrooms. The resulting interior is directly controlled by the desires of the eventual user. The standard system, if given to multiple people, will be able to accommodate many variations and registered whims.

In a survey of user participation methods, it seems that those presenting a tailored system on which a clientâ&#x20AC;&#x2122;s desires are registered or gleaned result in more successful products. Through the design of the system, the architect would be able to limit the options and opportunities available to a client, and therefore limit the chance for a client to make a major mistake. As the architect guides the client through the process, they should instruct along the way, making the client understand the impacts of each decision. What this has to do with the research here is the understanding that it could become possible to impart upon the project an indefinite end to its design.

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CONSTRUCTION OF TRANFORMABLE GEOMETRIC SYSTEMS

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Max Bill, 1949

Typically, a hand-drawn plan begins with a system of construction lines representing the nascent state of a spatial logic. Through the design process, this formal sub-system establishes very necessary boundaries and benchmarks in the development of a project. In much the same way, it would be prudent to employ a method that can provide that same

guidance from the beginning and through out the design of formally responsive systems. However, instead of lines demarcating the static organization of building material, they should choreograph the movements of architectural elements.

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In every work of art the basis of its composition is geometry… Thus, just as mathematics provides us with a primary method of cognition, so too some of its basic elements will furnish us with the laws to appraise the interactions of separate objects, or groups of objects, one to another.

By reducing the elements in play to the most fundamental and most primitive, we are allowed to develop a network of interactions on which we can later hang more specific decisions. What was intended was “a diagram of relationship, awaiting scale and materiality” (Reiser and Umemoto, 2006). As a means to structure an approach to developing a system capable of transitioning between different formal configurations,

Basic Properties of Geometric Primitives George Stiny, “How to Calculate with Shapes” (essay present as a part of the course Introduction to Design Inquiry at MIT, 2001)

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initial considerations can be limited to a set of pervasive geometric elements typically called Geometric Primitives. 4.1 GEOMETRIC PRIMITIVES The term Geometric Primitives refers to a set of elements that can be used to define and describe any spatial or formal composition. Geometric Primitives are divided into four classes of elements that are delineated by their respective dimensional levels. Figure 1 presents the basic properties and boundaries of these primitives. The first term in each line belongs to the industry of mathematics, while their graphic and architectural analogs are within parenthesis. The discipline-specific definitions of the terms differ somewhat. For the purposes of this investigation, deference will be given to their mathematical description. The first and second classes the chart, the vertex and the edge, are distinct from the third and fourth. In general, the vertex and edge can be considered primary classes of primitives.

What makes these classes of elements unique is that they can not be added to nor subtracted from to attain more complicated versions (Stiny, 2001). Through subtraction, if one were to dismantle an edge, the construction would be reduced to a single vertex. If one were to dismantle a vertex, the construction would be reduced to nothing. Through addition, if a third vertex were collinearly introduced into the construction of an edge, the result would simply be two edge segments. If a third vertex were added non-collinearly, the result would be three edge segments, and subsequently a triangular polygon. In each of the proceeding examples, the instances of these classes were not made more complex. As obvious as this issue may seem, being acutely aware of these attributes can simplify a notion and make more accessible an understanding of the geometric systems in which they will be deployed. The third and fourth classes, the polygon and the polyhedron, fall under the more general heading of polytope. Each of these classes

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4.2 REGULAR POLYHEDRONS The chart located here organizes the nine regular polyhedrons. A regular polyhedron means that the lengths of the edges in the construction are equal. They could also be called isotropic polyhedrons. The first five here have been credited to Plato and the last four have been credited to Kepler. The attributes listed here are the number of vertexes, edges and polygons that go into the construction of each polyhedron. The last number is the diurnal angle of the objects. If we compare the attributes of these polyhedrons, specifically

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has a base requirement that must be met in order for a construction of elements to enter into the dimensional level of either a polygon or polyhedron. In regard to the former, an area must be bound by a construction of at least three edges. In regard to the latter, a volume must be bound by a construction of at least four polygons. Unlike the primary primitives, these constructions can be built upon ad infinitum.

Nine Regular Polyhedrons in Ordinary Space H.S.M Coxeter, Regular Polytopes (London: Methuen, 1948)

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the proportional relationship between edges and polygons, we can see that there is a consistent ratio among those that are selfstabilizing, which is 3/2.

Shifting Q-Value

By itself, this doesn’t determine with certainty that some construction would not fail, but it does provide some orientation in conceptualizing the proper geometry of a structural system. This ratio is the basis of an isotropic omni-triangulated vector matrix, and the components of this vector matrix must follow a specific configuration of geometries. This necessary configuration is captured by the geometric notation of the Schläfli Symbol. 4.3 SCHLAFLI SYMBOL The Schläfli Symbol follows the form of {p, q}, where p is the number of sides to a polygon and q is the number of polygons that meet at a vertex. This symbol is used to describe both tessellation patterns and polyhedron constructions.

The Schläfli Symbol for a regular cube would be {4, 3}. The Schläfli Symbol for a regular tetrahedron would be {3, 3}. The Schläfli Symbol for an isotropic triangulated tessellation would be {3, 6}. By adding to the vertex configuration, a construction is affected. Moving from a q-value from 3 to 6 generates a flattened construction. With all edges being equal in length, a q-value of 7 is not valid. This notation is helpful when moving through the development of some system in that it determines what configurations are valid in an isotropic system. With this information, the decision was made that the tetrahedron and the triangle were dually suited for our purposes. 4.4 BEHAVIOR OF GEOMETRIC SYSTEMS These polytopes present the first degree of systems that would be choreographed in an actuated geometric system. The number and relationship of elements used in the

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The sphere is constructed with an infinite number of individual surfaces, and its geometry is such that it uses the least amount of surface area to enclose the most volume. The sphere has a high surface to volume ratio. The sphere is also the form in which the least vector protrusions occur, making it the least frictional polyhedron. The tetrahedron meets the most minimum requirements to be considered a polyhedron in that it uses only four polygons in its construction. Its geometry is such that it uses the most amount of surface area to enclose the least amount of volume. The tetrahedron also has the greatest amount of vector protrusions, making it the most frictional polyhedron. Although the above may begin to clarify the

notion of differing geometric behaviors, the tetrahedron becomes the most interesting figure to consider in the development of a formally responsive system owing to its exceptional character and ability.

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construction of some geometry will impart a certain behavior on that geometric system. A comparison of the three-dimensional geometries the sphere and the tetrahedron, these being located at opposite ends of the behavioral spectrum, can illustrate this notion.

With regard to how it operates statically, the tetrahedron is the only self-stabilizing polyhedron (Fuller, 1982). The component polygon of this volume, the triangle, shares the same unique characteristic. For this reason, they both can be used to design and evaluate the structural integrity of a construction within their respective dimensional levels. With regard to how the tetrahedron operates formally, any three-dimensional form can be divided into a collection of tetrahedrons. If there are no constraints on the regularity of edges, a three-dimensional tessellation process can output non-uniform pattern of tetrahedrons without omitting any part of the original volume. Given the preceding properties, and with regard to how it could operate dynamically, the tetrahedron could begin to be thought of

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as a dually-suited base unit from which an adaptable system could extend; structural integrity and formal manipulations resulting from the proper coordination of networked units. 4.5 INITIAL STUDIES It was at this time that a few key studies were done in order to understand what effects should be expected as a single component undergoes transformation, as well as studies aimed to model how the actuation of one area can be transmitted through out a configuration. Beginning by directly testing the understanding gained from above, a study was conducted that looking exclusively at the tetrahedron. The first step in the study limited the actuated element to being the top chord, to understand the affect of incremental dimension increases on the overall geometry. Following this, there was produced an array of variations in which two chords were the variables. In first set, the two variable chords were on opposite sides of the polyhedron. In the second set, the two

variable chords were adjacent and coplanar to one another. The variations that resulted were unfolded digitally and refolded physically to make these small shards that could be assembling together to begin seeing how the variable edges could be set up in relationship to one another within a construction. In addition to the above study, some simple systems were built using paper and cardboard to see what sorts of open folding patterns would offer in the way of transferring deformations. What became clear here was that there is a pervasive necessity to symmetry in the movement of these surfaces, and that this symmetry could be used to an advantage. The third study being presented here was about dissolving certain elements from a closed configuration. Between the three models produced, the configuration was the same; using the Schl채fli Symbol, the configuration was {3, 12}. However, each uses a different sort of triangle. The first was a 60 degree triangle, the second was a 45/90 degree triangle and the third was a 30/60/90

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Tetrahedron Study Adjustments to Adjacent Edges

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Common Surface Areas

Common Cell Volumes

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Tetrahedron Study Adjustments to Opposite Edges

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Common Surface Areas

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Adjustable Component Polygons

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Adjustable System: 01

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These system studies demonstrated certain constraints and limitations that require consideration in making an animated structure. The understanding is that symmetry is required in larger assemblies. From this, some understanding was received of how manipulating base units or individual cells would affect neighboring modules, and as such, highlighted the importance to include considerations for how any transformations must be distributed within a construction. 4.6 EUCLIDâ&#x20AC;&#x2122;S ELEMENTS Following the above investigation, the objective became focus on the development and use of some system of diagramming that could easily allow the conceptualization of dynamic and reconfigurable structures. The objective brought to light the elegance demonstrated by historic mathematical models. It is interesting to note that mathematicians

of antiquity did not have knowledge of arithmetic. This is because the numeric system employed by the Ancient Greeks and Babylonians contained only whole numbers; no zeros, no fractions and no negative numbers (Hartshorne, 2000). Despite this limitation, they were still able to carry out complex calculations with a high degree of accuracy. This was made possible with the use of Euclidean Geometry.

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degree triangle.

I had been previous aware of Euclidean Geometry, but only as a phrase that would be interchangeable with Plane Geometry, and that it finds its implications in architecture by virtue of orthographic projections. However, the method behind Euclidean Geometry offered itself to be a much more fertile subject. It was with its application that I moved through the development of actuated base unit and tested various larger assemblies according to differing configurations. To provide some background information, Euclid was a mathematician who lived in Ancient Greece sometime around 300 BC.

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He is sometimes referred to as the “Father of Geometry”. This label comes as a result of having been responsible for producing one of the earliest treatises on the subject. As a whole, this work is entitled Elements, and for 24 centuries following its inception, it remained a highly influential text.

this, the Euclidean approach provides the range offered by a particular relationship, within which any specific instance can be extracted. Because this research depends on tracking the changes within a configuration, the Euclidean approach is more appropriate for calculating the interactions of the components involved.

In thirteen books, Elements addresses the whole scope of mathematics and geometry, and lays down the foundation for its transmission and development. Through propositions, Euclid proves his postulates. This is to say that using Geometric Constructions, he is able to demonstrate the relationships among various mathematic organizations and interactions.

By employing this Euclidean method, calculations are made in a flat two-dimensional space. The components of the organization are simply geometric primitives.

A Euclidean approach is distinctly different from Common Arithmetic. In Arithmetic, numbers are assigned to designate varying magnitudes, and abstract operations -- such as addition, subtraction, multiplication and division – are applied to arrive at resulting quantities. This approach provides instances within a larger relationship; discrete moments in a field of interactions. Mutually opposed to

Geometric Constructions require two basic tools: the straightedge and the compass. With these tools, datums and ranges are inscribed and interrelated to produce various geometrical forms and figures. The natures of these tools are easily aligned with the fundamental types of motion: Linear and Angular. 4.7 MOTION TYPOLOGY If we were to use some actuator to manipulate these primitives, each would result in one of two types of motion; Linear or Angular. In

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4.8 CASES OF CONTROL There are four cases in which a triangle can be solved. Similarly, there are four cases in which a triangle can be controlled. These polytopes can also be used to subdivide any larger geometric construction. This is called faceting. We can take any rectangular surface and draw a line between cattycorner vertexes to yield two triangular facets. Gaining control of these facets and subjecting them to incremental dimensional alterations would

allow us to define and redefine the overall shape of which they are apart.

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order for motion to be perceived, calculated or defined, there needs to be two points within the system; one fixed and the other undergoing displacement. With reference to the fixed point, Linear Motion is simply defined as a displacement of a body in which the distance from the reference point undergoes change while the angle to it does not. Angular Motion is defined as the displacement of a body in which the angle to the reference point undergoes change while the distance to it does not.

Because the triangle is self-stabilizing, we can say that it is inner-stabilized. The six primitives that go into the construction of a triangle have a very direct relationship with each other. In the figure here, the edges and vertexes in blue are the variable primitives, and they control the value of those primitives opposite to them. So in each case only three of the six primitives need to be under our control in order to produce any triangle what so ever. Because we are interested in motion, and motion can not be perceived or calculated without a reference, we can understand that we need at least two vertexes to start diagramming an actuated component. 4.9 GEOMETRIC CONSTRUCTION So, we can say that these two vertexes will be in control within the module. Because we want this module to be structural, we need to

Cases of Control

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introduce more vertexes to begin to define the necessary system of triangulation. Because we need to maintain the structural integrity of the module as it undergoes motion, we need the location of the additional vertex to be informed by the positions of the other two. From the two known vertexes, we can locate two equidistant curves. At the intersection of these curves, the other points needed to generate an internally structural system in which the edge elements are located to connect each vertex. Each edge element here is equal in length. From this humble starting point, we can subject this basic modulus machine to various permutations and organize it within different configurations. The permutations of interest are according to how the module is affected by the application of motion. As mentioned above, there are only two types of motion. Applying these motions to the two points in which we began our geometric construction presents the first division of faculties. A modulus machine whose core vertexes are

moving linearly will cause the shape of the construction to deform. As the core vertexes move away from one another, the construction will flatten. As the core vertexes move closer to one another, the opposite will happen. A modulus machine whose core vertexes are moving angularly will not cause the shape to deform, but will enact a reaction external to itself. When connected to other like modules, this motion will cause the configuration to adjust. A variant on these constructions were produced according to the introduction of a third controlling vertex. The position of this, relative to one core vertex, does not change even as the same motions are applied. To accommodate this type of construction, the edge elements involved must become able to extend and contract. In the linear model of the module, the two components undergo a similar dimensional alteration; the two edge elements here contract and extend at the same rate.

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It was with this exercise that the interaction between the position of vertexes and lengths of edge elements began to surface, and as a result, it seemed possibly beneficial to recognize exactly how many variations could be conceived of if the investigation were to focus on the control of edge elements rather than simply the relative positions of core vertexes. To satisfy this interest, a methodical catalogue was produced. The edge elements in blue are those that would be able to change their lengths, while those donning a tick mark are both fixed and congruent edges. From this collection, two filters were used to identify the most viable combinations to test. The first filter was the ratio between static and dynamic edges. More important than making the construction transformable is having it not collapse, and it is to this end

that it seemed prudent to limit, if only for the time being, the investigation to those constructions whose fixed elements out number those able to extend and contract. The second filter is to identify the combinations that are symmetrical. I was able to understand the importance of this trait from the earlier studies. In addition, this quality lends it self well to Euclidean calculations.

Linear Machines seam

In the angular model, the same two components undergo an inverse dimensional alteration; as one edge element extends the other contracts.

It is in this way that three combinations were separated from the collection. We have already constructed two of these combinations through the consideration of the geometric construction at the vertex-level of relationship. However, one slipped past that initial investigation. I felt it was necessary to step back and consider the underlying logic to the new combination. As we can see, the results are effectively the same when either a linear motion or an angular motion is applied to the controlling vertexes. For this reason, we can consider them the same.

Angular Machines

Moving these machines into three-dimension

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ZERO Variable Edges

ONE Variable Edge

TWO Variable Edges

THREE Variable Edges

FOUR Variable Edges

FIVE Variable Edges

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4.10 CONFIGURATIONS OF GEOMETRIC CONSTRUCTIONS Each of these three-dimensional modulus machines were placed within a larger assembly to test what effect they might produce when in motion, and how particular configurations transmit this motion through out. There were two planes of reference used to conceive of these configurations; a vertical plane and a horizontal plane. The connections in each configuration are imaged to be located at the extreme points of their protrusions.

Looking with reference to a vertical plane and at the module along its main axis, there are a limited amount of configurations possible. Given that each module has only six protrusions, there seemed to be only three possible configurations; admittedly, the stability of only two can be certain from a geometric stand point. In these configurations, all the modulus machines are oriented in the same direction.

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was done by simply repeating the construction about the main axis at intervals of 60 degrees.

Looking at the module perpendicular to its main axis, we can play with the configurations to see what could be possible, however none of these are inherently stable. In these configurations, all the modulus machines oscillate in orientation according to a regular pattern.

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MODULUS MACHINES

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REFERENCES

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Christopher Alexander, “From a Set of Forces to Form” Man Made Object (New York: George Braziller, 1966) Massimo Banzi, Getting Started with Arduino (Cambridge: O’Reilly, 2009) Philip Beesely, Hylozoic Ground (Cambridge: Riverside, 2010) David Benjamin and Soo-in Yang, Life Size (New York: GSAPP, 2006) Henri Bergson, Matter and Memory (London: George Allen and Unwin Limited, 1962) Max Bill, “The Mathematical Way of Thinking in the Visual Art of Our Time” The Visual Mind (Cambridge: MIT Press, 1993) Robert M. Brown, 104 Projects for Electronic Gadgeteers (Blue Ridge: Tab, 1970) David Carroll, States of “Theory” (New York: Columbia, 1990) A.D. Coleman, The Digital Revolution (London: Oxford, 1998) Francis MacDonald Cornford, Plato’s Cosmology (Indianapolis, Hackett, 1997) H.S.M. Coxeter, Regular Polytopes (London: Methuen, 1948) Euclid, Elements trans. Dana Densmore (Ann Arbor: Green Lion, 2002) Michael A. Fox and Miles Kemp, Interactive Architecture (New York: Princeton, 2009) Ben Fry, Visualizing Data (Cambridge: O’Reilly, 2008) Mathew Fuller, Media Ecologies (Cambridge: MIT, 2005) R. Buckminster Fuller, Synergetics (New York: MacMillan, 1975) Deborah Gordon, Ants at Work (New York: Norton, 1999) Usman Haque, “Architecture – Interactive – Systems” AU: 149 Tom Igoe and Dan O’Sullivan, Physical Computing (Boston: Thompson, 2004) Steven Johnson, Emergence (New York: Scribner, 2001) Caroline A. Jones, Sensorium (Cambridge: MIT, 2006) Robert Kronnenburg, Transportable Environments 2 (London: Spoon, 2003) M.C. Mozer, “Lessons from an Adaptive House” Smart Environments, Technologies, Protocols and Applications (Hoboken: Wiley and Sons, 2005)

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Nicolas Negroponte, The Architecture Machine (Cambridge: MIT, 1973) ACTUATING GEOMETRIC PRIMITIVES

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Nicolas Negroponte, Soft Architecture Machine (Cambridge: MIT, 1975) Joshua Noble, Interactivity (Cambridge: O’Reilly, 2009) Kas Oosterhuis, “Trans-port Muscle at Architecture’s Non-Standars” (2003) http://www. oosterhuis.nl. (accessed December 2010) Plato, Timaeus trans. Desmond Lee (London: Penguin, 1965) Charles Platt, Make: Electronics (Cambridge: O’Reilly, 2009) Casey Reas and Ben Fry, Processing (Cambridge: MIT, 2007) Casey Reas and Ben Fry, Getting Started with Processing (Cambridge: O’Reilly, 2010) Casey Reas, Chandler McWilliams and LUST, Form + Code in Art and Architecture (New York: Princeton, 2010) Jesse Reiser and Nanako Umemoto, Atlas of Novel Tectonics (New York: Princeton, 2006) Willoughby Sharp, Kineticism (Mexico, 1968) Paul Scherz, Practical Electronics for Inventors (New York: McGraw, 2007) Peter Selze, Direction in Kinetic Sculpture (Berkley: UC Press, 1966) Tristan d’Estree Sterk, “Shape Control in Responsive Architectural Structures: Current Reasons and Challenges.” 4 World Conference on Structural Control and Monitoring (2006) Michael Sullivan, Algebra and Trigonometry (New Jersey: Princeton Hall, 2002) Kostas Terzidis, Expressive Form (London: Spoon, 2003) D’arcy Wentworth Thompson, on Form and Growth (Cambridge: Cambridge, 1961) Norbert Wiener, Cybernetics (Cambridge: MIT, 1948) Meejin Yoon and Eric Howeler, Expanded Practice (New York: Princeton, 2009)

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