UNIVERSITY OF CINCINNATI

Date: 28-May-2010

I, Peter Nevins McBride , hereby submit this original work as part of the requirements for the degree of: Master of Architecture in Architecture (Master of) It is entitled: BIOMIMETIC CONSTRUCTS

HIGH-TECHNOLOGY TOWARDS ECOLOGICAL DESIGN

Student Signature: Peter Nevins McBride

This work and its defense approved by: Committee Chair: Nnamdi Elleh, PhD Nnamdi Elleh, PhD

Rebecca Williamson, PhD Rebecca Williamson, PhD

5/27/2010 539 i BIOMIMETIC CONSTRUCTS HIGH-TECHNOLOGY TOWARDS ECOLOGICAL DESIGN

iii BIOMIMETIC CONSTRUCTS HIGH-TECHNOLOGY TOWARDS ECOLOGICAL DESIGN

PETER NEVINS MCBRIDE MASTERS THESIS v

BIOMIMETIC CONSTRUCTS HIGH-TECHNOLOGY TOWARDS ECOLOGICAL DESIGN

[BY] Peter Nevins McBride

A Thesis Submitted to The Division of Research and Advanced Studies in partial fulfillment of the requirements for the degree of:

Master of Architecture` University of Cincinnati College of Design, Architecture, Art & Planning School of Architecture & Interior Design

Committee Chairs: First Chair: Nnamdi Elleh, Ph.D. Second Chair: Rebecca Williamson, Ph.D. Third Chair: Brian Timothy Ringley CONTENTS ToC vii

Abstract...... ix Introduction...... xi Thesis Document

[1.0] BIOLOGY: A Biomimetic Imperative...... 003 1.1: Shortcomings of our Built Environment 1.2: Biomimicry 1.3: From Organic to Biomimetic 1.4: Morphogenesis and the Mathematics of Nature 1.5: Biological Structure 1.6: Digital Tools for Biological Optimization

Conclusion...... 068

List of Images...... 072

Bibliography...... 076 ABSTRACT ABS ix

[0.1] ue to advances in large-scale rapid-prototyping Dtechnology, the terms ‘standard’ and ‘non-standard’ are increasingly being challenged in the lexicon of modern construction. Driven by the ever-expanding versatility of digital software, architects find themselves in a position of greater design freedom and less constraint from modular building materials, thus allowing for a paradigmatic shift towards an architecture focused on performative characteristics. The following investigation will engage these contemporary technologies to mimic basic processes and morphologies found in our natural environment that account for its inherent abilities of material conservation and systems integration. Software scripting techniques and research into the fields of biological morphology and behavior, digital design, and rapid-manufacture direct the creation of a morphogenetic generative process that decreases material usage within architectural structures and allows for informed speculation into the future of systems integration and the construction automation. INTRODUCTION

“This century is going to be about biology”

-Wiscombe, Tom. “Emergent Processes.” Web. 10 September. 2009. INT xi

Introduction

[0.2] o matter how far we trace historical lineage Nof architectural design, a direct, arguably genetic, attachment to the natural world can be observed. From Laugier’s hut to Palladio’s villas to Sullivan’s skyscrapers, all architecture is influenced by nature in one form or another. However, until relatively recently, architectural interpretations of this biological genius and beauty has been solely relegated to either the formal, the spatial, and/or the ornamental. Our society has come to a precipice concerning the dire state of our current global climate, and this thesis posits that the built environment needs to look beyond issues of aesthetics, and learn to behave more like living organisms, specifically in their inherent proclivity for material conservation, systems integration, and self-assembly. INT xii

The following investigation acts as a knowledge base for the speculative proposal of a biomimetic model for architectural optimization. The vast disconnect between architecture and the natural world are readily apparent, and this thesis work asserts that high-technology, specifically in the fields of computational design and computer numerically-controlled (CNC) manufacture, can function to bridge this gap. Though technical at times, this research document lays the groundwork for speculation into the future of performative architecture and construction methodologies and for the creation of a bio-inspired, experimental, and algorithmically-driven model for structural design that boasts significant material savings through its mimicry of plant cell morphology.

Chapter One, entitled ‘A Biomimetic Imperative’, begins covering the general waste and over-consumption abundant within our built world and lays out a broad argument for a biomimetic path towards sustainability and for the usefulness of thinking of architecture in terms of how it can function more like a plant. It posits that buildings should not be considered a single entity in itself, but as an integral part of a larger integrated collection of systems, in which all outputs of one system or process act as inputs for another. It continues with a further investigation into the growing field of biomimicry and a brief dicussion on the available technologies that have come out of biologic study. From there it moves on, to discuss how the natural world has been exploited in architectural design largely for its aesthetic appeal, INT xiii

rather than its sustainable behavior. Lastly, the chapter looks into the math of natural morphogenesis and how the complex morphologies inherent to many biological organisms are driven by relatively simple rule systems. This serves to make the argument that efficiency and complexity aren’t necessary mutually exclusive and lays out rule system that will later act as the basis for the thesis projects’ structural armature.

Chapter Two, entitled ‘Computational Design’, acts as the knowledge base as well as the justification for the digital translation of biological rules into computational script or code. It begins with a discussion of the modern notion of the ‘Digital Tectonic’ and how digital architecture is more concerned with the dynamism of topology than the constraints of typology. The writing then covers relatively popular methods in which progressive designers are using the this dynamism and the iterative abilities of the digital to take on the topic of sustainability. This section sets the stage for a discussion on a multitude of tools and techniques available to the digital designer, with an obvious emphasis on the ones that exceedingly lent to the creation of my final process and building. Ultimately, chapter two ends with a thorough description of the translation of specific biological rules into a dynamic script and the employment of these rules towards the creation of a bio-inspired truss.

The third chapter, aptly called ‘Future of Construction Technologies’, serves to layout research on additive manufacturing methodologies, and how these INT xiv

technologies can be harnessed allow for a building-wide system integration. To preface this exploration I briefly review the history of CNC Technologies, and survey the current machines at work in the realm of Rapid-Prototyping and Rapid-Manufacture. From there, the discussion covers current research that is going on in the field of additive manufacturing and the concerns that one must take into consideration when traversing from small-scale rapid- manufacture to large-scale rapid-construction. Using the groundwork laid by the current researchers and companies involved in the large-scale additive manufacturing realm, whether they are working towards construction efficiency, building performance, or formal freedom, this chapter concludes by covering the many performative and formal advances that will come out of rapid-construction and laying out an informed speculative model for an automated additive construction process.

The final chapter, ‘Towards Biominetic Architecture’, linearly lays out the inputs and the processes involved in the creation of an urban headquarters for the Biomimcry Guild, a company involved in the integration of biomimetic technologies into our modern industry. Using the processes and technologies laid out in the three previous chapters, a design is created that, on many levels, attempts to bridge the gap between the biological world and architecture.

Simply put, the following thesis investigation searches for new methods of structural optimization in architecture. Existing in a disciplinary ‘grey-area’ at INT xv

the intersection of computer science, biology, and architecture, this research document will inform a biologically-inspired, algorithmically-driven structural system and speculate into the future of the construction process.

This investigation is significant for a handful of key reasons:

1. Architecture can benefit from 3.8 billion[ i ] years of evolutionary research and development. Looking to the biological world is a highly logical path towards sustainability, and architecture, with its predilection towards the synthesis of disparate fields of study, seems like a very logical place to institute these lessons. Though analogies only go so far to define an argument, architecture and biology, when reduced to their basic ideals, are not all that dissimilar - both are materially and organizationally based; both are concerned with morphology and structuring, and both are the product of multiple simultaneous systems. Through transformation of solar energy, air purification, integration of multiple complex systems, and general self-sufficiency, plants have been doing for millions of years, what the current sustainability movement hopes to do for our built environment. However, plants manage to accomplish this feat using only the most basic and inert earthly materials. The need for this investigation and ones like it stem from the deficient state of our natural environment today. If humankind ever hopes to reach a state of ecological equilibrium and stasis within its

i. Biomimicry Guild - Innovation Consultancy for Bio-Inspired Design. (http://www. biomimicryguild.com/indexguild.html) INT xvi

fragile ecosphere, the way we inhabit the planet will need to mimic the cradle-to-cradle cycling of energy and resources of the natural world.

2. Digital design allows for more precise modeling of complex systems. Digital techniques have proven themselves in the past decade to allow for a more precise, direct, and useful translation of metadata, or data that comprises data, into architectural application. This is most prominently seen in the use of environmental data to inform building facade strategies and forms, and this translational proclivity is a major asset in the ultimate goal of making the architecture function more like that of a plant.

3. Modern Construction is inherently wastetful. This study is important to discuss the future of construction methodologies. It is the place of the young designers to consistently challenge the current form of architectural and construction praxis. Speculation into the future of construction is important because construction methodologies are so closely intertwined with architectural design. Similar to the way in which progressive designs drive the creation innovative construction solutions, the feasibilities, economies, and materials involved in construction tend to drive the way in which buildings are designed. This study lays the groundwork for speculation into the future of construction processes, and proposes an automated model that minimizes material waste, allows for multi-system integration, and has the ability to efficiently and economically deal with complex and variable geometry. Moreover, with the capabilities of construction techniques and INT xvii

technology quickly closing the gap with those of digital design software, the economic incentive to continue building with standardized materials fading. We are approaching a new era in architectural history, in which complex geometries will be able to be constructed by the same means and for the same cost as Euclidian geometries. These new technologies will open up endless possibilities for architectural design, but more specifically, it will greatly increase designers ability to optimize structural system through morphological processes that were formally constrained by standardized construction methodologies.

The ultimate goal of this thesis is to transform the currently tenuous and wholly analogical relation between nature and architecture into an operative system and use that system to produce a biologically-inspired structural armature that can be constructed with less overall material compared to traditional construction methods. In the process, it hopes to shed light on the endless potential that natural precedent, digital design, and construction automation hold for the progression of sustainable architecture. We must draw our standards from the natural world. We must honor with the humility of the wise the bounds of the natural world and the mystery which lies beyond them, admitting that there is something in the order of being which evidently exceeds all our competence. w

-- VACLAV HAVEL, president of the Czech Republic 2

BIOLOGY A BIOMIMETIC IMPERATIVE

11.1 Shortcomings of our Current Built Environment 1.2 Biomimicry and Biomimetic Technologies

1.3 From Organic to Biomimetic

1.4 Morphogenesis and the Dynamics of Growth

1.5 Biological Structural System 1.1 1.1 4

Shortcomings of our Current Built Environment [1.1 ] he change can be felt throughout the design world. TA significant shift - one towards an architecture of optimization - is beginning to affect the way in which architects are positioning their practices. As an industry, we have adjusted our lenses to focus primarily on the performative qualities of architecture and momentarily put aside our shallow preoccupations with style and appearance. This paradigmatic metamorphosis aims to locate architectural discourse within a more objective framework where efficient use of resources supersedes the aesthetic indulgences of works that previously came under the broad heading of Postmodernism[ i ] . However, following the old i. Leach, Neal. “Digital Morphogenesis.” AD: Architectural Design. 79.1 (2004): 32-37. Print. (34) 1.1 5

Einsteinian adage, ”No problem can be solved from the same level of consciousness that created it”, many posit that simply readjusting and revising our current methodologies of design and construction will fall short in achieving the penultimate goal of a wholly sustainable built environment. Lasting change is going to necessitate a bottom-up transformation of the ways we think about architecture and architectural praxis.

We, as a species, have proven time and time again our limitless ability for waste and consumption. Most egregious is current state of our built environment. Though oil executives and Chinese fishing fleets are consistently being vilified by the media for the damage they have wrought on our environment, it is our buildings that are doing the major damage. Architecture’s seemingly genetic connection to archaic ideals from its industrialized past has left our generation with a contaminated present. With modern construction methods creating an average of 2.5 pounds of solid waste for every square foot of newly completed floor space and buildings accounting for sixty percent of total consumption of electricity[ i i ] , it is obvious that changes in our built environment are imperative to the

ii. LEED Reference Guide: New Construction & Major Renovations, v2.2. U.S. Green Building Council. Washington, DC: 2006. 1.1 6

success of future generations. And though there has been a major push for ‘green’ technologies in recent years, it is readily apparent that many of them are just re-branded versions of the same technologies that brought us into the current environmental crisis.

A common example is that of the compact fluorescent lamp (CFL) Figure( 1). This wonderful technology boasts a longevity several times greater than that of its predecessor, the incandescent, and consumes a quarter of the electricity. However, CFLs, akin to the many short-term ‘Band-Aid’ techs that FIGURE 1 : Compact have been forced upon us by popular media and by ill-informed legislation, Fluorescent Light Bulb. simply function to shift the way we are polluting rather than solving the problem of pollution. Bills passed by the Senate in 2007 announced the complete phase out of incandescent light bulbs in the United States by 2012[ iii ], however no attention was paid to updating our antiquated electrical platforms to account for the truncated amperage needed to support this new bulb. Due to this government oversight (and/or corporate calculation), every consumer retail unit has been married to its very own electronic ballast to moderate amperage to the fixture. Consequently, the much improved life span and substantial energy reduction of a CFL is quickly offset by the amount of embedded energy used in the manufacturing

iii. FIX!!!! Library of Congress - http://thomas.loc.gov/cgi-bin/bdquery/ z?d110:h.r.00006: 1.1 7

FIGURE 2 : CFL ballast. process of the product’s ballasting element.[ i v ] Moreover, this ‘upgrade’ is proving to be far more noxious than its recycled cardboard packaging would lead one to believe. Landfills are being inundated with abandoned incandescent bulbs, a portion of which were brand new or functioning, to make way for the next generation of ‘low-energy’ lighting. Similar to the predicaments caused by our ‘e-waste’, the lack of federal recycling regulations[ v ] has relegated our landfills as the de facto storage facility for defunct CFLs[ v i ] , leading to the needless waste of solid-state ballasts (Figure 2) (the life solid-state electronics is relatively inexhaustible) and to the leaching of poisonous chemicals, including a significant amount of the notoriously deleterious neurotoxin, mercury, into our earth, our water table, and our air. However, compact fluorescent bulbs are not the problem. Though they are simply an example of how the promise of cutting-edge

iv. Bram, Thursday. “CFL Bulbs: Greener than most, but not Green Enough”. WiseBread. com. (http://www.wisebread.com/cfl-bulbs-greener-than-most-but-not-green-enough) v. At this point, only nine states in the U.S. have reasonable CFL recycling programs. vi. Bram, Thursday. “CFL Bulbs: Greener than most, but not Green Enough”. WiseBread. com. (http://www.wisebread.com/cfl-bulbs-greener-than-most-but-not-green-enough) 1.1 8

‘green’ technologies can be sullied due to a lack of substantial integration and transformation on multiple levels. Ideally, buildings should be designed with efficiency as a primary consideration from the bottom up, as opposed to the all-too-common practice of pasting green technologies on at the end of the schematic phase of design realization.

We, as architects, are just beginning to see the economic, social, and environmental benefit of structuring design process within a framework of energy and material conservation, and in doing this, we are abstractly mimicking the way the natural world has gone about designing for billions of years. Much like the evolutionary banishment into the realm of extinction that was wrought upon organisms with shortcomings in the field of conservation, this recent paradigmatic shift in architectural praxis will certainly result in fewer and fewer designs that do not articulate a performative intent to be realized. Similarly, many professionals have begun searching for technological and scalable abstractions or replications for naturally occurring solutions to deficiencies in their industries. The mining of nature’s relatively untapped evolutionary wisdom for applicable use within our industrial world has recently been filed under the apropos heading of ‘Biomimicry’, and the resultant bio-inspired technologies are allowing many to increase efficiency and do so in a highly sustainable manner. 1.1 9

FIGURE 3 : Barbed wire. FIGURE 4 : Rose thorn. 1.2 10 [COMP]

Biomimicry and Biomimetic Technologies [3.5] iomimicry, at its simplest, is the emulation of Bbiological forms and processes. The etymology is derived from the Greek words ‘bios’, meaning life, and ‘mimesis’, meaning imitation[ vii ]. However, biomimicry does not entail solely the direct mimicking natural forms and processes, but it carries with it the connotation of natural abstraction. Much in the way barbed wire can be considered a manmade cognate of a rose thorns, biomimetic techs are not meant to be an exact copy, but reductive abstraction of a useful form or process found in nature.

Pioneer and champion of the Biomimetic Movement, and, by popular belief, the originator of the term ‘Biomimicry’, biologist Janine Beynus has been

vii. Beynus, Janine. Biomimicry: Innovation Inspired by Nature. New York: HarperCollins Publishers, Inc., 1997. 9. 1.2 11

touting the benefits of biologically-inspired design since the early 1990s.[ v i i i ] Her influential book Figure( 5), Biomimicry: Innovation inspired by Nature, has positioned her as the preeminent authority on the subject, led to the creation of two separate companies, and paved the way for more than a decade of influential and insightful dialogue concerning the way in which we, as a society, should frame our understanding of sustainability and the natural world.

She makes the assertion that evolution has left us with nature as the best FIGURE 5 : Cover of solution to many of the problems we face within our industrialized world. A Benyus’ Biomimicry: Innovation Inspired by few of the principles of biological life described in Beynus’ book are that it Nature self-assembles, it minimizes material waste, it adapts to cycles, it is always locally appropriate, it uses free energy, it can evolve, and it uses non-toxic materials[ i x ] . She follows the mantra that humans should see nature as a model, as a measure, and as a mentor[ x ] . She claims that this new type of sustainable design can be applied everywhere, from the materials industry to computer engineering.

The popularity of her book led to ultimately creating a company based

viii. Interview: Janine Beynus. (http://www.cnn.com/2008/TECH/science/07/04/ beynus.interview/index.html) Accessed Feb 5, 2010. ix. Beynus, Janine. Biomimicry: Innovation Inspired by Nature. New York: HarperCollins Publishers, Inc., 1997. 95-145. x. Beynus, Janine. Biomimicry: Innovation Inspired by Nature. New York: HarperCollins Publishers, Inc., 1997. 13. 1.2 12

around these concepts which she called The Biomimicry Guild (Figure 6). Beynus refers to the company as a chance to ‘bring biologists to the design table’, and the company has thus far FIGURE 6 : Biomimicry Guild Logo been rather successful. All interested parties often gain insight from the perspectives of other disciplines. On a basic level, The Biomimicry Guild acts as sustainability consultancy, but their main goal is to show major industries that there are often multiple solutions to a problem and that it is often the case that some organism in our natural world has managed to solve it already. By acting as a conduit between these large corporations and the, often small, up and coming biomimetic technology firms, she serves to shed light on the wonderful technologies that are currently in production and make it harder and harder to ignore the significant profit stream coming out this small yet burgeoning collection of products and processes inspired by nature.

Many biomimetic technologies are already on the market or are being tested for their feasibility within our industrialized society and they are often more efficient and far less environmentally destructive solutions than had been previously considered. During a lecture at the TED Conference in 1.2 13

2005, Beynus uses her experience with a group of engineers from an urban infrastructure company to illustrate the notion that humans are the only creatures that have come up with solutions to problems that harm the environment in which they live. She touts the undeniable truth that “life creates conditions conducive to life”[ xi ], and goes onto chronicle her experience with these civil engineers that decided to come along on a Caribbean retreat hosted by the Biomimcry Guild in hopes of finding more sustainable solutions to some of their pressing problems by looking to biology. She recalls that one of their main problems was ‘scaling’, or the aggregation of large calcium deposits that occurred within most of the plumbing in their city. Their current “solution” involved excavation of clogged conduits and either the application of a noxious metal stripping cocktail or replacement of that section of pipe. Once they brought up this problem, Janine went onto describe how their problem had most likely been solved millions of years prior by the common abalone. Abalones, she explicated, self-assembled shells of a material called nacre, often referred to by its pseudonym, ‘mother of pearl’. Nacre is made up of calcium carbonate, the same mineral that was causing their scaling problems. She explained that shellfish excrete a protein template that attracts and crystallizes calcium in the seawater. The engineers quickly became more interested in the discussion and inquired, “Well, if these organisms are constantly crystallizing calcium from seawater,

x i . Beynus, Janine. “Biomimicry in Action.” TEDGlobal 2009. TED©. Oxford, UK, July 2009. (http://www.ted.com/talks/janine_benyus_shares_nature_s_designs.html) 1.2 14

why are their shells not infinite in size?”. Much as the abalone created a protein that stimulated the synthesis of calcium carbonate, at the end of the creature’s growth cycle, it secretes a protein that blocks further mineral accumulation. She goes on to tell them that a company has recently come to market with a product that mimics the function of this protein in order to prevent mineral crystallization, and thus corrosion[ xii ], in industrial machines and it does so in an environmentally-friendly way[ xiii ].

Biomimicry opens the door to technologies that have been proven ‘sustainable’ simply by the very existence of their precedent organism. We are at the beginning of a new era in that will redefine how we view and value nature. This century will bring greater import to what society can learn from nature instead of focusing solely on what society can extract from it. Though there is still an endless amount of natural wisdom that science and industry has yet to harness, there have been many inspiring advancement in the field of biomimetic technologies. By utilizing high-technology, we can begin close the seemingly irreparable chasm that has formed between modern society and the natural world though a close understanding of its inner working. The following only covers a handful of the many biomimetic technologies currently on the market or in late stages of development, but

xii. NanoChem Biopolymer Products. Nanochemsolutions.com. (http://www. nanochemsolutions.com/biopolymer/products.shtml) Accessed March 6, 2010. xiii. Beynus, Janine. “Biomimicry in Action.” TEDGlobal 2009. TED©. Oxford, UK, July 2009. (http://www.ted.com/talks/janine_benyus_shares_nature_s_designs.html) 1.2 15

it briefly mentions most of the ‘big ideas’ or areas of innovation that are currently being informed by biology. Each tech is not individually vetted for its usefulness within the realm of architecture, though it is very easy to imagine how they will one day fuel the future of sustainable design.

One process that many companies have begun to study is nature’s ability of self-assembly. The aforementioned material nacre (Figure 7), found primarily in the shells of mollusks, is a naturally occurring ceramic that has twice the density of our manmade ceramics, and is manufactured and hardened in seawater, rather than in the extreme heat of a kiln. Companies have begun to mimic this process on a small scale by inducing self-assembly of a thin, high density ceramic coating to form on electrical components at assembly using only the energy of evaporation[ xiv ]. Self-assembly has been looked at by a handful of communications companies, as well. Creatures have been discovered that are able to self-assemble highly complex communications FIGURE 7 : Abalone shells washed up on the components out of inert materials found in their salt water environment. beach. Scientists have found that the brittle star is able to grow an almost distortion free lens as part of its exoskeleton, a feat that manmade technologies have never been able to do with a far larger palette of materials at hand

xiv. Beynus, Janine. “Janine Benyus shares nature’s designs.” TED2007. TED©. Long Beach, California, 2007. (http://www.ted.com/talks/janine_benyus_shares_nature_s_ designs.html) 1.2 16

(Figure 8).[ x v ] Moreover, biologists have become, appropriately, very interested in a species of sea sponge that lives in the pacific that is able self-assemble a natural strands of fiber optics that transmit a clearer signal than our currently available

FIGURE 8 : Brittle star. technology and can be tied into a knot FIGURE 9 : Basel Fibers without breaking or distorting said signal of Sea Sponge. (Figure 9).[ xvi ] It is amazing to find these technologies being assembled in the bodies of relatively ‘simple’ creatures out of inert material found in sea water, when the man made cognates necessitate a thoroughly complex manufacturing process that involves the use of toxic chemicals. We know that there are only four polymer fibers that exist naturally: cellulose in plants, collagen in animals, chitin in insects and crustaceans, and silks in spiders’ webs”[ x v i i ] , yet modern manufacturing utilizes hundreds of different polymers, most of which eventually find their way into a landfill. By considering the architectural implementation of

xv. Beynus, Janine. “Janine Benyus shares nature’s designs.” TED2007. TED©. Long Beach, California, 2007. (http://www.ted.com/talks/janine_benyus_shares_nature_s_ designs.html) xvi. Beynus, Janine. “Janine Benyus shares nature’s designs.” TED2007. TED©. Long Beach, California, 2007. (http://www.ted.com/talks/janine_benyus_shares_nature_s_ designs.html) xvii. Joshi, Atri. Emergence in Architecture. Diss. University of New Delhi, 2006. Print. 72. 1.2 17

nature’s materials and methods of self-assembly, we are steering our built environment towards a sustainable future.

Another characteristic of many organisms that companies have started to look into is the ability to use carbon dioxide as a feedstock. In the natural world, CO2 is not considered the global-warming cause and poisonous off-gas that its name connotes today. Many organisms, most notably plants in their process if photosynthesis, use CO2 as a feedstock for biological processes. It is a very logical for companies to be looking for different ways of dealing with this gas rather than just pumping it into the air or into fissures in the earth. These solutions seem to be coming from the same train of thought that led to the dumping of our garbage into the middle of the ocean that continued up until twenty years ago. Currently there is a company called Calera© that claims, “We make coal and natural gas power plants and cement plants cheaper and cleaner than solar and wind by reducing carbon by more than 100%, in a scalable and economic way”[ x v i i i ] , and they are managing this feat by mimicking a process that coral polyps have implemented for hundreds of thousands, possibly millions, of years. Similar to the way in which coral pulls carbon dioxide out of the water in order to build its a calcium carbonate skeleton, Calera© is using CO2 siphoned from the burning of coal and natural gas and sequestering

xviii. Calera: Sequestering CO2 in the Built Environment. Website. (http://www.calera. com) Accessed 4/20/2010. 1.2 18

it by using in the creation of cement.[ x i x ] Companies such as this, are paving the way for a sustainable human ecology, in that the outputs of one system (energy production), act as the input for another system (building materials), and thus bring us closer to a systemic cyclical methodology for the future. These biomimetic technologies are very important due to the fact that using carbon produced by a separate process as an input makes them more than carbon “neutral”, it makes them carbon “negative”. Carbon sequestration technologies that use carbon dioxide as a feedstock are going to play a large role in our societal push for ‘clean’ energy.

The shapes and forms found in nature have begun to inform biomimetic products in recent years. One company has mimicked the geometry of the bumps on a whales fin because they have proven to make them FIGURE 10 : Whale fin. FIGURE 11 : Bio-inspired more aerodynamic, increasing the efficiency turbine prototype. of their wind turbines.[ x x ] (Figure 10 & 11) Another company has started producing countertops for hospitals that mimic

xix. Beynus, Janine. “Janine Benyus shares nature’s designs.” TED2007. TED©. Long Beach, California, 2007. (http://www.ted.com/talks/janine_benyus_shares_nature_s_ designs.html) xx. Beynus, Janine. “Biomimicry in Action.” TEDGlobal 2009. TED©. Oxford, UK, July 2009. (http://www.ted.com/talks/janine_benyus_shares_nature_s_designs.html) 1.2 19

sharks skin, for studies have shown that the minute ridges that exist on the rough sharks scales do not collect bacteria, thus, eliminating the need for antibacterial soaps.[ x x i ] Moreover, surface materials and paints are now available that mimic the surface geometry of the lotus leaf that causes the surfaces to become self-cleaning.[ x x i i ]

Along with solar cells that function like leaves and structural materials that can self-heal when they develop cracks, these are just of handful of the many promising technologies that are under development, but it is easy to see how these technologies will play a crucial role in making our lifestyles and architecture more sustainable. Most notably, biomimicry offers a new way for us to think about how we can design our built environment. It has become part of the accepted wisdom to say that the twentieth century was the century of physics and the twenty-first century will be the century of biology[ x x i i i ] , but it will be the role of the architect to delineate how biological lessons are translated into architectural form and whether or not they will lead towards a sustainable building stock in the future. Barring a few wonderful exceptions, historically we have seen natural forms used in architecture solely for its their ornamental beauty. However, we have

xxi. Beynus, Janine. “Biomimicry in Action.” TEDGlobal 2009. TED©. Oxford, UK, July 2009. (http://www.ted.com/talks/janine_benyus_shares_nature_s_designs.html) xxii. Beynus, Janine. “Biomimicry in Action.” TEDGlobal 2009. TED©. Oxford, UK, July 2009. (http://www.ted.com/talks/janine_benyus_shares_nature_s_designs.html) xxiii. Freeman Dyson, ‘Our Biotech Future, 2007 1.2 20

reached a plateau of technological advancement in which designers can begin to speculate how the built structure and architectural design can become more efficient by using nature to inform the way they are designed and the way they function. Respected architectural theorist Neal Leach claims that “Biomimetics - the study of what we can learn by replicating the mechanisms of nature - has...emerged as an important field of research.”[ x x i v ] If we hope to one day reach a level equilibrium with our natural surrounds and our planet, it is imperative that architectural design embrace this new functional way of looking at our natural environment. Architecture must look beyond its preoccupation with the aesthetic beauty of nature, and move its focus to its ability to sustain life.

xxiv. Leach, Neal. “Digital Morphogenesis.” AD: Architectural Design. 79.1 (2004): 32-37. Print. 35. 1.2 21 1.3 22 [BIO]

From Organic to Biomimetic [3.5] istorically, nature has been a fundamental and Hrecurring inspiration for architecture and for centuries the natural world has been used to augment architectural design. However, it is most often used in a strictly formal, ornamental, or metaphorical manner. The type of architecture that employs nature in this way is regularly lumped under the nebulous heading of ‘organic’ architecture. Though the word ‘organic’, as defined in the English language, denotes something characteristic of a living organism, it has been re-appropriated in art and architecture and rarely references anything that is akin to a biological entity. In addition, due to the consequent over-use of the word in the current trend to be ‘green’, its linguistic attachment to nature has become tenuous 1.3 23

at best. In order for architecture to truly connect with the natural world, a new architecture based in the study of biomimetics must be employed. Though nature has been used metaphorically, ornamentally, and formally in ‘organic’ architecture, ‘biomimetic’ architecture will utilize nature as a functional model to progress the overall sustainability of the design.

Frank Lloyd Wright was arguably the most famous architect to use nature as a metaphor for his design process. He proclaimed,

“An Organic Architecture means more or less an organic society. Organic ideals of integral building reject rules imposed by exterior aestheticism or mere taste, and so would the people to whom such architecture would belong reject external impositions upon life as were not in accord with the nature and character of the man who had found his work and the place where he could be happy and useful because of it... beauty seems to have made no sense for long at any time. I believe that time has come when beauty must make sense for anytime. I believe that time has come when beauty must make sense for our time at least... In this modern era Art, Science, Religion - these three will unite and be one, unity achieved with organic architecture as centre.”[ xxv ]

xxv. Wright, Frank Lloyd. Address to the Royal Institute of British Architects. 1939. 1.3 24

Though Wright forecasts a novel utopian future, his ‘organic’ architecture has little to with a real veritable connection to nature. He uses the notion of biology solely as a metaphor to justify his infamous insular design methodologies, rather that coherently making a true connection to biology itself. Though not very apparent in Wright’s proclamation, metaphors can be useful if used correctly. Metaphors allow one to quickly contextualize and familiarize a foreign or complex topic. The first cars were referred to as “horseless carriages” in order frame the strange loud mechanism within general comprehension. Modern computers still today use the terms ‘file’, ‘folder’, and ‘document’ in order to contextualize the concept computer storage. However, too often designers use metaphor as a basis from which to conceptualize a design. There are far too many complex interactions that must be considered to base design decisions off something as intangible and temporal as a metaphor. Especially when proposing an architecture of biology, it is the job of the architect to move beyond the metaphor and ground the project within a framework of objectivity. Killian Axel writes, in an article discussing the validity of models in architecture, that, “scientific processes are crucial in elevating design explorations of complex dependencies over guess work and provide results that can feed into the form and other aspects of architecture. Architectural design needs its metaphors but aspects these metaphors need to be translated into models that inform the architectural process in a much more rigorous and creatively 1.3 25

exciting way”[ x x v i ] .

In addition, the process of mimicking natural forms for the purpose of ornamentation is a beautiful, yet undeniably wasteful way that biology has been (literally) applied to architecture. As far back as the Ancient Greeks, natural forms have been replicated as architectural decoration through painting, relief, and sculpture, of which the most excessive use of biologically-based ornament can be found in the Italian Baroque of the seventeenth century and, even more so, in the eighteenth century Rococo, most notably in Austria, Germany, and France. However, these monuments to the power of religion and government can barely be considered ‘organic’ architecture, for the grandiose decor no more defined the building than icing would define a Regionally Classicistic cake.

However, throughout the eighteenth and nineteenth century, research expeditions began that focused a new lens on nature and would serve as the foundation biological. This empirical research allowed the natural world to be categorized and systematized, as can be seen in Carl Linnaeus’ classification of nature and Darwin’s evolutionary tree of life Figure( 12).[ x x v i i ] The natural sciences began to influence art and architecture as their popular interpretations, such as Ernst Haekel’s Kunstformen der Natur (“Artforms of

xxvi. Abruzzo, Emily, Eric Ellingsen, Johnathan D. Solomon, ed. Models. 306090 11 (306090). New York: Princeton Architectural Press, 2008. Print. 211. xxvii. Ed. Sachs, Angeli. Nature Design. Lars Muller Publishers: Switzerland, 2007. Print. 13. 1.3 26

FIGURE 12 : Darwin’s Nature”) (Figure 13), made them more early sketches of accessible to the masses. “Nature was evolutionary tree. no longer used only as ornament, but as a constituent element in the discovery of form.”[ xxviii ]

Due to the extensive proliferation of the empirical findings of these biological research expeditions, the flowing fluid forms of plants and animals became a the basis for much of the architecture created under the heading of ‘Art Nouveau’. Also, periodically referred to as Decorative Industrialism[ xxix ] when referencing the architectural style independently of the art movement, Art Nouveau employed an integrated and organic vocabulary to an create ornate and expressive designs in which the model of nature, most prominently of the plant world and the dynamics of botanical growth, is highly influential to its thematics. The structural systems, as well as the ornamentation, were often constructed of cast metal and made use of the industrial construction methods

xxviii. Ibid. 13. xxix. Melvin, Jeremy. ...Isms, Understanding Architectural Styles. Universe Publishing: New York, 2006. Print. 89. 1.3 27

FIGURE 13 : Ernst Haekel’s Artforms of Nature. 1.3 28

made popular by the automotive and maritime manufacturing industry[ x x x ] . Composed of iron and steel, this natural ornament could transform seamlessly from decoration to structure, as can be seen in the facade of Sullivan’s Carson Pirie Scott FIGURE 14 : Carson Department Store (Figures Pirie Scott Department 14 & 17), or it can function Store. FIGURE 15 : Paris simultaneously as both decor Metro Entrance. and structural armature, as is FIGURE 16 : Paris Metro Entrance. Detail. the case in Hector Guimard’s famed Parisian Metro entrances (Figures 15 & 16). Other prominent figures in the movement included Victor Horta and Henry van de Velde in Brussels; René Binet in Paris; and

xxx. Melvin, Jeremy. ...Isms, Understanding Architectural Styles. Universe Publishing: New York, 2006. Print. 90. 1.3 29 1.3 30

FIGURE 17 : Carson Hermann Obrist and Pirie Scott Department August Endell in Munich Store. Detail. FIGURE 18 : August (Figure 18) [ x x x i ] .Though Endell. Elvira house. these projects are not Munich, 1897. scientific in method and are solely artistic interpretations of nature, the designs were conceptualized through a close understanding of plant morphology. In this understanding we can begin to move towards a biomimetic architecture. Architecture based in biomimicry similarly calls for an in-depth understanding of biological processes and forms, but it moves beyond that to question how that knowledge can inform sustainability and optimization of a building.

Although, from this era came arguably the first biomimetic architect, Antonio Gaudí. Throughout his illustrious, though limited, collection of works, it is easy to see that Gaudí was influenced greatly by the aesthetics of the natural world. From the ‘tree-columns’ at Parc Güell (Figure 19) to the undulating structure of Casa Batlló (Figure 20), Gaudí’s palette often referenced the

xxxi. Ed. Sachs, Angeli. Nature Design. Lars Muller Publishers: Switzerland, 2007. Print. 46. 1.3 31

FIGURE 19 : Antonio Gaudi. Parc Guell. Barcelona. Detail. FIGURE 20 : Casa Batllo. Barcelona. 1.3 32

natural world in his range of colors, his variability of form, and his almost preternatural understanding of multidimensional geometric logic. Gijs van Hensbergen, the author of Gaudí: A Biography, playfully recounts that the young Antonio, based on his grades from his Catalan elementary school, was a markedly inferior student for someone that was to grow up to be revered for their architectural genius. However, he consistently excelled in mathematics, with quite the proclivity for geometry[ xxxii ]. And although he may not have been privy to the seminal work of D’Arcy Wentworth Thompson[ xxxiii ], a pioneering mathematical biologist that will be covered in Section 1.4, entitled On Growth and Form, he certainly developed a keen understanding of the inherent connection between the structure and form of nature and geometry.[ xxxiv ] His fixation with the natural models of structural efficiency, aesthetics, and composition is well documented. From the beginning of his professional career, Gaudí searched for architectural inspiration in the both the plant and animal kingdoms, as well as “the inorganic realm of crystallography”.[ xxxv ] Though this interest is readily apparent in all his work, it initially manifests itself solely in a formal or a decorative manner that could be considered as artistic abstraction, rather than applying his depth of knowledge in natural morphology as design

xxxii. Van Hensbergen, Gijs.Gaudí: A Biography. Perennial:2003. 24. xxxiii. D’Arcy Wentworth Thompson was a pioneer in the field of mathematical biology and he will be covered in greater depth in Section 1.4. xxxiv. Burry, Mark. “Virtually Gaudí.” Digital Tectonics (2004): 25. xxxv. Burry, Mark. “Virtually Gaudí.” Digital Tectonics (2004): 25. 1.3 33

FIGURE 21 : Antonio Gaudi. The Expiatory Temple of the Sagrada Familia.Barcelona. Interior. 1.3 34

principles. It was not until late in his career that he began work on his final, and most well-known project, The Expiatory Temple of the Sagrada Familia (Figure 22), that his design work can be called ‘biomimetic’. For FIGURE 22 : Sagrada this project, Gaudí wanted incorporate the Familia. Barcelona. spirit of the Gothic, but do so with “freer expression” and truly exultant character. In order to do this, he felt that he had to ‘correct’ what he called the ‘errors’ of Gothic Architecture. By this he meant that he planned to rid his cathedral of the need for flying buttresses, which he referred to as ‘crutches’ (les muletas).[ xxxvi ] In order to take on this take, Gaudí studied tree morphology and gleaned from it an understanding of the growth angle, material distribution, and branching patterns, and he used that knowledge to design columns that draw loading stress from multiple points and transfers it uniformly down a single column (Figure 21). In this one design move, Gaudí was able to take biologic morphogenetic rules and apply them to the design of a column, thus negating the need for extra buttressing in the building. This type of bio-inspired innovation is the basis for Janine Beynus’ biomimicry movement, and is one of many sophisticated design decisions

xxxvi. Masini, Lara Vinca. Gaudí. Hamlyn: New York, 1969. 46. 1.3 35

he made that harnessed the evolutionary genius gleaned from biologic inquiry. Moreover, Gaudí believed in the importance of high technology in the realization of his designs. His design process was characterized by “a continuous and stimulating review and revision”, regardless of the project’s level of completion, periodically altering designs to allow for the incorporation of “current advances in construction techniques and other technological discoveries”[ xxxvii ]. He even went as far to design the towers at the Sagrada Familia in such a way that they could not physically be constructed with the materials available during his lifetime. He speculated that by the time it came to cap the towers, a much higher- strength concrete would be available to form the thin tight curvatures that his elevations called for[ xxxviii ]. Though nature’s predilection for energy and material conservation has become a more popular topic of study in many progressive design firms, this thesis investigation considers Antonio Gaudí as one of the first, if not the first, biomimetic architects.

Possibly due to the consistently mixed reviews of Gaudí’s work or due to the growing separation between divergent fields of study, regrettably, there have been relatively few architects of note since Gaudí’s death that can be considered ‘biomimetic’. However, the few that have followed in his bio-inspired footsteps have been quite influential and have paved

xxxvii. Masini, Lara Vinca. Gaudí. Hamlyn: New York, 1969. 12. xxxviii. Masini, Lara Vinca. Gaudí. Hamlyn: New York, 1969. 15. 1.3 36

the for the formal freedom and the cross-disciplinary interactions that we are beginning to become more common place within many of the more progressive architectural firms.

One of the more influential dominant voices in this group belongs to the German-born architect and structural engineer, Frei Otto. Otto is well known for his prolific research into the use of natural models as a source for architectural and engineering design, while keeping his focus directed on advancing construction applications[ xxxix ]. Much like Gaudí, Otto often employed novel physical-form finding experiments in his research, and has claimed in an interview with the periodical AD:Architectural Design that he uses as many as 200 different physical modeling methods at the University of Stuttgart, where he founded the Institute of Lightweight Structures.[ xl ] Much like the ‘biologists at the design table’ found at the Biomimicry Guild, Otto paired up with a leading biologist and anthropologist and founded a research group called “Biology and Building”.[ xli ] Currently they are looking into ways in which biological structures can inform a structural system that

xxxix. Hensel, Michael and Achim Menges. “Frei Otto” AD: Architectural Design. 74.4 (2004): 18-25. Print. 20. xl. Hensel, Michael and Achim Menges. “Frei Otto” AD: Architectural Design. 74.4 (2004): 18-25. Print. 22. xli. Hensel, Michael and Achim Menges. “Frei Otto” AD: Architectural Design. 74.4 (2004): 18-25. Print. 20. 1.3 37

can resist the “domino effect”[ x l i i ] caused by tearing in skyscrapers. He posits that the skin should carry the loads of the building, much in the way it does in many exoskeletal organisms, and the skin should be comprised of a web of fibers. However, he claims that living skins are very different than the man made skins that are shaped by simple geometries. Irregularity of each element of the skin is the reason it is so resilient to tearing, his research suggests.[ x l i i i ] However, Otto makes certain to convey a lesson similar to that of Beynus’ Biomimicry: Innovation Inspired by Nature, when he warns, “It is necessary that we architects try to understand living nature, but not...copy it. This is one very important task for the future.”[ x l i v ]

As Italian engineer and architect, Pier Luigi Nervi, and American architect and futurist, Buckminster Fuller, had laid the foundation for Otto’s research into the biological-technical structures and material organization, Otto has invested his life’s work into building a solid footing for the new generation of biomimetic architecture.

It is time to begin to design responsibly, and put concerns of building performance before that of building aesthetics. However, in order to bring

xlii. The term ‘domino effect’ in this context refers to the collapse of one floor in a skyscraper resulting in the subsequent collapse of every floor below it. The domino effect caused the ultimate collapse of the World Trade Center. xliii. Hensel, Michael and Achim Menges. “Frei Otto” AD: Architectural Design. 74.4 (2004): 18-25. Print. 25. xliv. Hensel, Michael and Achim Menges. “Frei Otto” AD: Architectural Design. 74.4 (2004): 18-25. Print. 25. 1.3 38

about the creation of a truly biomimetic architecture, there must exist a knowledge of the science as well as a knowledge of the technology that is needed to translate biologic principle into built form. Furthermore, it all must be synthesized within a framework of good design. Arup’s famed structural engineer to the stars, Cecil Balmond, parallels this sentiment in a cross-disciplinary colloquium:

I just want to say that architecture is very interested in biology, it always has been. Biology is intricate at many levels: it’s highly structural, highly dynamic and has all sorts of architectures in it. Nature has always been the paradigm for architecture. It is erroneous to think we can just copy these processes into architecture; we absolutely can’t and it’s dangerous. But having said that, my research is set up in the belief that science has great analytical powers, but architecture has great synthetic powers, powers of synthesis.[ x l v ]

Moreover, the Emergence and Design Group reminds us that we are currently living in a time of high-technology. Our computational power is progressing exponentially; our knowledge of the biological world increasing rapidly; and we find ourselves “...facing a very exciting moment where architecture can leave behind both mindless standardization, fetishism, and current hapless formal caprioles, and instead take on new significance through

xlv. Abruzzo, Emily, Eric Ellingsen, Johnathan D. Solomon, ed. Models. 306090 11 (306090). New York: Princeton Architectural Press, 2008. Print. 130. 1.3 39

intelligence, performance and beauty.”[ xlvi ] Designers have the technology and the skill to durably depart from the fraudulent iconoclastic veneration of nature that ‘organic’ architecture embodies. The future of biomimetic architecture will draw from nature’s ability to optimize and specialize and integrate. The formal nature of architectural structures will be imbued with principles of material conservation, and the construction waste that is customary to the use of standardized materials will be a thing of the past. Form will follow performance, and our built environment will evolve over time into a human ecology in which every architectural structure has an ongoing and continual relationship with every other element that makes up the built environment.[ x l v i i ]

However, Beynus, Otto, and now, Cecil Balmond warn that it is futile and even “dangerous” to try copy biological processes directly into architecture. So the question remains - how can we as designers begin to be able to harness the genius of nature? And though there is not a single answer, nor even a single optimum approach to this question, understanding the rules that govern the organization of biological processes and the mathematical functions that drives natural growth offer much potential for translation

xlvi. Hensel, Michael and Achim Menges. “Designing Morpho-Ecologies: Versatility and Vicissitude of Heterogeneous Space.” AD: Architectural Design. 78.2 (2008): 102-113. Print. 111. xlvii. Abruzzo, Emily, Eric Ellingsen, Johnathan D. Solomon, ed. Models. 306090 11 (306090). New York: Princeton Architectural Press, 2008. Print. 149. 1.3 40

into architectural application. The current study of ‘biological emergence’ proposes that the systematic complexities that we see in nature are often the result of a small set of very simple rules or interactions.[ xlviii ] Following this logic, a specialized study into biological morphology, and more specifically morphogenetics, will be very useful in the process of translating biological wisdom into architectural application for structural design.

xlviii. Johnson, Steven. Emergence: The Connected Lives of Ants, Brains, Cities, and Software. New York: Penguin Books, 2002. Print. 18. 1.4 41 1.4 42 [BIO]

Morphogenesis and the Dynamics of Growth [3.5] orphogenesis means literally, “the beginning Mof shape”[ xlix ], and it is a field of study that how the formal nature of an organism develops over time. Eric Bonabeau defines this topic in his research compendium entitled, “From Classical Models of Morphogenesis to Agent-Based Models of Pattern Formation.” He states, “Morphogenesis is the development of pattern and form in living systems”[ l ] , and, though the topic is considerably broad in scope, it is an important field to Biomimics and it should be an important field to architects. Much of the architectural design process is involved with the generation of xlix. Johnson, Steven. Emergence: The Connected Lives of Ants, Brains, Cities, and Software. New York: Penguin Books, 2002. Print. 42. l. Bonabeau, Eric. “From Classical Models of Morphogenesis to Agent-Based Models of Pattern Formation.” Artificial Life. 3.3 (1997): 191-211. Print. 191. 1.4 43

form. The role of an architect constantly involves the analysis of internal, external, and, oftentimes, metaphysical conditions and arrange them within a logical framework to drive a set of formal decisions. It is rational to posit that designers could benefit from a more clear understanding of how the natural world transforms its conditional inputs into physical form. Neil Leech, an authoritative voice in progressive digital design, affirms the assertion that architectural praxis could be strengthened through the integration of morphogenetic methodologies. “Used initially in the realm of biological sciences, the term refers to the logic of form generation and pattern making in an organism through the processes of growth and differentiation. More recently it has been appropriated within architectural circles to designate an approach to design that seeks to challenge the hegemony of top-down processes of form-making, and replace it 1.4 44

with a bottom-up logic of form-finding.”[ li ]

In short, with the current abilities of architects to impregnate code with multiple generative rules, there has been a large escalation of interest into the mathematical parameters that drive form, rather than the form itself. By breaking down the growth of biological forms into simple genetic rule systems, it makes it possible for designers to translate these rules into digital scripts and thus, an operative process that can inform architectural design.

For centuries, philosophers, scientists, and artisans, alike, have been arguing methods for the articulation and understanding of nature within a mathematical framework. From Plato and Pythagoras up to and through Seurat and Le Corbusier (Figure 25), an almost divine import has been given to the proportions derived from nature. However, the study of morphology inquires into the process involved in the creation of form, rather than the post-rationalization of form itself. A pioneer in the study of plant and animal morphology, poet and writer Johann Wolfgang von Goethe, “defined morphology as the study of forms; he combined the study of ‘Gestalt’, or structured form, with the process of ‘Bildung’, or formation, FIGURE 25 : Le which acts continuously upon form.”[ l i i ] And this focus on the dynamic nature Corbusier. The Modular Man. li. Leach, Neal. “Digital Morphogenesis.” AD: Architectural Design. 79.1 (2004): 32-37. Print. 34. lii. Hensel, Michael and Achim Menges. “Designing Morpho-Ecologies: Versatility and Vicissitude of Heterogeneous Space.” AD: Architectural Design. 78.2 (2008): 102-113. Print. 103. 1.4 45

of form was continued into the 20th century, as can be seen in D’Arcy Wentworth Thompson’s influential work On Growth and Form (Figure 26). “D’Arcy Wentworth Thompson argued in On Growth and Form that the morphology of living forms has a dynamical aspect, under which we deal with the interpretation, in terms of force, of the operations of Energy.”[ l i i i ] His writing on the relationship between species and his work under the heading of ‘homology’ is still used as a important precedent in modern biological investigation. ‘Homology’ is very relevant to the integration of technology and nature because it intertwines the fields of mathematics FIGURE 26 : Cover of and biology. Moreover, It has two different definitions depending on Thomson’s On Growth and Form how they are contextualized. “To biologists it mean organs or body parts that have the same evolutionary origin but quite different functions. To mathematicians, it is a classification of geometric figures according to their properties.”[ l i v ] D’Arcy argues that two forms found in nature are related if one can deformed into another by transformation of Cartesian coordinates (Figure 27 & 28). These similarities between biologic forms is often referred to as “morphogenetic tendency”[ l v ] , offer much insight into the parametric organization of our natural world. If one form can be transformed into

liii. Weinstock, Michael. “Metabolism and Morphology.” AD: Architectural Design. 78.2 (2008): 27-33. Print. 27. liv. Joshi, Atri. Emergence in Architecture. Diss. University of New Delhi, 2006. Print. 2 7. lv. Weinstock, Michael. “Morphogenesis and the Mathmatics of Emergence.” AD: Architectural Design. 74.3 (2004): 10-17. Print. 12. 1.4 46

FIGURE 27 : Catesian mapping of hip homologous pelvis bones. FIGURE 28 : Fish with homologous morphologies. 47 another through deformation of a system coordinate, then it clearly is a system amenable to being modeled mathematically.

Biological morphology is dependent upon systems of basic rules that are affected by inputs to the system. These lessons offer a methodology for the creation of a structural system that integrates a certain dynamism, which will allow for its implementation across multiple architectural projects, while imposing the material optimization that is inherent in natural structures. The following section will cover the investigation into a biological precedent and the derivation of a basic set of rules that describe the geometry inherent in its structural organization. It will serve to elucidate how breaking down the formal nature of organisms into simple morphogenetic rule sets can allow designers to implement them within architectural design. 48 1.4 49 1.5 50 [BIO]

Biological Structural Systems [3.5] he biological precedent that will be referenced Tthroughout the investigation is the giant lily pad (Victoria amazonica). (Figure 29 & 30) This giant species of water lily was chosen for its structural clarity and its spanning abilities. This structural system will serve to inform a digital translational model of the natural ‘homologies’ existing within this species morphogenetic geometry in order to creative architecturally relevant tools.

As can be clearly differentiated without an invasive examination, there is a clearly defined primary structure as well as secondary structural membranes that connect the vascular veins of the lily (Figure 31). Both systems follow a similar cellular logic, though the membrane functions two dimensionally FIGURE 29 : Artist’s and the primary structure functions three dimensionally. The pattern that Rendering of Giant Lily structure and it drives the growth of the system is based on what has come to be known flowering body. 1.4 51

FIGURE 30 : Giant Lily. Top View. FIGURE 31 : Underside of Giant Lily.

as ‘Voronoi’ patterns. These patterns a based on a decomposition of measured space into a set of discreet objects. As can be seen by the diagram (Figure 33), the pattern is reliant on the input of a point array, and depending on the arrangements of the points within the two-dimensional array, the system can create many of the tessellation patterns that we find in nature. This is because nature is based on a geometry that searches to minimize material usage and this system of spatial division divides space in such a way that it allows for the shortest possible boundary connections. As seen in this analysis of spatial division based on input arrays, the use of orthogonal geometries become more and more inefficient in comparison 52 53 to the biologically-based geometric system the more non-uniform the inputs become. In order to build more efficient structures for the future of architecture we must be able to harness this inherent genius for material conservation. Niel Leech agrees that “...nature itself can teach us important lessons about the efficiency of structural organizations.”[ l v i ] He goes on to reiterate that “Biology provides one of the major sources of inspiration for research into morphogenesis in architecture. Nature operates largely through a logic of optimization...”[ l v i i ]

As is the case with most seemingly complex morphologies found in nature, this biological patterning follows a list of simple rules (Figure 32). Though our physical world exists in three dimension, for the purposes of understanding these natural geometries, it is helpful to initially limit them to abstracted two dimensional representations. As mentioned before, this mathematical system depends on the input of a system of points. The output of this generative process completely depends on the locations of the input points, which make it very useful in a dynamic system.

Step 1 - Within the array of points a single point must be selected for analysis.

lvi. Leach, Neal. “Digital Morphogenesis.” AD: Architectural Design. 79.1 (2004): 32- 37. Print. 35. lvii. Leach, Neal. “Digital Morphogenesis.” AD: Architectural Design. 79.1 (2004): 32- 37. Print. 35. II. RULE-BASED SYSTEM OF SPRINGS

Movement of any one vertex triggers a gradient of movement in neighboring vertices. 54 Vertices that are close together try to keep their relative position. Vertices that are part of unstable lattices are more affected by FIGURE 32 : Abstracted forces. rules system based on 1 Points 2 Bisectors Vertices that are deep in the middle of the building try to move cellular structures. more closely to the rim (creating ‘rooms’). Horizontal movement is more likely than vertical movements (creating ‘floors’). II. ITERATION Vertices are attracted or repelled by forces (creating random mutation).

Grand Hall Select one point in a set of points. Bisect all lines connecting point to all other points.

4 Boundary 3 Intersections

Trace boundary and repeat for all other points in Cell is formed by the of the local bisectors. the set. 55

Step 2 - The selected point is then connected to all other points in the array and the parallel bisectors of those line are extended into the 2 dimensional plane.

Step 3 - The boundaries for the cell is formed by the intersections of these local bisectors.

Step 4 - Once the boundary is defined, remove construction lines and repeat for all the point in the array.

Once this process is completed and spacial boundaries have been defined for all sets of point the process is over. What is left is a system of spaces that have been divided using the smallest possible spans and the least amount of acute angles or the decided input.

Moreover, because this system is able to adapt to an infinite number of different inputs and it has obvious the obvious ability of optimizing overall spanning length, it is east to see how this geometry could benefit how we design our built environment. Material savings alone make this type of system a valuable asset to the future of architectural design, but, even more so, it boasts the ability of being able to take more a randomized system of inputs and do so without interrupting a unified structure.

As can be in the following diagrams (Figure 32 & 33), the voronoi geometry

FIGURE 33 : Voronoi serves to do better that the strictly orthogonal geometries when looking geometry in nature. 1.4 56 Point Array Point Translational Matrix Translational Functional Geometry Functional 57

FIGURE 34 : Diagram 100’ - 0” Orthogonal Voronoi 2500 showing how orthogonal and 2000 voronoi geometries can 1500 divide discreet space depending on a the - 0” 100’ 1000

input of a point array 500

1 0

15

12

9

6

2 3

0

60

50

40 3 30 20

10

0

4 58

FIGURE 35 : Graphs at the saving in the total length of show that the voronoi spanning members, the average ft. Total Length of Members geometry is better 2500 0%* 3.07%* suited to deal with length of spanning members, and 2000 0.11%* 0.71%* nonuniform inputs and length of the longest spanning could lead to material 1500 members. As can be clearly seen, savings in structural 1000 systems. the more nonuniform the input 500 array becomes the better suited the 0 voronoi geometry to take on the task 1234 *percent shorter of division of space. ft. Average Length of Members 15 15.40%* By breaking this biological system 3.49%* 12 0%* down into basic rules, it allows 9 29%* it to transcend realms, from the 6 biological and be used as a tool 3 in the hand of the architectural 0 designer. Methods of digital design 1234 *percent shorter have made seemingly esoteric fields ft. 60 Length of Longest Member of study such as biology to be more 50 11.1%* easily accessed and functionally 40 36.4%* translated. The following chapter 45.61%* 30 briefly shows how a knowledge of 20 0%* digital design software and scripting 10

techniques can take a biological rule 0 1234 *percent shorter 59 system and make it useful within the design of architectural structures. 60 [BIO]

Digital Tools for Biological Optimization [3.5] For more than a decade, digital processes have taken part in making the un-buildable buildable. Early monuments to digital production, such as the Guggenheim in Bilbao designed by Frank Gehry and Lord Norman Foster’s dome for the German Reichstag in Berlin, proved to the world the computer’s ability to bring highly complex structures to reality. However, until recently this powerful tool was categorized within architectural practices exclusively as a representational or analytical device. As designers and architects have become more technologically savvy, a trend towards integration of the computer into the design process has occurred. Kostas Terzidis, author of Algorithmic Architecture, lectures on the notion that “digital is a process not a product.”

In order to get away from the ideal of the computer as a solely representational means, it is up to the designer to have the technical abilities to work outside and around the constraints prescribed within available design softwares. Much of the criticism of digital architecture lies in the argument that the architecture is largely affected by the software platform in which it is created. And there certainly is merit in the argument. Different design programs were 61 written privileging certain capabilities over others. For example, Revit, one of the more celebrated and prevalent competitors in the world of Building Information Modeling (BIM), creates digital models embedded with information from the physical world. A wall in Revit, is not simply an extruded plane, but it exist as a layered entity, containing the properties of common construction materials (ie. stick-built construction, fiberglass insulation, and gypsum paneling). This type of modeling software, though it does allow for much improved systems integration, it greatly constrains the design process. BIM often favors design efficiency of design creativity. Complex geometries and nontraditional material systems become extremely hard to engineer within BIM, and thus the designs are often reworked to fit within a more Euclidian construct. On the other side of the spectrum, is a piece of software called Maya, that offers far more freedom of design. Initially known for its popularity in the video game and film industries, Maya quickly became a mainstay in progressive architectural design circles searching for a greater degree of formal articulation within architecture. Moreover, the software is ‘open source’ and could thus be changed and specialized to the user’s needs. The initial shock of all this geometric flexibility, completely detached designers from the architecture’s materiality and physicality and incited the onset of what is now commonly, and often resentfully, referred to as ‘blobitecture.’ And though these two software platforms are polar opposites within the spectrum of digital tools, it still elucidates the notion of architectural design being driven by the chosen architectural tool. Because 62 of this, the future of digital design will lie in technical capabilities of the architect. Digital design will rely on the architect to take on a partial role as computer programmer. For the most success within digital design will come from those who augment and specialize existing softwares to meet their needs and the needs of their clients.

The process of augmenting digital design software is most common done through a process called ‘scripting’. Scripting is a term used to refer to the writing of computer code, however, within the architectural field, this coding is usually relegated strictly to a single design software.

In order to use scripting to take our previously laid out two-dimensional system and transform in into a ‘script’ that will be useful in the design of useful structural systems, the two-dimensional system must be translated into three dimensions. This will be done by inserting vectors in the place of lines. Once we do this the rule systems changes as follows: II. RULE-BASED SYSTEM OF SPRINGS

Movement of any one vertex triggers a gradient of movement in neighboring vertices. 63 Vertices that are close together try to keep their relative position. Vertices that are part of unstable lattices are more affected by forces. Vertices that are deep in the middle of the building try to move more closely to the rim (creating ‘rooms’). Horizontal movement is more likely than vertical movements (creating ‘floors’). II. ITERATION Vertices are attracted or repelled by forces (creating random mutation).

Grand Hall II. RULE-BASED SYSTEM OF SPRINGS

Movement of any one vertex triggers a gradient of movement in neighboring vertices. 64 Vertices that are close together try to keep their relative position. Vertices that are part of unstable lattices are more affected by FIGURE 36 : Graphs forces. show that the voronoi Vertices that are deep in the middle of the building try to move geometry is better more closely to the rim (creating ‘rooms’). suited to deal with Horizontal movement is more likely than vertical movements (creating ‘floors’). II. ITERATION nonuniform inputs and Vertices are attracted or repelled by forces (creating random could lead to material mutation). savings in structural systems.

Grand Hall Option Explicit

'global naming variables Dim XX : XX = 0 Dim YY : YY = 1 Dim ZZ : ZZ = 2 Main Sub-Routine GenerateCells

Sub GenerateCells() Randomize

Dim arrBoundingVolume ' array of polysurfaces indicating bounding volume Dim arrPoints ' array of string references to voronoi points

Dim i,j

Dim startTime : startTime = Now

Rhino.EnableRedraw(False)

' select bounding volume and point array to solve

arrBoundingVolume = Rhino.GetObjects("Select a Bounding Volume",16+8,vbTrue,vbTrue) If IsNull(arrBoundingVolume) Then Exit Sub HideObjects arrBoundingVolume

arrPoints = Rhino.GetObjects("Select Cell Points",1,vbFalse,vbFalse)

ShowObjects arrBoundingVolume

If IsNull(arrPoints) Then Exit Sub

Dim strCell, strName Rhino.Print "Beginning cell divisions: " & UBound(arrPoints)+1 & " cells total." For i = 0 To UBound(arrPoints) ' for each point to make a cell around ' one point at a time

strCell = GenerateCell(arrPoints(i),arrPoints,arrBoundingVolume) Dim value : value = Int(Rnd()*255) Rhino.objectColor strCell, RGB(255,255,value) strName = "Cell #" & i Rhino.objectname strCell, strName

Dim strTime : strTime = GetTimeDescription(startTime, (i+1) * 1.0 / (UBound(arrPoints)+1) )

Rhino.Print i+1 & " of " & UBound(arrPoints)+1 & " cells ("& Int((i+1) * 100 / (UBound(arrPoints)+1)) & "%) completed. " & strTime

Next

' hide input geometry HideObjects arrPoints HideObjects arrBoundingVolume

Rhino.EnableRedraw(True)

End Sub

Function GenerateCell(centerPoint,arrPoints,arrBoundingVolume) Dim arrBlocks Function One: Generates Cell arrBlocks = CreateBlocks(centerPoint, arrPoints) geometry given a point in an array, Dim strCell a bounding volume; Delete strCell = IntersectBlocks(arrBlocks,arrBoundingVolume) construction geometries; and return Dim m: For m = 0 To UBound(arrBlocks) individual Cell. If IsPolySurface(arrBlocks(m)) Then DeleteObject(arrBlocks(m)) Next

GenerateCell = strCell End Function

Function CreateBlocks(centerPoint, arrPoints) Function Two: Using a point array Dim arrBlocks ReDim arrBlocks(UBound(arrPoints)) create a set of blocks that when intersected create a 3D cellular Dim newPlane Dim numBlocks : numBlocks = 0 volume; Blocks are created by Dim i extruding a face perpendicular to Dim midpoint, normal the midpoint of a line created by the Dim greatestdiagonalspread center point and the rest of the greatestdiagonalspread = FindGreatestDiagonalSpread(arrPoints) points in the array. Dim centercoords,pointcoords centercoords = Rhino.PointCoordinates(centerPoint)

For i = 0 To UBound(arrPoints) '

If Not centerPoint = arrPoints(i) Then

pointcoords = Rhino.PointCoordinates(arrPoints(i)) Dim strPlane strPlane = CreateBisectingPlane(centercoords, pointcoords, greatestdiagonalspread)

If(Rhino.IsSurface(strPlane)) Then 'if it's a valid object, add To the array 'newPlane has been created

midpoint = VectorMidpoint(centercoords, pointcoords)

normal = VectorUnitize(VectorSubtract(centercoords, pointcoords))

Dim strPath strPath = Rhino.AddLine(midpoint, VectorAdd(midpoint,VectorScale(normal, greatestdiagonalspread)))

Dim strExtrusion strExtrusion = Rhino.ExtrudeSurface( strPlane, strPath ) Rhino.objectColor strExtrusion, RGB(128,128,128)

arrBlocks(numBlocks) = strExtrusion numBlocks = numBlocks + 1

If(Rhino.IsObject(strPath)) Then Rhino.DeleteObject(strPath) If(Rhino.IsObject(strPlane)) Then Rhino.DeleteObject(strPlane) End If 'end if it's a surface End If 'end if considering different points Next 'i

ReDim Preserve arrBlocks(numBlocks-1) 'Rhino.Print(numBlocks & " blocks created.")

CreateBlocks = arrBlocks 65 End Function

Function CreateBisectingPlane(arrPtOne, arrPtTwo, reach) Dim i Option Explicit Dim center

center = VectorMidpoint(arrPtOne, arrPtTwo) 'global naming variables

Dim XX : XX = 0 ' make new coordinate system p,r,s: p is the line between 1 and 2, r Is To the side, s Is up(ish) from the line Dim YY : YY = 1 Dim p : p = VectorSubtract(arrPtTwo,arrPtOne) : p = VectorUnitize(p) Dim ZZ : ZZ = 2 FIGURE 37 : Rhinoscript Dim up : up = Array(0,0,1)

Main Sub-Routine Dim r : r = VectorCrossProduct(p,up) : If IsVectorZero(r) Then r = Array(0,1,0) GenerateCells r = VectorUnitize(r) '' points to the right

Dim s : s = VectorCrossProduct(p,r) : s = VectorUnitize(s) '' points To perpendicular To p (forward) And r (side) Sub GenerateCells() translation of Randomize ' now find four points, 1 up 2 left 3 down 4 right (looking from one to two)

Dim arrCorners(3) Dim arrBoundingVolume ' array of polysurfaces indicating bounding volume arrCorners(0) = VectorAdd(center,VectorScale(s,reach)) Dim arrPoints ' array of string references to voronoi points 3-Dimensional Voronoi arrCorners(1) = VectorAdd(center,VectorScale(r,reach * -1))

arrCorners(2) = VectorAdd(center,VectorScale(s,reach * -1)) Dim i,j Function Three: Takes two point arrCorners(3) = VectorAdd(center,VectorScale(r,reach))

coordinate arrays, draws a line Dim startTime : startTime = Now system. Dim strPlane between them, finds the midpoint, strPlane = Rhino.AddSrfPt( arrCorners ) Rhino.EnableRedraw(False) and creates a plane normal the line

CreateBisectingPlane = strPlane v e c t o r . ' select bounding volume and point array to solve End Function

arrBoundingVolume = Rhino.GetObjects("Select a Bounding Volume",16+8,vbTrue,vbTrue) If IsNull(arrBoundingVolume) Then Exit Sub Function IntersectBlocks(arrBlocks, arrBoundingVolume) HideObjects arrBoundingVolume Dim i

arrPoints = Rhino.GetObjects("Select Cell Points",1,vbFalse,vbFalse) IntersectBlocks = Null

i = 0 ShowObjects arrBoundingVolume Dim results, pendingresults Function Four: Generate Blocks Dim strBlock If IsNull(arrPoints) Then Exit Sub Dim group2 from plane and performs a boolean

Dim strCell, strName intersection Do Rhino.Print "Beginning cell divisions: " & UBound(arrPoints)+1 & " cells total." strBlock = arrBlocks(i) For i = 0 To UBound(arrPoints) ' for each point to make a cell around ' one point at a time group2 = array(strBlock)

pendingresults = Rhino.BooleanIntersection(arrBoundingVolume,group2,vbFalse) strCell = GenerateCell(arrPoints(i),arrPoints,arrBoundingVolume) i = i + 1 Dim value : value = Int(Rnd()*255) Loop While Not IsArray(pendingresults) Rhino.objectColor strCell, RGB(255,255,value)

strName = "Cell #" & i results = pendingresults Rhino.objectname strCell, strName

Dim j Dim strTime : strTime = GetTimeDescription(startTime, (i+1) * 1.0 / (UBound(arrPoints)+1) ) For j = i To UBound(arrBlocks)

strBlock = arrBlocks(j) Rhino.Print i+1 & " of " & UBound(arrPoints)+1 & " cells ("& Int((i+1) * 100 / (UBound(arrPoints)+1)) & "%) completed. " & strTime group2 = array(strBlock)

pendingresults = Rhino.BooleanIntersection(results,group2) Next If IsArray(pendingresults) Then results = pendingresults

' hide input geometry Next HideObjects arrPoints

HideObjects arrBoundingVolume IntersectBlocks = results(0)

End Function Rhino.EnableRedraw(True)

Function FindGreatestDiagonalSpread(arrPoints) End Sub If(Not IsArray(arrPoints)) Then FindGreatestDiagonalSpread = 0

Dim max : max = Rhino.PointCoordinates(arrPoints(0)) Function Five: Finds maximum Function GenerateCell(centerPoint,arrPoints,arrBoundingVolume) Dim min : min = Rhino.PointCoordinates(arrPoints(0)) Dim arrBlocks diameter of point array Function One: Generates Cell Dim i, pt, spread arrBlocks = CreateBlocks(centerPoint, arrPoints)

geometry given a point in an array, For i = 0 To UBound(arrPoints) Dim strCell a bounding volume; Delete pt = Rhino.PointCoordinates(arrPoints(i)) strCell = IntersectBlocks(arrBlocks,arrBoundingVolume) If(max(XX) < pt(XX)) Then max(XX) = pt(XX) construction geometries; and return If(max(YY) < pt(YY)) Then max(YY) = pt(YY) Dim m: For m = 0 To UBound(arrBlocks) individual Cell. If(max(ZZ) < pt(ZZ)) Then max(ZZ) = pt(ZZ) If IsPolySurface(arrBlocks(m)) Then DeleteObject(arrBlocks(m)) If(min(XX) > pt(XX)) Then min(XX) = pt(XX) Next If(min(YY) > pt(YY)) Then min(YY) = pt(YY)

If(min(ZZ) > pt(ZZ)) Then min(ZZ) = pt(ZZ) GenerateCell = strCell Next 'i End Function

FindGreatestDiagonalSpread = VectorLength(VectorSubtract(max,min)) End Function Function CreateBlocks(centerPoint, arrPoints) Function Two: Using a point array Dim arrBlocks Function GetTimeDescription(startTime, fractioncomplete) ReDim arrBlocks(UBound(arrPoints)) create a set of blocks that when Dim strDescription

intersected create a 3D cellular strDescription = "" Dim newPlane Dim elapsedseconds : elapsedseconds = DateDiff("s",startTime,Now) Dim numBlocks : numBlocks = 0 volume; Blocks are created by Dim m,h,s : s = elapsedseconds Dim i extruding a face perpendicular to m = Int(s/60) : s = s - m * 60 Dim midpoint, normal h = Int(m/60) : m = m - h * 60 the midpoint of a line created by the If h = 1 Then strDescription = strDescription & " " & h & " hour" Dim greatestdiagonalspread center point and the rest of the If h > 1 Then strDescription = strDescription & " " & h & " hours" greatestdiagonalspread = FindGreatestDiagonalSpread(arrPoints) If m = 1 Then strDescription = strDescription & " " & m & " minute" points in the array. If m > 1 Then strDescription = strDescription & " " & m & " minutes" Dim centercoords,pointcoords If s = 1 Then strDescription = strDescription & " " & s & " second" centercoords = Rhino.PointCoordinates(centerPoint) If s > 1 Then strDescription = strDescription & " " & s & " seconds"

strDescription = strDescription & " elapsed:" For i = 0 To UBound(arrPoints) '

Dim secondstogo : secondstogo = elapsedseconds / fractioncomplete * (1-fractioncomplete) If Not centerPoint = arrPoints(i) Then Dim ETA : ETA = DateAdd("s",secondstogo,Now)

pointcoords = Rhino.PointCoordinates(arrPoints(i)) If(fractioncomplete < 1) Then Dim strPlane

strPlane = CreateBisectingPlane(centercoords, pointcoords, greatestdiagonalspread) strDescription = strDescription & " should be finished at " & FormatDateTime(ETA,4)

If(DatePart("d",ETA) = DatePart("d",Now)) Then If(Rhino.IsSurface(strPlane)) Then 'if it's a valid object, add To the array strDescription = strDescription & " today." 'newPlane has been created Else

strDescription = strDescription & " in " & DateDiff("d",Now,ETA) & " day(s)." midpoint = VectorMidpoint(centercoords, pointcoords) End If

Else normal = VectorUnitize(VectorSubtract(centercoords, pointcoords)) strDescription = strDescription & " finished " & Now & "!"

End If Dim strPath

strPath = Rhino.AddLine(midpoint, VectorAdd(midpoint,VectorScale(normal, greatestdiagonalspread))) Function Six: Calculates time needed GetTimeDescription = strDescription

for solution Dim strExtrusion End Function strExtrusion = Rhino.ExtrudeSurface( strPlane, strPath )

Rhino.objectColor strExtrusion, RGB(128,128,128)

Public Function VectorCreate(p1, p2) arrBlocks(numBlocks) = strExtrusion VectorCreate = Array(p2(0) - p1(0), p2(1) - p1(1), p2(2) - p1(2)) numBlocks = numBlocks + 1 End Function

If(Rhino.IsObject(strPath)) Then Rhino.DeleteObject(strPath) Public Function VectorUnitize(v) If(Rhino.IsObject(strPlane)) Then Rhino.DeleteObject(strPlane)

End If 'end if it's a surface VectorUnitize = Null Public Vector Functions: Various End If 'end if considering different points Dim dist, x, y, z, x2, y2, z2 Next 'i vector calculations used in the

x = v(XX) : y = v(YY) : z = v(ZZ) aforementioned functions ReDim Preserve arrBlocks(numBlocks-1) x2 = x * x : y2 = y * y : z2 = z * z 'Rhino.Print(numBlocks & " blocks created.")

dist = x2 + y2 + z2 CreateBlocks = arrBlocks If dist <= 0.0 Then Exit Function End Function dist = Sqr(dist)

x = x / dist Function CreateBisectingPlane(arrPtOne, arrPtTwo, reach) y = y / dist Dim i z = z / dist Dim center

center = VectorMidpoint(arrPtOne, arrPtTwo) VectorUnitize = Array(x, y, z)

End Function ' make new coordinate system p,r,s: p is the line between 1 and 2, r Is To the side, s Is up(ish) from the line

Dim p : p = VectorSubtract(arrPtTwo,arrPtOne) : p = VectorUnitize(p) Public Function VectorLength(v) Dim up : up = Array(0,0,1)

Dim r : r = VectorCrossProduct(p,up) : If IsVectorZero(r) Then r = Array(0,1,0) VectorLength = Null r = VectorUnitize(r) '' points to the right

Dim s : s = VectorCrossProduct(p,r) : s = VectorUnitize(s) '' points To perpendicular To p (forward) And r (side) Dim dist, x, y, z, x2, y2, z2

x = v(XX) : y = v(YY) : z = v(ZZ) ' now find four points, 1 up 2 left 3 down 4 right (looking from one to two) x2 = x * x : y2 = y * y : z2 = z * z Dim arrCorners(3) dist = x2 + y2 + z2 arrCorners(0) = VectorAdd(center,VectorScale(s,reach))

arrCorners(1) = VectorAdd(center,VectorScale(r,reach * -1)) VectorLength = Sqr(dist) arrCorners(2) = VectorAdd(center,VectorScale(s,reach * -1)) Function Three: Takes two point arrCorners(3) = VectorAdd(center,VectorScale(r,reach)) End Function coordinate arrays, draws a line

Dim strPlane between them, finds the midpoint, Public Function VectorDotProduct(v1, v2) strPlane = Rhino.AddSrfPt( arrCorners ) VectorDotProduct = v1(XX) * v2(XX) + v1(YY) * v2(YY) + v1(ZZ) * v2(ZZ) and creates a plane normal the line End Function CreateBisectingPlane = strPlane v e c t o r . End Function Public Function VectorCrossProduct(v1, v2)

VectorCrossProduct = Null Function IntersectBlocks(arrBlocks, arrBoundingVolume) Dim x, y, z Dim i x = v1(YY) * v2(ZZ) - v1(ZZ) * v2(YY)

y = v1(ZZ) * v2(XX) - v1(XX) * v2(ZZ) IntersectBlocks = Null z = v1(XX) * v2(YY) - v1(YY) * v2(XX) i = 0 VectorCrossProduct = Array(x, y, z) Dim results, pendingresults Function Four: Generate Blocks Dim strBlock End Function Dim group2 from plane and performs a boolean

intersection Public Function VectorAdd(v1, v2) Do VectorAdd = Null strBlock = arrBlocks(i) VectorAdd = Array(v1(XX) + v2(XX), v1(YY) + v2(YY), v1(ZZ) + v2(ZZ)) group2 = array(strBlock) End Function pendingresults = Rhino.BooleanIntersection(arrBoundingVolume,group2,vbFalse) i = i + 1 Public Function VectorSubtract(v1, v2) Loop While Not IsArray(pendingresults) VectorSubtract = Null

VectorSubtract = Array(v1(XX) - v2(XX), v1(YY) - v2(YY), v1(ZZ) - v2(ZZ)) results = pendingresults End Function

Dim j Public Function VectorMultiply(v1, v2) For j = i To UBound(arrBlocks) VectorMultiply = Null strBlock = arrBlocks(j) VectorMultiply = Array(v1(XX) * v2(XX), v1(YY) * v2(YY), v1(ZZ) * v2(ZZ)) group2 = array(strBlock) End Function pendingresults = Rhino.BooleanIntersection(results,group2)

If IsArray(pendingresults) Then results = pendingresults Public Function VectorScale(v, d)

VectorScale = Null Next VectorScale = Array(v(XX) * d, v(YY) * d, v(ZZ) * d)

End Function IntersectBlocks = results(0)

End Function

Public Function VectorCompare(v1, v2) VectorCompare = vbFalse Function FindGreatestDiagonalSpread(arrPoints)

If(Not IsArray(arrPoints)) Then FindGreatestDiagonalSpread = 0 If v1(XX) = v2(XX) And v1(YY) = v2(YY) And v1(ZZ) = v2(ZZ) Then

VectorCompare = vbTrue Dim max : max = Rhino.PointCoordinates(arrPoints(0)) Function Five: Finds maximum End If Dim min : min = Rhino.PointCoordinates(arrPoints(0)) diameter of point array Dim i, pt, spread End Function

For i = 0 To UBound(arrPoints) pt = Rhino.PointCoordinates(arrPoints(i)) If(max(XX) < pt(XX)) Then max(XX) = pt(XX) If(max(YY) < pt(YY)) Then max(YY) = pt(YY) If(max(ZZ) < pt(ZZ)) Then max(ZZ) = pt(ZZ) If(min(XX) > pt(XX)) Then min(XX) = pt(XX) If(min(YY) > pt(YY)) Then min(YY) = pt(YY) If(min(ZZ) > pt(ZZ)) Then min(ZZ) = pt(ZZ) Next 'i

FindGreatestDiagonalSpread = VectorLength(VectorSubtract(max,min)) End Function

Function GetTimeDescription(startTime, fractioncomplete) Dim strDescription strDescription = "" Dim elapsedseconds : elapsedseconds = DateDiff("s",startTime,Now) Dim m,h,s : s = elapsedseconds m = Int(s/60) : s = s - m * 60 h = Int(m/60) : m = m - h * 60 If h = 1 Then strDescription = strDescription & " " & h & " hour" If h > 1 Then strDescription = strDescription & " " & h & " hours" If m = 1 Then strDescription = strDescription & " " & m & " minute" If m > 1 Then strDescription = strDescription & " " & m & " minutes" If s = 1 Then strDescription = strDescription & " " & s & " second" If s > 1 Then strDescription = strDescription & " " & s & " seconds" strDescription = strDescription & " elapsed:"

Dim secondstogo : secondstogo = elapsedseconds / fractioncomplete * (1-fractioncomplete) Dim ETA : ETA = DateAdd("s",secondstogo,Now)

If(fractioncomplete < 1) Then

strDescription = strDescription & " should be finished at " & FormatDateTime(ETA,4) If(DatePart("d",ETA) = DatePart("d",Now)) Then strDescription = strDescription & " today." Else strDescription = strDescription & " in " & DateDiff("d",Now,ETA) & " day(s)." End If Else strDescription = strDescription & " finished " & Now & "!" End If Function Six: Calculates time needed GetTimeDescription = strDescription for solution End Function

Public Function VectorCreate(p1, p2) VectorCreate = Array(p2(0) - p1(0), p2(1) - p1(1), p2(2) - p1(2)) End Function

Public Function VectorUnitize(v)

VectorUnitize = Null Public Vector Functions: Various Dim dist, x, y, z, x2, y2, z2 vector calculations used in the

x = v(XX) : y = v(YY) : z = v(ZZ) aforementioned functions x2 = x * x : y2 = y * y : z2 = z * z

dist = x2 + y2 + z2 If dist <= 0.0 Then Exit Function dist = Sqr(dist)

x = x / dist y = y / dist z = z / dist

VectorUnitize = Array(x, y, z) End Function

Public Function VectorLength(v)

VectorLength = Null

Dim dist, x, y, z, x2, y2, z2 x = v(XX) : y = v(YY) : z = v(ZZ) x2 = x * x : y2 = y * y : z2 = z * z dist = x2 + y2 + z2

VectorLength = Sqr(dist)

End Function

Public Function VectorDotProduct(v1, v2) VectorDotProduct = v1(XX) * v2(XX) + v1(YY) * v2(YY) + v1(ZZ) * v2(ZZ) End Function

Public Function VectorCrossProduct(v1, v2)

VectorCrossProduct = Null Dim x, y, z x = v1(YY) * v2(ZZ) - v1(ZZ) * v2(YY) y = v1(ZZ) * v2(XX) - v1(XX) * v2(ZZ) z = v1(XX) * v2(YY) - v1(YY) * v2(XX) VectorCrossProduct = Array(x, y, z)

End Function

Public Function VectorAdd(v1, v2) VectorAdd = Null VectorAdd = Array(v1(XX) + v2(XX), v1(YY) + v2(YY), v1(ZZ) + v2(ZZ)) End Function

Public Function VectorSubtract(v1, v2) VectorSubtract = Null VectorSubtract = Array(v1(XX) - v2(XX), v1(YY) - v2(YY), v1(ZZ) - v2(ZZ)) End Function

Public Function VectorMultiply(v1, v2) VectorMultiply = Null VectorMultiply = Array(v1(XX) * v2(XX), v1(YY) * v2(YY), v1(ZZ) * v2(ZZ)) End Function

Public Function VectorScale(v, d) VectorScale = Null VectorScale = Array(v(XX) * d, v(YY) * d, v(ZZ) * d) End Function

Public Function VectorCompare(v1, v2) VectorCompare = vbFalse

If v1(XX) = v2(XX) And v1(YY) = v2(YY) And v1(ZZ) = v2(ZZ) Then VectorCompare = vbTrue End If

End Function Option Explicit

'global naming variables Dim XX : XX = 0 Dim YY : YY = 1 Dim ZZ : ZZ = 2 Main Sub-Routine GenerateCells

Sub GenerateCells() Randomize

Dim arrBoundingVolume ' array of polysurfaces indicating bounding volume Dim arrPoints ' array of string references to voronoi points

Dim i,j

Dim startTime : startTime = Now

Rhino.EnableRedraw(False)

' select bounding volume and point array to solve

arrBoundingVolume = Rhino.GetObjects("Select a Bounding Volume",16+8,vbTrue,vbTrue) If IsNull(arrBoundingVolume) Then Exit Sub HideObjects arrBoundingVolume

arrPoints = Rhino.GetObjects("Select Cell Points",1,vbFalse,vbFalse)

ShowObjects arrBoundingVolume

If IsNull(arrPoints) Then Exit Sub

Dim strCell, strName Rhino.Print "Beginning cell divisions: " & UBound(arrPoints)+1 & " cells total." For i = 0 To UBound(arrPoints) ' for each point to make a cell around ' one point at a time

strCell = GenerateCell(arrPoints(i),arrPoints,arrBoundingVolume) Dim value : value = Int(Rnd()*255) Rhino.objectColor strCell, RGB(255,255,value) strName = "Cell #" & i Rhino.objectname strCell, strName

Dim strTime : strTime = GetTimeDescription(startTime, (i+1) * 1.0 / (UBound(arrPoints)+1) )

Rhino.Print i+1 & " of " & UBound(arrPoints)+1 & " cells ("& Int((i+1) * 100 / (UBound(arrPoints)+1)) & "%) completed. " & strTime

Next

' hide input geometry HideObjects arrPoints HideObjects arrBoundingVolume

Rhino.EnableRedraw(True)

End Sub

Function GenerateCell(centerPoint,arrPoints,arrBoundingVolume) Dim arrBlocks Function One: Generates Cell arrBlocks = CreateBlocks(centerPoint, arrPoints) geometry given a point in an array, Dim strCell a bounding volume; Delete strCell = IntersectBlocks(arrBlocks,arrBoundingVolume) construction geometries; and return Dim m: For m = 0 To UBound(arrBlocks) individual Cell. If IsPolySurface(arrBlocks(m)) Then DeleteObject(arrBlocks(m)) Next

GenerateCell = strCell End Function

Function CreateBlocks(centerPoint, arrPoints) Function Two: Using a point array Dim arrBlocks ReDim arrBlocks(UBound(arrPoints)) create a set of blocks that when intersected create a 3D cellular Dim newPlane Dim numBlocks : numBlocks = 0 volume; Blocks are created by Dim i extruding a face perpendicular to Dim midpoint, normal the midpoint of a line created by the Dim greatestdiagonalspread center point and the rest of the greatestdiagonalspread = FindGreatestDiagonalSpread(arrPoints) points in the array. Dim centercoords,pointcoords centercoords = Rhino.PointCoordinates(centerPoint)

For i = 0 To UBound(arrPoints) '

If Not centerPoint = arrPoints(i) Then

pointcoords = Rhino.PointCoordinates(arrPoints(i)) Dim strPlane strPlane = CreateBisectingPlane(centercoords, pointcoords, greatestdiagonalspread)

If(Rhino.IsSurface(strPlane)) Then 'if it's a valid object, add To the array 'newPlane has been created

midpoint = VectorMidpoint(centercoords, pointcoords)

normal = VectorUnitize(VectorSubtract(centercoords, pointcoords))

Dim strPath strPath = Rhino.AddLine(midpoint, VectorAdd(midpoint,VectorScale(normal, greatestdiagonalspread)))

Dim strExtrusion strExtrusion = Rhino.ExtrudeSurface( strPlane, strPath ) Rhino.objectColor strExtrusion, RGB(128,128,128)

arrBlocks(numBlocks) = strExtrusion numBlocks = numBlocks + 1

If(Rhino.IsObject(strPath)) Then Rhino.DeleteObject(strPath) If(Rhino.IsObject(strPlane)) Then Rhino.DeleteObject(strPlane) End If 'end if it's a surface End If 'end if considering different points Next 'i

ReDim Preserve arrBlocks(numBlocks-1) 'Rhino.Print(numBlocks & " blocks created.")

CreateBlocks = arrBlocks End Function

Function CreateBisectingPlane(arrPtOne, arrPtTwo, reach) Dim i Dim center center = VectorMidpoint(arrPtOne, arrPtTwo)

' make new coordinate system p,r,s: p is the line between 1 and 2, r Is To the side, s Is up(ish) from the line Dim p : p = VectorSubtract(arrPtTwo,arrPtOne) : p = VectorUnitize(p) Dim up : up = Array(0,0,1) Dim r : r = VectorCrossProduct(p,up) : If IsVectorZero(r) Then r = Array(0,1,0) r = VectorUnitize(r) '' points to the right Dim s : s = VectorCrossProduct(p,r) : s = VectorUnitize(s) '' points To perpendicular To p (forward) And r (side)

' now find four points, 1 up 2 left 3 down 4 right (looking from one to two) Dim arrCorners(3) arrCorners(0) = VectorAdd(center,VectorScale(s,reach)) arrCorners(1) = VectorAdd(center,VectorScale(r,reach * -1)) arrCorners(2) = VectorAdd(center,VectorScale(s,reach * -1)) Function Three: Takes two point arrCorners(3) = VectorAdd(center,VectorScale(r,reach)) coordinate arrays, draws a line Dim strPlane between them, finds the midpoint, strPlane = Rhino.AddSrfPt( arrCorners ) and creates a plane normal the line CreateBisectingPlane = strPlane v e c t o r . End Function

Function IntersectBlocks(arrBlocks, arrBoundingVolume) Dim i

IntersectBlocks = Null i = 0 Dim results, pendingresults Function Four: Generate Blocks Dim strBlock Dim group2 from plane and performs a boolean intersection Do strBlock = arrBlocks(i) group2 = array(strBlock) pendingresults = Rhino.BooleanIntersection(arrBoundingVolume,group2,vbFalse) i = i + 1 Loop While Not IsArray(pendingresults)

results = pendingresults

Dim j For j = i To UBound(arrBlocks) strBlock = arrBlocks(j) group2 = array(strBlock) pendingresults = Rhino.BooleanIntersection(results,group2) If IsArray(pendingresults) Then results = pendingresults

Next

IntersectBlocks = results(0) End Function

Function FindGreatestDiagonalSpread(arrPoints) If(Not IsArray(arrPoints)) Then FindGreatestDiagonalSpread = 0

Dim max : max = Rhino.PointCoordinates(arrPoints(0)) Function Five: Finds maximum Dim min : min = Rhino.PointCoordinates(arrPoints(0)) diameter of point array Dim i, pt, spread

For i = 0 To UBound(arrPoints) pt = Rhino.PointCoordinates(arrPoints(i)) If(max(XX) < pt(XX)) Then max(XX) = pt(XX) If(max(YY) < pt(YY)) Then max(YY) = pt(YY) If(max(ZZ) < pt(ZZ)) Then max(ZZ) = pt(ZZ) If(min(XX) > pt(XX)) Then min(XX) = pt(XX) If(min(YY) > pt(YY)) Then min(YY) = pt(YY) If(min(ZZ) > pt(ZZ)) Then min(ZZ) = pt(ZZ) Next 'i

FindGreatestDiagonalSpread = VectorLength(VectorSubtract(max,min)) End Function

Function GetTimeDescription(startTime, fractioncomplete) Dim strDescription strDescription = "" Dim elapsedseconds : elapsedseconds = DateDiff("s",startTime,Now) Dim m,h,s : s = elapsedseconds m = Int(s/60) : s = s - m * 60 h = Int(m/60) : m = m - h * 60 If h = 1 Then strDescription = strDescription & " " & h & " hour" If h > 1 Then strDescription = strDescription & " " & h & " hours" If m = 1 Then strDescription = strDescription & " " & m & " minute" If m > 1 Then strDescription = strDescription & " " & m & " minutes" If s = 1 Then strDescription = strDescription & " " & s & " second" If s > 1 Then strDescription = strDescription & " " & s & " seconds" strDescription = strDescription & " elapsed:"

Dim secondstogo : secondstogo = elapsedseconds / fractioncomplete * (1-fractioncomplete) Dim ETA : ETA = DateAdd("s",secondstogo,Now)

If(fractioncomplete < 1) Then

strDescription = strDescription & " should be finished at " & FormatDateTime(ETA,4) If(DatePart("d",ETA) = DatePart("d",Now)) Then strDescription = strDescription & " today." Else strDescription = strDescription & " in " & DateDiff("d",Now,ETA) & " day(s)." End If Else strDescription = strDescription & " finished " & Now & "!" End If Function Six: Calculates time needed GetTimeDescription = strDescription for solution End Function

Public Function VectorCreate(p1, p2) VectorCreate = Array(p2(0) - p1(0), p2(1) - p1(1), p2(2) - p1(2)) End Function

Public Function VectorUnitize(v)

VectorUnitize = Null Public Vector Functions: Various Dim dist, x, y, z, x2, y2, z2 vector calculations used in the

x = v(XX) : y = v(YY) : z = v(ZZ) aforementioned functions x2 = x * x : y2 = y * y : z2 = z * z

dist = x2 + y2 + z2 If dist <= 0.0 Then Exit Function dist = Sqr(dist)

66 x = x / dist y = y / dist z = z / dist

VectorUnitize = Array(x, y, z) End Function

Public Function VectorLength(v)

VectorLength = Null By mapping out the three dimensional

Dim dist, x, y, z, x2, y2, z2 x = v(XX) : y = v(YY) : z = v(ZZ) x2 = x * x : y2 = y * y : z2 = z * z dist = x2 + y2 + z2 translation visually, it allows it to

VectorLength = Sqr(dist)

End Function

Public Function VectorDotProduct(v1, v2) be translated into computer code, VectorDotProduct = v1(XX) * v2(XX) + v1(YY) * v2(YY) + v1(ZZ) * v2(ZZ) End Function

Public Function VectorCrossProduct(v1, v2) thus making it part of generative VectorCrossProduct = Null Dim x, y, z x = v1(YY) * v2(ZZ) - v1(ZZ) * v2(YY) y = v1(ZZ) * v2(XX) - v1(XX) * v2(ZZ) z = v1(XX) * v2(YY) - v1(YY) * v2(XX) VectorCrossProduct = Array(x, y, z) system that can inform the future of

End Function

Public Function VectorAdd(v1, v2) VectorAdd = Null VectorAdd = Array(v1(XX) + v2(XX), v1(YY) + v2(YY), v1(ZZ) + v2(ZZ)) a more sustainable, more waste- End Function

Public Function VectorSubtract(v1, v2) VectorSubtract = Null VectorSubtract = Array(v1(XX) - v2(XX), v1(YY) - v2(YY), v1(ZZ) - v2(ZZ)) conscious architecture in our future. End Function

Public Function VectorMultiply(v1, v2) VectorMultiply = Null VectorMultiply = Array(v1(XX) * v2(XX), v1(YY) * v2(YY), v1(ZZ) * v2(ZZ)) End Function With the institution of large scale

Public Function VectorScale(v, d) VectorScale = Null VectorScale = Array(v(XX) * d, v(YY) * d, v(ZZ) * d) End Function rapid-construction, technologies in

Public Function VectorCompare(v1, v2) VectorCompare = vbFalse

If v1(XX) = v2(XX) And v1(YY) = v2(YY) And v1(ZZ) = v2(ZZ) Then the realm of additive manufacture VectorCompare = vbTrue End If

End Function are going to bring about a change the way we understand how architecture is buit and rid the construction field of the waste that we now see through the use of standardized construction materials. That savings compounded by the material saving that we will find through the institution of natural models, such as this one, will pave the way for our a truly sustainable future. 67

FIGURE 38 : Example of script dividing 3-Dimensional space 68 [BIO]

Conclusion

[3.5] ith these new and long-awaited freedoms Wthe stage is set to realize the construction of a biologically-inspired architecture that is designed to take advantage of 3.8 billion years of evolutionary research and development[ lviii ] towards optimizing material and energy distribution. Dennis Dollens agrees that, “architecture deserves to be re- conceptualized in a biologic frame, not merely in a frame of materials, systems, and aesthetics.”[ lix ] The utilization and integration of natural morphologies and processes into the architectural design process

lviii. . Beynus, Janine. “Janine Benyus Share’s Nature’s Designs.” TED© Talks Conference. April 2007. Guest Lecture. lix. . Dollens, Dennis. Digital-Botanic Architecture. Santa Fe: SITES Books, 2005. Print. 12 69 holds incredible potential for the future of sustainable design, and this generation will have the tools to bring those applications out of the theoretical realm and into physical reality.

This generation will witness an interdisciplinary collaboration resulting in a change from metaphor to model, from ‘nature’ as a source of formal inspiration to ‘nature’ as a mine of interrelated dynamic processes that are available for analysis and digital simulation.[ lx ] Also, this research is important for it will add to the ongoing debate over the effect of ‘the digital’ the role of the architect and further discussion of the notion of ‘digital tectonics’, and, furthermore, because the subject matter is relatively novel. New questions bear new answers, especially in a field as readily and optimistically synthetic as architecture, or as Allen Cunrow more pointedly wrote in his poem Landfall in Unknown Seas, “simply sailing in a new direction you could enlarge the world.”[ l x i ]

lx. . Weinstock, Michael. “Metabolism and Morphology.” AD: Architectural Design. 78.2 (2008): 27-33. Print. 27. lxi. . Abruzzo, Emily, Eric Ellingsen, Johnathan D. Solomon, ed. Models. 306090 11 (306090). New York: Princeton Architectural P, 2008. 70 LIST OF IMAGES LoI 72

FIGURE 1: p. 6 – Compact Flourecent Light. (http://store.applebazaar.com/blog/wp-content/ uploads/2010/01/cfl_green.jpg)

FIGURE 2: p. 7 – CFL ballast. (http://stoppingatthegreenlight.wordpress.com) Accessed 2 May 2010.

FIGURE 3: p. 9 – Barbed Wire Closeup. (http://commons.wikimedia.org/wiki/File:Barbed_ Wire_Closeup.jpg) Accessed 12 Feb 2010.

FIGURE 4: p. 9 – Thorn. (http://www.chuckryor.com/wp-content/uploads/2009/10/thorn- photo_if.jpg) Accessed 12 Apr. 2010.

FIGURE 5: p. 11 – Biomimicry Ccver. (http://www.mediabistro.com/unbeige/aiga_next/ janine_benyus_biomimicry_mama_68911.asp) Accessed 3 Jan. 2010.

FIGURE 6: p. 12 – Biomimicry Guild Logo. (http://www.icse.nl/site/newsletter. php?newsletterid=15 Accessed) 12 Apr. 2010.

FIGURE 7: p. 15 – Abalone Beach. (http://discoveryspace.upei.ca/mhl/system/files/ u1/25ABALONE_BEACH_narrowweb__300x363,0.jpg) Accessed 12 Apr. 2010.

FIGURE 8: p. 16 – Brittle Star. (http://media-2.web.britannica.com/eb-media/80/6880-004- AACBC768.jpg) Accessed 12 Apr. 2010.

FIGURE 9: p. 16 – Sea Sponge. (http://www.cinvin.com/testvb/wcc/forums/showthread. php?t=24416) Accessed 12 Apr. 2010.

FIGURE 10: p. 18 – Wind turbines inspired by Whales. (http://www.thenakedscientists.com/ HTML/content/interviews/interview/1282) Accessed 7 Feb 2010.

FIGURE 11: p. 18 – Wind Turbine Prototype. (http://www.thenakedscientists.com/HTML/ content/interviews/interview/1282) Accessed 7 Feb 2010.

FIGURE 12: p. 25 – Darwin’s Evolutionary Tree. (http://www.curatedobject.us/the_curated_ object_/2008/03/exhibitions-t-1.html) Accessed 12 Apr. 2010. LoI 73

FIGURE 13: p. 27 – Haekel, Ernst. “Siphonophorae”. Kunstformen der Natur. (http://www. chuckryor.com/wp-content/uploads/2009/10/thorn-photo_if.jpg) Accessed 12 Mar. 2010.

FIGURE 14: p. 27 – Sullivan, Louis. Carson Pirie Scott Department Store. (http://www.chuckryor. com/wp-content/uploads/2009/10/thorn-photo_if.jpg http:// www.bc.edu/bc_org/avp/cas/fnart/fa267/sullivan.html) Accessed 12 Apr. 2010.

FIGURE 15: p. 28 – Paris Metro Entrance. (http://gatewayparis.wordpress.com/2010/02/24/ metro-i-paris-for-dummies/) Accessed 12 Apr. 2010.

FIGURE 16: p. 28 – Paris Metro Signage. (http://gatewayparis.wordpress.com/2010/02/24/ metro-i-paris-for-dummies/) Accessed 12 Apr. 2010.

FIGURE 17: p. 30 – Sullivan, Louis. Carson Pirie Scott Department Store. Detail. (http://vcande. blogspot.com/2010/04/48-evolutions-influence-on-other.html) Accessed 12 Apr. 2010.

FIGURE 18: p. 30 – Endell, August. Elvira house. Munich, 1897. (http://www.jahsonic.com/ AugustEndell.html) Accessed 12 Apr. 2010.

FIGURE 19: p. 31 – Gaudi, Antoni. Parc Guell. Barcelona, 1914. (http://www.eurotrip.com/ content/parc-g%C3%BCell-barcelona) Accessed 12 Apr. 2010.

FIGURE 20: p. 32 – Gaudi, Antoni. Batllo house. Barcelona, 1906. (http://www.eurotrip.com/ content/parc-g%C3%BCell-barcelona) Accessed 12 Apr. 2010.

FIGURE 21: p. 33 – Gaudi, Antonio. The Expiatory Temple of the Sagrada Familia. Barcelona. Exterior. (http://www.bruceeisner.com/fiximage/gaudi_barcelona. jpg) Accessed 12 Apr. 2010.

FIGURE 22: p. 33 – Gaudi, Antonio. The Expiatory Temple of the Sagrada Familia. Barcelona. Columns. (http://paultoenjes.wordpress.com/) Accessed 12 Apr. 2010.

FIGURE 23: p. 41 – Barbed Wire Closeup. (http://commons.wikimedia.org/wiki/File:Barbed_ Wire_Closeup.jpg) Accessed 12 Feb 2010.

FIGURE 24: p. 41 – Thorn. (http://www.chuckryor.com/wp-content/uploads/2009/10/thorn- photo_if.jpg) Accessed 12 Apr. 2010.

FIGURE 25: p. 44 – Le Corbusier. Le Modular. 1948. (http://www.borxu.com/corbu/html/ modular.html) Accessed) 12 Apr. 2010. LoI 74

FIGURE 26: p. 45 – On Growth and Form. Cover. (http://www.bookrags.com/studyguide- ongrowthform/) Accessed 12 Apr. 2010.

FIGURE 27: p. 46 – Thompson, D’Arcy. Catesian Mapping from On Growth and Form. Pelvis bone. (http://www.christianhubert.com/writings/mapping.html) Accessed 12 Apr. 2010.

FIGURE 28: p. 46 – Thompson, D’Arcy. Catesian Mapping from On Growth and Form. Mola- mola, (http://www.oceansunfish.org/evolution.php) Accessed 12 Apr. 2010.

FIGURE 29: p. 50 – Analyses of Victoria Regia. 1851. (http://upload.wikimedia.org/wikipedia/ commons/0/04/Victoria_Regia._(Analyses)_(1851).jpeg) Accesed 7 Feb 2010.

FIGURE 30: p. 51 – Giant Lilies. (http://www.flickr.com/photos/woojinhan/3891332466/) Accessed 30 Apr. 2010.Courtesy of Woojin Han.

FIGURE 31: p. 51 – Underside of a Giant Lily. (http://www.flickr.com/photos/ woojinhan/3891332904/) Accessed 30 Apr. 2010.Courtesy of Woojin Han.

FIGURE 32: p. 54 – 2-D Voronoi Rule System (author)

FIGURE 33: p. 55 – Voronoi system deployed in nature (author)

FIGURE 34: p. 57 – Voronoi vs. Orthogonal geometry diagram (author)

FIGURE 35: p. 58 – Voronoi vs. Orthogonal geometry graphs (author)

FIGURE 36: p. 64 – 3-D Voronoi Rule System (author)

FIGURE 37: p. 66 – Breakdown of 3-D Voronoi Script (author)

FIGURE 38: p. 67 – Example: 3-D Voronoi Script (author) BIBLIOGRAPHY BI 76

BOOKS

Abruzzo, Emily, Eric Ellingsen, Johnathan D. Solomon, ed. Models. 306090 11 (306090). New York: Princeton Architectural P, 2008.

Allen, Stan. “From Object to Field.” Architecture After Geometry. Ed. Greg Lynn. Academy Press, 1998. Print.

Benyus, Janine M. Biomimicry: Innovation Inspired by Nature. New York: Perennial, 2002.

Dollens, Dennis, ed. Genetic Architectures / Arquitecturas geneticas. Santa Fe: SITES Books, 2004. Print.

Dollens, Dennis. Digital-Botanic Architecture. Santa Fe: SITES Books, 2005. Print.

Johnson, Steven. Emergence: The Connected Lives of Ants, Brains, Cities, and Software. New York: Penguin Books, 2002. Print.

Kolarevic, Branko, ed. Architecture In the Digital Age: Design and Manufacturing. London: Taylor & Francis, 2003.

LEED Reference Guide: New Construction & Major Renovations, v2.2. U.S. Green Building Council. Washington, DC: 2006.

Langton, Christopher G., ed. Artificial Life: The Proceedings of an Interdisciplinary Workshop on the Synthesis and Simulation of Living Systems, held September, 1987 in Los Alamos, New Mexico. Redwood City: Addison-Wesley, 1989.

Lynn, Greg. Animate Form. New York: Princeton Architectural Press, 1999.

Payne, Andy. Grasshopper Primer: For Rhinoceros 4.0 SR4. LIFT Architects, 2009.

Renner, Gábor, and Anikó Ekárt. “Genetic algorithms in computer aided design..” BI 77

Computer-Aided Design 35.8 (2003): 709. EBSCOhost. Web.

Spuybroek, Lars. The Architecture of Continuity: Essays and Conversations. Rotterdam: V2_Publishing, 2008.

Terzidis, Kostas. Algorithmic Architecture. 1st ed. Oxford: Architectural Press, 2006. Print.

Verb natures. Barcelona: Actar, 2006.

PERIODICALS

Bollinger, Klaus, Manfred Grohmann, and Loiver Tessmann. “Form, Force, Performance Multi-Parametric Structural Design.” AD: Architectural Design. 78.2 (2008): 20-25. Print.

Bonabeau, Eric. “From Classical Models of Morphogenesis to Agent-Based Models of Pattern Formation.” Artificial Life. 3.3 (1997): 191-211. Print.

Castle, Helen. “Editorial - Versioning: Evolutionary Techniques in Architecture.” AD: Architectural Design. 72.5 (2002): 4. Print.

Crayton, Tim. “Design Implications of Mass Customization.” AD: Architectural Design. 71.2 (2001): 74-81. Print.

Dyson, Anna. “Recombinant Assemblies.” AD: Architectural Design. 72.5 (2002): 60- 66. Print.

Garber, Richard. “Alberti’s Paradigm.” AD: Architectural Design. 79.2 (2009): 88-93. Print.

Garber, Richard. “Optimization Stories: The Impact of Building Information Modeling on Contemporary Design Practice.” AD: Architectural Design. 79.2 (2009): 6-13. Print.

Goulthorpe, Mark. “Precise Indeterminacy: Three Projects by deCOI and an Interview with Mark Gouldthorpe Conducted by Amanda Reeser and Ashley Schafer on October 8, 2003.” Praxis. 1.6 (2004): 28-45. Print.

Hensel, Michael and Achim Menges. “Aggregates.” AD: Architectural Design. 78.2 (2008): 80-87. Print. BI 78

Hensel, Michael and Achim Menges. “Designing Morpho-Ecologies: Versatility and Vicissitude of Heterogeneous Space.” AD: Architectural Design. 78.2 (2008): 102-113. Print.

Hensel, Michael and Achim Menges. “Membrane Spaces.” AD: Architectural Design. 78.2 (2008): 74-79. Print.

Hensel, Michael and Achim Menges. “Versatility and Vicissitude: An introduction to Performance in Morpho-Ecological Design.” AD: Architectural Design. 78.2 (2008): 5-11. Print.

Hensel, Michael, Achim Menges, and Michael Weinstock. “Emergence in Architecture.” AD: Architectural Design. 74.3 (2004): 6-10. Print.

Hensel, Michael, Achim Menges, and Michael Weinstock. “Fit Fabric: Versatility through Redundancy and Differentiation.” AD: Architectural Design. 74.3 (2004): 40-47. Print.

Hensel, Michael, Achim Menges, and Michael Weinstock. “Frei Otto in Conversation with the Emergence and Design Group.” AD: Architectural Design. 74.3 (2004): 18-25. Print.

Hensel, Michael, Defne Sunguroglu and Achim Menges. “Material Performance.” AD: Architectural Design. 78.2 (2008): 34-41. Print.

Hensel, Michael. “Finding Exotic Form: An Evolution of Form Finding as a Design Method.” AD: Architectural Design. 74.3 (2004): 26-33. Print.

Hensel, Michael. “Performance-Oriented Design: Precursors and Potential.” AD: Architectural Design. 78.2 (2008): 48-53. Print.

Jaeschke, Aleksandra. “Environmental Intensifiers.”AD: Architectural Design. 78.2 (2008): 88-95. Print.

Jeronimidis, George. “Biodynamics.” AD: Architectural Design. 74.3 (2004): 90-95. Print.

Joshi, Atri. Emergence in Architecture. Diss. University of New Delhi, 2006.

Kwinter, Sanford. “J’Accuse.” Praxis. 1.6 (2004): 5-7. Print.

Leach, Neal. “Digital Morphogenesis.” AD: Architectural Design. 79.1 (2004): 32-37. BI 79

Print.

Lynn, Greg. “Constellations in Practice.” Praxis. 1.6 (2004): 9-17. Print.

Melvin, Jeremy. “Building Profile - The Kunsthaus at Graz.”AD: Architectural Design. 74.3 (2004): 101-105. Print.

Menges, Achim “Morpho-Ecologies: Approaching Complex Environments.” AD: Architectural Design. 74.3 (2004): 80-89. Print.

Menges, Achim. “Inclusive Performance: Efficiency Versus Effectiveness - Towards a Morpho-Ecological Approach for Design.” AD: Architectural Design. 78.2 (2008): 54- 63. Print.

Menges, Achim. “Manufacturing Performance.” AD: Architectural Design. 78.2 (2008): 42-47. Print.

Moussavi, Farshid and Alejandro Zaera Polo. “Types, Style and Phylogenesis.” AD: Architectural Design. 74.3 (2004): 34-39. Print.

O’Reilly, Dr Una-May, Martin Hemberg, and Achim Menges. “Evolutionary Computation and Artificial Life in Architecture: Exploring the Potential of Generative and Genetic Algorithms as Operative Design Tools.” AD: Architectural Design. 74.3 (2004): 48-53. Print.

Pasquarelli, Sharples Holden. “Eroding the Barriers.” AD: Architectural Design. 72.5 (2002): 90-100. Print.

ELECTRONIC AND MISCELLANEOUS

Beynus, Janine. “Janine Benyus Share’s Nature’s Designs.” TED Talks Conference. April 2007. Guest Lecture.

Dyson, Freeman “Our Biotech Future.” New York Review of Books 54.12 (2007): 4-8. Academic Search Complete. EBSCO. Web. 14 Nov. 2009.

Keefe, Greg. “Daffodils and Polar Bears: Towards a Biomimetic Architecture.” GREEN MODERNISM, the weblog. BlogSpot. Web. 10 June. 2009.

Roche, Francois. “(n)certainties2 - Columbia - Fall 08.” Wordpress. Web. 10 June. BI 80

2009.

Wiscombe, Tom. “Emergent Processes.” Web. 10 September. 2009.