Sunday, July 26, 2009

architectural felt

i'm working on my paper for kathy's contemporary discourses in architecture. the gist of it is that i would like to do a kudless/kolarevic-type emergent material experiment. so i thought of an exhibit which i saw at the mexican pavilion (venice biennale 2008) called wavefunction. 50 eames molded plastic chairs were mounted on pistons which raised or lowered the chairs based on a wave pattern generated by movement around the room. (in the next room was the computer which calculated the response to movement and showed the waves radiating out from people in proportion to the intensity of their movement. i love that exhibit in particular...it was curious and inviting and a little bit magical and it made children and adults alike run around the room, stop dead suddenly, whirl around and run back the other way - just to see and here these chairs rise and fall in waves. and then i thought of felt...i don't know much about felt. there is a felt-making workshop at the art gallery in the school, if i remember correctly. i googled it and found this among other fabulously whimsical creations:but before i even got that far, i googled felt-making and the first two video hits are of architectural felt - mongolians use felt to clad their buildings! the process of felt-making is fantastically visceral - beating the wool and rolling it to make and shape it. so my thought is to try and combine these two ideas to create a felt shape which is the result of a digital translation of movement in a space into variable forces applied to the wool.

Tuesday, July 21, 2009

A Dangerous Thesis - Thesis Group Assignment

Just like the clock maker metaphors of the Enlightenment, or the dialectical logic of the nineteenth century, the emergent worldview belongs to this moment in time, shaping our thought habits and colouring our perception of the world. (Steven Johnson. 2002. Emergence : The connected lives of ants, brains, cities, and software. 1st Touchstone ed. New York. p.66)
Emergence as a theory is philosophically challenging to many people. The shift in thinking from top-down to bottom-up requires new cultural narratives which reimagine human agency and fundamentally challenge existing narratives. A design rooted within an emergent worldview risks knee-jerk dismissal not only because of it's new-ness but because of it's implicit challenge to the reviewer to reimagine their own place in the world as both individual agent and member of the emergent collective both acting-upon and affected-by the group. In mapping public space, hegemony, social interactions, and social/cultural response to interventions in public places and advocating for further interventions which support adaptive emergence in the citizens of the downtown core, I risk initiating a process with a highly uncertain outcome. Not only will Galt naturally resist change, but it may also revolt against its role as the subject of my thesis experiments.

Saturday, July 4, 2009

Contemporary Discourses Seminar Notes

Emergent Material Methodologies:
Genetics, Biomimesis and Performative Structures


Introduction

“Just like the clock maker metaphors of the Enlightenment, or the dialectical logic of the nineteenth century, the emergent worldview belongs to this moment in time, shaping our thought habits and colouring our perception of the world.”1

If we accept Steven Johnson’s2 analysis of our current cultural circumstance, that “the emergent worldview belongs to this moment in time” then the question for us is: what happens to architecture if we think and design from the bottom-up?



Johnson shows us what natural urban emergence looks like in his analysis of Engels’ writing on Manchester (Figure 1):
...what Engels observed are patterns in the urban landscape, visible because they have a repeated structure that distinguishes them from the pure noise you might naturally associate with an unplanned city. They are patterns of human movement and decision-making that have been etched into the texture of city blocks, patterns that are then fed back to the Manchester residents themselves, altering their subsequent decisions. (In that sense, they are the very opposite of the traditional sense of urban complexity - they are signals emerging where you would otherwise only expect noise.) A city is a kind of pattern amplifying machine: its neighbourhoods are a way of measuring and expressing the repeated behavior of larger collectivities - capturing information about group behavior, and sharing that information with the group. Because those patterns are fed back to the community, small shifts in behavior can quickly escalate into larger movements: upscale shops dominate the main boulevards, while the working class remains clustered invisibly in the alleys and side streets; the artists live on the Left Bank, the investment bankers in the Eighth Arrondissement. You don’t need regulations and city planners deliberately creating these structures. All you need are thousands of individuals and a few simple rules of interaction. The bright shop windows attract more bright shop windows and drive the impoverished toward the hidden core. There’s no need for a Baron Haussmann in this world, just a few repeating patterns of movement, amplified into larger shapes that last for lifetimes: clusters, slums, neighbourhoods.3
What architects are wrestling with today is the proliferation of artificial emergence, eg. amazon’s “you might also consider...” (Figure 2), which means not only recognizing emergence in architecture and the city, but tackling how architecture can best absorb and instrumentalise a shift in thinking as drastic as top-down to bottom-up.

Figure 2: amazon.ca “you might also consider...”


As thesis for this week’s discussion is the Architectural Association’s Emergent Architecture Programme run by the Emergence and Design Group (Michael Weinstock, Achim Menges, and Michael Hensel).

First, some definitions.

Definitions
Defining the phenomenon:
Complex behavior: a system with multiple agents dynamically interacting in multiple ways, following local rule and oblivious to any higher level instructions.4

Emergent behavior: a higher-level pattern arising out of parallel complex interactions between local agents.5

Adaptive emergent behavior: the system would use local rules between interacting agents to create higher-level behavior well suited to its environment.6

Adaptive Emergent Architecture: ‘Emergence’ is the scientific mode in which natural systems can be explored and explained in a contemporary context. It provides ‘models and processes for the creation of artificial systems that are designed to produce forms and complex behavior, and perhaps even real intelligence’.7

Defining the Methods:
Biomimesis: bionics is the application of biological methods and systems found in nature to the study and design of engineering systems and modern technology.8

Generative modeling: a shape is described by a sequence of processing steps, rather than just the end result of applying these operations. Shape design becomes rule design.9

Performative Structure: (as defined in Integrating Knowledge Modeling and Multi-Agent Systems by Mario G´omez and Enric Plaza from the Artificial Intelligence Research Institute and the Spanish Scientific Research Council) a network of connected scenes that captures the relationships among scenes. A performative structure constrains the paths agents can traverse to move from one scene to another, depending on the roles they are playing.10

Other Definitions:
Derivative: in calculus ... the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point. For example, the derivative of the position (or distance) of a vehicle with respect to time is the instantaneous velocity (respectively, instantaneous speed) at which the vehicle is traveling. Conversely, the integral of the velocity over time is the vehicle's position.11

Differentiate: to obtain the mathematical derivative of.12

Differential: a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics and other disciplines.13

Operation: in its simplest meaning in mathematics and logic, an operation is an action or procedure which produces a new value from one or more input values.14

Parametric Model: It maintains consistent relationships between elements as the model is manipulated. For example, in a parametric building modeler, if the pitch of the roof is changed, the walls automatically follow the revised roof line.”15

Phenotype: is any observable characteristic or trait of an organism: such as its morphology, development, biochemical or physiological properties, or behavior. Phenotypes result from the expression of an organism's genes as well as the influence of environmental factors and possible interactions between the two. The genotype of an organism is the inherited instructions it carries within its genetic code. Not all organisms with the same genotype look or act the same way, because appearance and behavior are modified by environmental and developmental conditions. Similarly, not all organisms that look alike necessarily have the same genotype.16

Proliferation: the growth or production of cells by multiplication of parts or a rapid and often excessive spread or increase: nuclear proliferation.17

Emergent Architecture Programme
Architecture Association School of Architecture: EmTech MSc/MArch


The Emergent Technologies and Design programme (Figure 3) is open to graduates in architecture, engineering and industrial design who wish to pursue design research that proceeds from innovative technologies.

The programme focuses on the development of skills and knowledge located in new production paradigms. Phase 1 of the programme is structured around seminar courses, the core studio and supervised research. Phase 2 consists of further supervised research, culminating in the design dissertation. Seminar courses provide the theoretical context, setting out the origins, theories, instruments and practices of Emergent Technologies and exploring their relation to contemporary architectural debate.18
AA Programme Thesis: “Through its advocacy of emergence, the Emergence and Design Group (Achim Menges, Michael Weinstock, Michael Hensel) is intentionally setting out to produce a new research-based model for architectural enquiry....The research that has been undertaken is as important for its redefinition of architectural working relationships as the iterative techniques and new material models it proposes.”19
(here is the complete EmTech programme outline)

EmTech Directors:



Michael U Hensel (Dipl Ing Grad Dipl Des AA Architekt AKNW) is an architect, researcher and writer. He is a member of the independent, interdisciplinary and international research network OCEAN, professor for research by design at AHO – the Oslo School of Architecture and Design, innovation fellow at the University of Technology in Sydney, board member of BIONIS – the Biomimetics Network for Industrial Sustainability, editorial board member of AD Wiley and JBE – Journal of Bionic Engineering, Elsevier Scientific Press. (Figure 4)


Figure 5: Michael Weinstock with a student (above left), and
a Yale Architecture student project (above right)



Michael Weinstock is an architect. Born in Germany, lived as a child in the Far East and then West Africa, attended an English public school. Ran away to sea at age 17 after reading Conrad. Years at sea in traditional sailing ships, with shipyard and shipbuilding experience. Studied architecture at the AA, where he has also taught since 1989. Founder and Director of Emergent Technologies Masters Programme, Master of Technical Studies since 1997, and Academic Head of the AA since 2006. He has lectured and published widely, and been Visiting Professor at Rome, Barcelona and Yale. He is currently International Advisor to the Delft School of Design PhD programme and editorial board member of AD Wiley. (Figure 5)

EmTech Studio Master:


Figure 5: Achim Menges (above left), and
an image from OCEAN’s Computational Morphogenesis (above right)


Achim Menges (AA Dipl (Hons) RIBA II) is an architect and partner in OCEAN NORTH, the Emergence and Design Group and the Differentiated Structures Research Group. He studied at the Technical University of Darmstadt, Germany and graduated from the AA School of Architecture with Honours. He has been a visiting professor at Rice University School of Architecture, Houston and is currently Unit Master of Diploma Unit 4 and Studio Master of the Emergent Technologies and Design Master Programme at the AA. Achim Menges recently received the FEIDAD (Far Eastern International Digital Architectural Design) Outstanding Design Award in 2002, the FEIDAD Design Merit Award in 2003, the Archiprix International Award 2003, RIBA Tutor Price 2004 and the International Bentley Educator of the Year Award 2005.

Professional Research:

Figure 6: Jväskylä Music and Arts Center by OCEAN NORTH 2004-05

OCEAN/OCEAN NORTH:
OCEAN20 is an international, interdisciplinary and independent research network that conducts research by design in the intersection between architecture, urban, regional and landscape design, industrial and product design, computational science, biology, music, engineering, climatology and other disciplines and fields of inquiry. (Figure 6)

Applied Principles of Emergence: Summary
A new generator of diagrams or a synthesised process of formation and materialisation?

Two general methods of applying the principles of emergence to architecture drawn from this week’s readings:

Phylogram(genetics):
The evolutionary history of architecture (within a practice)

Phylogram (or Phylogenetic tree): a device of classification in biology which is used for systematic study of evolutionary history and the relationships among organisms that have common ancestors.21

Morpho-ecologies(biomimesis/performative structures):
The integration of ecological, topological and structural performances (using generative design strategies)

Morphology (biology): the form, structure and configuration of an organism. This includes aspects of the outward appearance (shape, structure, colour, pattern) as well as the form and structure of the internal parts like bones and organs. This is in contrast to physiology, which deals primarily with function.22

Ecology: the interdisciplinary scientific study of the distribution and abundance of organisms and their interactions with their environment. The environment of an organism includes all external factors, including abiotic ones such as climate and geology, and biotic factors, including members of the same species (conspecifics) and other species that share a habitat. If the general life science of biology is viewed as a hierarchy of levels of organization, from molecular processes, to cells, tissues and organs, and finally to the individual, the population and the ecosystem, then the study of the latter three levels belongs within the purview of ecology.23
Applied Principles of Emergence: Phylogram
“The phylogram operates to identify consistency across the different design processes, projects, and the overall body of the architects’ work”24

FOA’s Phylogenetic Tree
(the categories, descriptions and diagrams below are all quoted/copied directly from foa’s Phylogenesis)25
“Typology provides raw material, a kind of “genetic pool” that we carry with us. We regard type not as fixed structures but as open organization structures we can proliferate and modify.”26

“We don’t think that one can solve all architectural problems by using these generative systems. It would be completely mad; neither pragmatic nor efficient. You have to rely on your experience as an architect, on your acquired knowledge to focus the experiment, and then in some areas of the project these methods will be viable.”27


Function
(ground/envelope)
This first differentiation divides the projects into two major lineages that relate obviously with the particular nature of our work. The manipulation of surface is a crucial trait of our work and therefore the first division relates to the predominant function of the surface. Projects are here classified into those which relate to the formation of enveloping surfaces, or surface whose primary function is the enclosure of space, and those surfaces whose primary function is the construction of a connective ground.


Faciality
(single face - multiple face)
A surface will have at least one face depending on how many of its surfaces are inhabited. For example, a monolith or a ground are experienced only on one of their faces, while usually a slab or a facade have an outside and an inside, or a floor and a ceiling. Depending on the number of layers into which the surface slices spaces, the order of faciality increases.


Balance
(constant: parallel/perpendicular - shifting)
This discriminator classifies surfaces in reference to the force of gravity, which becomes critical in establishing the relationship between the surface and the structure and drainage systems. This classification determines, in the first instance, whether the surface remains constant in the alignment to gravity, or whether it alternates orientation within the project. If the surface remains constantly perpendicular to gravitational force, it will become mostly a ground or a roof. If it is constantly in parallel, it will mainly be a wall or a facade.

If the surface shifts between parallel and perpendicular to gravitational force, the building will be a blob or a shed, where the roof and the walls are continuous. Depending on this alignment the quality of the surface will vary substantially, in both its geometrical definition and its material qualities.


Discontinuity
(planar - rippled - pinched - perforated - bifurcated)
This attribute of the species describes the typology of singularity that determines discontinuities on the surface, and is classified in a gradation depending on the intensity of the surface singularities. If the surface of is continuous, does not have interruptions excepts in its limits, and does not have any surface singularities, it is planar. If it has some local deformation but no interruptions, it becomes rippled; if the singularities are more accentuated to the point where the tangent varies more than 90°, it is pinched. If it is locally interrupted, the surface is perforated. If it is locally interrupted but is continuous on a different level, layer or space, simultaneously establishing continuity and discontinuity, then the surface is bifurcated. Pierced organisations usually correspond to the resolution of specific connections between well-demarcated spatial segmentations, while bifurcations tend to be more common in projects that require loose spatial segmentations.


Orientation
(oriented: striated/polar - non-oriented)
This category divides surfaces with respect to the spatial ordering of their singularities. Independent of their nature, surface singularities can be organised following a consistent law, or they can be entirely contingent. The second category tends to correspond to organisations more dependent upon pre-existing traces or local singularities, responding to pre-existing focalisations of parameters in certain zones of space, while the first category corresponds to organisations with a weak relationship to pre-existing fields and a more self-supporting scale or quality. Among those surface singularity fields that are oriented, they can be oriented following a striated distribution - that is, following a parallel order - or to respond to centres or poles. The striated variety is usually related to fields with a prevailing flow direction, while polar structures relate to either strong focal pre-existences or central or polycentric organisations of the project.


Geometry
(continuous - discontinuous)
The geometrical discriminator refers to the geometrical continuity of the surface. It classifies the projects between those which have a continuous variation of the tangent, and therefore produce a smooth surface, and those which have points of indeterminate tangent to the surface at certain moments, producing breaks in the geometrical continuity of the surface. Those projects produce edges or ridges rather than seamless discontinuities.


Diversification
(patterned - contingent)
Every branch of the phylogenetic tree is split between those projects where a patterned system of discontinuities, accidents or shift in orientation occur on a regular basis across the surface, and those where they appear contingently based on local specificity. Contingent diversification responds usually to organisations constructed from the bottom-up or that are highly responsive to local specificities, while patterned textures correspond to organisations deployed from the top-down, or where the scale of the organisations is such that the capacity of self-determination is stronger than the local singularities.

Applied Principles of Emergence: Morpho-Ecologies
“The increasing complexity of space-use cycles requires an understanding of the built environment as ecological, topological, and structural provisions that facilitate human activities. Ecology refers to all the relationships between human groups and their physical and social environments. Topology is ... the connections between all the material elements in an environment. Structure refers to organisational capacities above and beyond load bearing.”28

The morpho-ecological approach to design is more difficult for me to understand than phylogenesis, because of the differential math and computer programming necessary for design. The emTech program solicits students from a variety of backgrounds, including engineering, computer sciences, math, biology and more to research and develop design strategies and tools. Without these experts at hand, I grasp the concepts but fail utterly at comprehending the particular application of those concepts.

One of the keys to understanding this approach is an acute awareness of the shift from geometric to differential mathematics in architectural design: that is to say the shift from static to dynamic forms in architecture.29 Parametric modeling is one of the tools architects can use to design using differential mathematics. “Parametric Model: It maintains consistent relationships between elements as the model is manipulated. For example, in a parametric building modeler, if the pitch of the roof is changed, the walls automatically follow the revised roof line.”30

Postagriculture
“The Postagriculture project begins with the recognition of the importance of environmentally and socially sustainable food production. The project needed to negotiate multiple programmatic claims on a limited space.... (The) location needs to facilitate both time-intensive agricultural production ... and extensive public leisure activities.... The aim is to articulate an inclusive and responsive strategy, one that enables a mode of agricultural production that is a highly integrated, mutable and vital urban programme. The project promotes a local hybridisation of intensified agroproduction with public recreation. This in turn demands an architecture that is capable of negotiating and adapting to different system requirements.”31

Postagriculture, one of Achim Menges’ designs using a morpho-ecological approach, is designed through multiple acts of differentiation. (A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics and other disciplines.)32 For example, the light level within the structure is a function of available light and transparency of material, the transparency of the material is a function of its density, the structural capacity of the material is also a function of its density and so on. If particular light levels are required within a building, a differential equation will be necessary to solve the relationship between light, material thickness, and structural capacity.(Figures 7 and 8).


Figure 7: Organisational model of differential intersystemic relations (above left)
derived by a digital-mapping technique of system-specific light and climatic conditions
(above right).
33


Figure 8: Component evolution based on parametric variations of the boundary definition points, the seam layout, the pressure of the compressed air volume and the consequent geometry and prestressing of the membranes.34

(here is a detailed description of the postagriculture project)

Conclusion
Re-imagining architecture from the bottom up
I agree with Steven Johnson’s assertion that the emergent worldview belongs to this moment in time and that it represents a fundamental shift in thinking from the clockmaker metaphor of the enlightenment. I think this week’s authors have been tackling how architecture can best absorb this shift in thinking: from top-down to bottom-up.

Two broad methods of instrumentalising emergent thinking in architecture have been investigated in this paper: phylogenesis, the development of an evolutionary history of architecture within a practice, and morpho-ecologies, the integration of ecological, topological and structural performances using generative design strategies.

The phylogenesis approach has been developed by foreign office architects (foa) while the morpho-ecological approach has been developed by the Emergence and Design Group, which is composed of the three men who run the EmTech programme at the Architectural Association.

These two approaches differ principally in their application to architecture: phylogenesis is used to generate diagrams for architectural design, while morpho-ecologies are formal, structural and programmatic solutions to architectural problems.

Can/will emergent design make it out of the research studio?

foa is up front about the fact that their phylogenesis experiment, while interesting, has yet to be instrumentalised. Despite that fact, their approach is the most accessible method for immediate application by practising architects because it uses a tool most architects already use - diagramming.


The EmTech programme’s morpho-ecological approach is more complex, requiring specialists that architects are not accustomed to working with: mathematicians, biologists, computer scientists and more. That being said, it presents, in my opinion, the more exciting of the two approaches because it proposes a significant shift in the role of architects - from form-maker to rule-maker - which would fundamentally change architecture. Because this method requires such significant changes to the role of architects, the organization of architectural practices and, ultimately, to the construction of buildings, it can only be considered to be in a nascent phase which will be unlikely to leave the studio for quite some time.

There are many questions about the validity of emergent design (is it effective? what is the goal? is there a benefit to responsive architecture? does it impede free-will? does it make a architecture for the “lowest-common-denominator”?) which i will not tackle here, but which are being and will continue to be discussed in contemporary architectural discourse. I am personally intrigued by the work done by the Emergent Design Group and OCEAN and I hope to contribute to that discourse through analysis of existing “emergent” architectures.

Theses from this week’s readings
Mertins, Bioconstructivisms:
“Art need no longer dedicate itself to the production of wholeness, since it is inherently part of the cosmos, whatever limited understanding of it we humans may believe.”35


Zaera-Polo, Breeding Architecture:
“A coherent Practice might emerge from a phylo genetic process in which a few seeds proliferate across different environments over time, generating distinct yet consistent results.”36


Menges, Polymorphism:
“A design approach using (morphogenetic design techniques and technologies) enables architects to define specific material systems through the combined logics of formation and materialisation.”37


Hensel, Material Performance Part 1: “The integral relationship between formalisation and materialisation processes based on the interaction between material and environment will have the most profound impact on the discipline of architecture and our human environment by providing exciting, performative and beautiful settings for human inhabitation.”38

Menges, Material Performance Part 2:
“This high level of integration of form, structure, and material performance enables a direct response to environmental influences without the need for additional electronic or mechanical control.”39


Lynn, Animate Form: “If there is a single concept that must be engaged due to the proliferation of topological shapes and computer-aided tools it is that in their structure as abstract machines, these technologies are animate.”40

Zaera-Polo, Types, Style and Phylogenesis: “The working techniques of FOA over many years indicate a strong interest in methods based on incremental development. It seemes logical to suggest that a more explicit use of evolutionary computational techniques could be part of the architects’ future research for the practice.”41

Endnotes
1 Johnson, Steven. 2002. Emergence : The connected lives of ants, brains, cities, and software. 1st Touchstone ed. New York. p.66
2 Steven Berlin Johnson is an American popular science author who has worked as a columnist for magazines such as Discover Magazine, Slate, and Wired. He is also a Distinguished Writer in Residence at New York University.(http://en.wikipedia.org/wiki/Steven_Berlin_Johnson accessed June 10, 2009, 11:49pm) He is a condenser of cultural phenomena much like Malcolm Gladwell or Stephen J. Dubner, blending science and pop culture to make accessible transformative ideas in academic work.
3 Johnson 2002. p.40
4 Johnson 2002. p.18
5 Johnson 2002. p.19
6 Johnson 2002. p.19
7 Menges, Achim. “Emergence in Architecture,” Emergence: Morphogenetic Design Strategies, AD 74 No. 3 (May/June 2004): 6.) (Castle, Helen. “Editorial,” Emergence: Morphogenetic Design Strategies, AD 74 No. 3 (May/June 2004): 4
8 http://en.wikipedia.org/wiki/Biomimetic
9 http://en.wikipedia.org/wiki/Generative_Modelling_Language
10 www.iiia.csic.es/People/enric/papers/ORCAS.pdf
11 http://en.wikipedia.org/wiki/Derivative
12 http://www.merriam-webster.com/dictionary/differentiate
13 http://en.wikipedia.org/wiki/Differential_equation
14 http://en.wikipedia.org/wiki/Operation_(mathematics)
15 http://encyclopedia2.thefreedictionary.com/parametric+modeling
16 http://en.wikipedia.org/wiki/Phenotype
17 http://dictionary.reference.com/browse/proliferation
18 http://www.aaschool.ac.uk/Default.aspx?section=school&page=emtech%20MSc/March&sst=2
19 Castle, Helen. “Editorial,” Emergence: Morphogenetic Design Strategies, AD 74 No. 3 (May/June 2004): 4
20 The mission of the network is to initiate, develop, promote and host collaboration in research by design with the aim to improve the current built environment and anthropobiosphere, by means of delivering new paradigms to the design of a human environment that is post-conflict, heterogeneous, stimulating, performative, context-specific, and socially and environmentally sustainable. The OCEAN network was founded in 1994 and registered in Norway as a not-for-profit organisation in 2008. Research groups are located in Frankfurt, Istanbul, London, Oslo, Sydney and Tel Aviv with currently 20 members and principal researchers.
21 Zaera Polo, Alejandro. 2006. “Types, Style and Phylogenesis” Techniques and Technologies in Morphogenetic Design, AD 76, No2 (March/April 2006). p.36
22 http://en.wikipedia.org/wiki/Morphology_(biology)
23 http://en.wikipedia.org/wiki/Ecology
24 Zaera Polo 2006. p.36
25 Foreign Office Architects. 2004. Phylogenesis: foa’s ark. Barcelona, Spain : Actar. p.12 - 15
26 Zaera Polo 2006. p.36
27 Zaera Polo 2006. p.39
28 Menges, Achim. 2006. “Morphoecologies” Techniques and Technologies in Morphogenetic Design, AD 76, No2 (March/April 2006). p.73
29 Lynn,Greg. 1999. Animate form. Princeton Architectural Press. New York.
30 http://encyclopedia2.thefreedictionary.com/parametric+modeling
31 Menges 2006. p.75
32 http://en.wikipedia.org/wiki/Differential_equation
33 Menges 2006. p.73
34 Menges 2006. p.73
35 Mertins, Detlef. 2004. “Bioconstructivisms” NOX: Machining Architecture, Lars Spruybroek. Thames and Hidson. London. p.369
36 Zaera-Polo, Alejandro. 2003. “Breeding Architecture” The State of Architecture at the Beginning of the 21st Century. Monacelli Press. New York. p.56
37 Hensel, Michael. 2006. “Polymorphism” Techniques and Technologies in Morphogenetic Design, AD 76, No2 (March/April 2006). p.86
38 Menges, Achim. 2008. “Material Performance” Performance Design AD 78, No 2 (March/April 2008). p.38
39 Menges 2008. p.41
40 Lynn 1999. p.41
41 Zaera Polo 2006. p.39