An Approach to Architectural Form Through the Complexity Theories [Kutay Karabag]

8/8/2019 An Approach to Architectural Form Through the Complexity Theories [Kutay Karabag]

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An Approach to Architectural Form through the Complexity Theories

By Kutay Karaba

submitted as a part of the requirements of ARCH 52705th.01.2006

I

What we call forms. Whether they are natural or artificial, are only the

visible trading posts of integrating and disintegrating forces mutating atlow rates of speed.

1

Frederick Kiesler

In this paper, I will develop a discussion on the position of digital architecture2

and the

way it copes with the architectural form under the light of modern chaos and complexitytheories. In order to do this, I will begin with investigating the paradigm shift in art and

architecture that seems to be occurring through the vast use of digital technology. I will

try to demonstrate some earlier examples and efforts questioning this paradigm shift in

modern avant-garde. Finally, I will try to explain the contribution of the modern chaosand complexity theories and of course the development of computer for a new approach

to the design of artistic and architectural form.There is a large domain of discussions on form, yet I will not go into the ramifications of

these discussions, neither try to develop a definition about form. On this point I willbegin with accepting the general assumptions of Wilhelm Worringer and Henri Focillon,

possessing an immense and abstract designation considering form as continuity in time.But I will try to lucidify the continuity of form, approaching it from the point of view of

modern chaos and complexity theories supported by digital technologies.

I wish to start with a rough assumption about the modernist world view of abstraction. In

his famous work Wilhelm Worringer stresses mans urge of abstraction and signifiesthat empathy with an artwork can only be structured through this urge of abstraction.

3

What Worringer defines as urge of abstraction

, and discusses on an abstract basis, can1 Kiesler, Frederick. "On Correalism and Biotechnique: A Definition and Test of a New Approach toBuilding Design",Architectural Record 86, no. 9, September 1939, p. 60.2 The term digital architecture here is not used for a certain meaning nor indicating a determined body of

architects or architectures. My intention is to recall all the activity investigating the potential of the digital

technologies as an important parameter in the field of architecture and particularly in relation to the

architectural form.3 Worringer, Wilhelm.Abstraction and Empathy: A Contribution to the Psychology of Style. New York:

International University Press, 1967, pp. 3-25.


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be described as an inherit reaction for understanding the object in general, from the point

of view that I will try to construct about the abstractionist view of modernity. Aestheticenjoyment, as defined by Worringer, occurs by constructing an empathy with the object,

an operation which necessitates an activity. This process, for Worringer, can be

understood as the combination of objective and subjective factors. Abstraction is

necessary for grasping the objective qualities. And empathy, in Worringers terms,requires a self-relation with the object, or in other words, there has to be something

related with the inner self of the being and the object for empathy to occur.4

Seeing abstraction in this way, as an inherited desire of man for understanding or

grasping what he senses, modernism can be identified as the utmost point of a history ofprocessing knowledge. From the very beginning, man tries to understand what is going

on in the exterior world of his inner self. Trying to understand such a complexity without

any introductory knowledge is a very hard task for even an intelligent creature. Mancopes with this difficulty by splitting what he senses into pieces, and trying to understand

the whole piece by piece. Sometimes it is more effective to understand the pieces and

then combine this information to get the whole picture, and sometimes there is a single

important piece of information as the essence of the whole picture.

the urge of abstraction is the outcome of a great unrest inspired in

man by the phenomena of the outside world; 5

Hence, it is possible to see abstraction in general, as a strategy for comprehending what is

happening outside. Usually the human senses are able to sense much more than thehuman being can comprehend. Turning back again to my rough assumption on

abstraction, it is possible to say that, human beings have produced knowledge employing

this strategy of abstraction, consisting of tactics such as, splitting into fragments, figuringout the essence and neglecting the details. Gestalt principles constitute a systematically

formulated set of these tactics. Through the careful use of these tactics, knowledge has

been produced and accumulated one on another. Critical points in the history ofknowledge, such as Renaissance, Enlightenment and Kants categorization of sciences

can be seen as the final successive stations in the path of the accumulation andcategorization of knowledge in this conventional way. As human beings produced and

accumulated knowledge, they have also developed certain ways of structuring and

categorizing it. My assumption is that, modernity have provided the utmost point in

utilizing these tactics to produce, gather and manage the knowledge, which have beenaccumulated too much for a long history.

After the industrial revolution and with the beginning of mass-production in various

fields, Modernism has reached the final point in a rational and reductionist world view.

Mass-production, standardization, and efficiency were some of the tools and methods

offered by modern ideology. These tools and methods have been applied in various fieldsand in various parts of the world, as the function of a highly systematic and rational

worldview.

As the mass-production and standardization were spreading to various parts of the orderof the practical life, notions such as simplicity, pure geometry and abstraction became the

4 Ibid, pp. 3-25.5 Ibid, p. 15.


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mainstream theoretical framework in the fields of art and architecture. Modern art have

became an art of highly abstract forms of pure geometry.

Aside this mainstream approach in art and architecture, there are many exceptionalexamples, some of them by very popular names of modernism, that can be interpreted as

researches for other ways of looking to the world than the rational and reductionist

worldview of modernism. On the one hand modernism had been running forward throughthe path of rationale, and on the other, modern avant-garde had been questioning the

alternative ways of looking. Avant-garde approach includes various intentions and tools

mainly located around a closer relation with the organic forms, which modernism had

estranged itself probably for the requirements of its production technologies.6

Avant-garde styles such as Cubism, Surrealism, Dadaism and Futurism can be assumed to be

offering alternative ways of looking to the world.

Hence, the way modernism, or international style looked to the world was efficient in a

way to understand and handle certain things. Yet as the number of interrelations betweencategories, series and pieces of knowledge increase drastically, the current way of

understanding and categorizing knowledge became insufficient. Avant-garde in

modernism looked for other understandings, other readings of the modern era, and as aramification of this; other visualities to see and perceive the form. Modern avant-garde

styles had developed their own way of looking to the form.

The primary reason for modern avant-garde necessitating a distinct way of looking and

expressing was their intensive effort for underlying other factors that are hidden behindthe forms and objects, than the ones revealed by modernity. The rationalist and

reductionist worldview of modernity, the furthest point in abstraction and standardization,

cannot handle and manage certain kind of information. This is both true as a worldviewand also its implications are valid in art and architecture.

Parallel to this search of distinctive ways of looking and perceiving the world, alternative

geometries for the Euclidean geometry was also popular in the modern avant-gardecircles, since geometric constitution and perception is very important in the sense of

human visuality. As Theo Van Doesborgs below statement indicates, an important

attempt was also about enforcing the limits of three dimensions and researching aboutother dimensions and geometrical systems.

In architectures next phase of development the ground-plan must

disappear completely. The two-dimensional spatial composition fixed in a

ground-plan will be replaced by an exact constructional calculation acalculation by means of which the supporting capacity is restricted to the

simplest but strongest supporting points. For this purpose Euclidean

mathematics will be of no further use but with the aid of calculation that

6 The idea of approaching the modern avant-garde as a distinctive path opposing the international style, and

searching on the possibilities of organic forms and other experimental aims, is mainly based on a series of

lectures for ARCH 527 course by Zeynep Mennan performed in Department of Architecture in METU in

Fall 2005.

A collection of images as an iconography selected with a similar intention described here can be seen in thebook; Migayrou, Frdric and Zeynep Mennan (eds.).Architectures Non Standard. Paris: Centre

Pompidou, 2003.


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is non-Euclidean and takes into account the four dimensions everything

will be very easy.7

It is probably not a coincidence that modern avant-garde had been seeking for newgeometries and mathematics for basing a new way of looking and understanding the

world on, simultaneously with certain scientific developments nourishing these efforts.

Certain discoveries realized in 17th and 18th centuries, have begun to find fields ofapplication in the late 19

thand early 20

thcentury. In this sense, Zeynep Mennan explains

some of these scientific developments as follows;

The opposition remains unresolved until the discovery of other

geometries, in other words, the recognition that the so-called natural andabstract forms may not have a common geometric ground. Non-Euclidean

geometry, named after its proposition to Euclids famous fifth postulate,

owed its initial formulations to Gauss, Lobachevsky and Bolyai, as early

as in the first decades of the 19th

century. Later in 1867, Riemannformulated still another alternative to Euclids system, a geometry as the

study of manifolds of any number of dimensions and of any curvature,

using differential geometry as the measure of this curvature. 8

Development of differential calculus and curved geometries were important for a newperception of space and conceptual counterpart of these mathematical developments in

art came forth as efforts of representation of the notion of time. Time had meant

dynamism and motion against the timeless and static qualities of modernity. Mennancontinues;

The challenge that these alternative non-Euclidean geometries

represented was the possibility of surfaces or spaces with variable

curvature, on which a figure could not be moved without being affected bychanges in its own shape and properties, thus invalidating the Euclidean

assumption of indeformability of figures in movement, that is, the positingof an absolute unchanging form.

9The fallibility of Euclid meant then also

the fallibility of the Kantian a-priori categories of space and time without

which perception cannot occur. This first refutation of mathematicalaxioms would mean a turn from the absolute to the relative nature of

truths, as pronounced in Poincares conventionalist view of the axioms,

stating that geometric axioms are neither synthetic a priori, norempirical, but conventions.

10

7

Proposition 9: 1924 Theo van Doesburg: Towards a plastic architecture. Quoted from;Bury, Mark. Notes on the Non Standard: numerical and architectural production tomorrow in Migayrou,

Frdric and Zeynep Mennan (eds.).Architectures Non Standard. Paris: Centre Pompidou, 2003, pp. 54-57.8 English original of: Mennan, Zeynep. Des Formes Non Standard: Un Gestalt Switch ., Migayrou,

Frdric and Zeynep Mennan (eds.).Architectures Non Standard. Paris: Centre Pompidou, 2003, pp. 37-38.

Original footnote: Henderson, Linda Dalrymple. The Fourth Dimension and Non-Euclidean Geometry inModern Art. Princeton, NJ: Princeton University Press, 1983. (Henderson, op. cit, 5)9

Original footnote: Henderson, Linda Dalrymple. The Fourth Dimension and Non-Euclidean Geometry in

Modern Art. Princeton, NJ: Princeton University Press, 1983. (Ibid., 6)10 Ibid, pp. 37-38.


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With the introduction of time and motion, a certain quality of dynamism had been

reflected in some of the works of modern avant-garde. I will demonstrate three examplesin order to create an idea of depiction of time in the paintings. Figure 1 displays Umberto

Boccionis famous painting, Dynamism of a Soccer Player from 1913. Boccioni had

overlapped various interpretations or perceptions of forms of bodily movements of a

soccer player in time. Figure 2 is the Marcel Duchamps famous 1912 work titled Nudeon a Staircase, which has a very similar approach for understanding or depicting the

forms of bodily movement, whereas with a separate interpretation style. Final example is

Figure 3, which is a painting by Giacomo Balla from 1912; Dynamism of a Dog on aLeash. Possessing the same intention with the previous two, Ballas work is less

interpretive and more like a photograph exposed for a long time, overlapping the ghost-

like motion traces of the object. These three examples from the very same period exhibithow the notions of time and motion affected deeply the artists of modern avant-garde.

A further example can be Antonio Gaudi, whom Lars Spuybroek, leader of NOX

Architectural Studio, calls as the first computer architect;

(Mentioning about one of his projects) It is in a sense like Gaud's

studies, when he was calculating the exact curves of the Sagrada Familiain Barcelona by hanging small sandbags from chains. In his studies, the

floor plan of that church was on the ceiling of his studio. By suspending

chains from that floor plan and interconnecting them he was not justcalculating the form of their curves, but also a form that could be

implemented in masonry. This makes Gaud the first computer

architect.11

In this sense, Le Corbusiers, (who is one of the great figures of the international style butnot very far from the avant-garde either), appreciation of Gaudi as a great artist is also

noteworthy.12

Le Corbusier celebrates Gaudis work, indicating that it will be criticized

unconsciously for being out of the fashion of his time. Furthermore, as Mark Burryinforms us Le Corbusier had employed similar techniques in Ronchamp, years later his

visit to Sagrada Familia.13

Using the technique mentioned above, namely suspendingchains, Gaudi had been able to create complex curves that were not calculated or

represented before the differential mathematics. Differential mathematics was known in

the time of Gaudi, yet it was impossible to make, alter and modify the necessary

calculations for the design process of the form of the building continuously by hand.Instead he devised a technique to physically create the curve and then copy it to the

required surface and material. He did this, since he did not want to give up from his

complex curvatures for the sake of Euclidean curves.

Original footnote: Henderson, Linda Dalrymple. The Fourth Dimension and Non-Euclidean Geometry in

Modern Art. Princeton, NJ: Princeton University Press, 1983. (Ibid., 15)11 Spuybroek, Lars, http://www.vividvormgeving.nl/vormgeverpagina/spuybroeknrc.htm, 02nd.01.2006,

00:17. This interview with Lars Spuybroek was done by Arjen Mulder and Maaike Post for their book

called 'Book for the electronic arts', published by de balie/V2_Organisation (2000).12 Quoted from Bury, 2003, p. 55.

Original footnote: Evans, Robin, The projective cast: architecture and its three geometries. Cambridge,Mass.:MIT Press, 1995, p. 298.13 Ibid, p. 57.


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Architects, except a number of examples like Gaudi, usually work with certain

representations of the end-product of architecture. There are probably numberlessmethods for design process in architecture, applied by architects, each with its own

subjectivity and interpretation. However, in order to transform the architectural form and

other information to other persons or medium, or even to create the form as a

materialization of the conceptual, architects utilize certain methods of representation.Orthogonal drawings (including isometric) where the building is not perceived as

demonstrated , perspective views which are highly interpretive and fixed to a certain

point of vision and 3-dimensional models which possess the highest level ofabstraction - are the primary ways of representation of architecture. The rules and

standards are strictly determined, discipline of architecture have employed these methods

of representation for thousands of years, without much alteration. Besides these standardsand norms of architectural practice create a high level of abstraction, these methods of

representation are already great abstractions of the end-product. Hence conventional

practice of architecture employs a second degree abstraction, in the materializationprocess of the conceptual design of the form. This is what Theo Van Doesborg complains

about and offers a substitute approach denying the ground plan.Structuring a whole system of abstraction through the history, man is at the same time

aware of certain kinds of knowledge or entity that cannot be abstracted or reduced. Gaudidid not want to abstract these curvatures into Euclidean curves which are formally not

identical but quite similar. He was aware of the distinction between the two and he was

caring for this distinction, for he believes in the idea that it worth. Similarly, the most

famous ambiguity in painting is certainly Mona Lisa, who has a mysterious meaning inher face which is never certain, and worth a lot in this sense. Ernest Gombrichs words on

Mona Lisa provide a clear elucidation of the situation;

"Even in photographs of the picture we experience this strange effect, butin front of the original in the Paris Louver it is almost uncanny.

Sometimes she seems to mock at us, and then again we seem to catch

something like sadness in her smile."14

Mona Lisa is not reducable or abstractable in any sense. With all this ambiguity, it is the

complexity which can not be abstracted into something decisive or determinant. Its

complex form can not be reduced to its fragments. Mona Lisa is a form, existing as a

whole, possessing the potential of various interactions with the viewer, and the result ofits effect can never be predicted.

14 Gombrich, Ernest Hans Josef, The Story of Art. New York: Phaidon, 1995.


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II

The new sciences of complexity -- fractals, nonlinear dynamics, the newcosmology, self-organizing systems - - have brought about the change in

perspective. We have moved from a mechanistic view of the universe toone that is self-organizing at all levels, from the atom to the galaxy.Illuminated by the computer, this new world view is paralleled by changes

now occurring in architecture.15

Charles Jencks

In the above quotation, Charles Jenks notes the relation of complexity theories and the

paradigm shift in architecture triggered by the flashing developments in digitaltechnologies. Scientifically and theoretically supported by the employment of non-

Euclidean geometries, differential equations, relativity theory, splines and NURBS curves

and other similar developments this paradigm shift in architecture have found its field ofapplication through the computer, which was probably the lacking ingredient figure in the

investigation of modern avant-garde for pushing the borders and constraints of 3-

dimensional Euclid geometry and the classical space understanding. The position of the

modern avant-garde asking for an inquiry on the borders of Euclidean space, have beenmodestly mystified under the effect of industrial requirements of mass-production and

lacking of sufficient scientific and technological support. Modern complexity and chaos

theories, as a unified array, developed almost simultaneously in various disciplines, is thekey factor for locating the essence of this paradigm shift in architecture and its formal

ramifications.

Modern Chaos and complexity theories is a body of knowledge explaining the working

principles of complex systems, developed particularly in the 20th

century. There are

different theories varying in some points, yet I will not go in the details of these theoriesand will handle them as a whole set of theories in this study.

16Many applications exist in

various fields such as mathematics, physics, chemistry, meteorology, biology, economy,computation, cosmology and system engineering.

A complex system, understood in the context of chaos and complexity theories, is a

system that could not be analyzed through the classical linear cause-and-effect relations.

Very simply, as the actors in the system and the relations between these actors increase toa complex level, the system starts to behave differently and the factors that can be

neglected in the classical sciences become potentially effective on the numerous relations

in the system. The system does not work linearly and instead has a self-order of non-

linear multiplicity, differentially related in itself. In this case, the system begins to be

holistic and emergent, namely cannot be abstracted or simplified, and able to emergeunpredictable behavior or results based on simple changes in details. A complex system

is not reducable in any sense.

15 Jencks, Charles, The New Paradigm in Architecture Theory, in The Architectural Review, February

2003.16

The pioneer studies generating the modern chaos and complexity theories can be numbered as DarcyThompsons studies on growth and form, Rene Thoms Theory of Catasthropes, Benoit B. Mandelbrots

Theory of Fractals and Hans Jemys work on Cymatics.


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The linear cause-and-effect metaphor of organization as a machine, the

Newtonian/Cartesian perspective, has supported the development ofmodern systems and practices. As this paradigm has reached its limits,

chaos and complexity theory has been guiding evolution of contemporary

thought and practice. This theory of nonlinear systems dynamics spread

through the physical sciences as, increasingly, newly discoveredphenomena could not be explained or predicted with linear models.17

I will not go into the details of chaos and complexity theories, yet I will try to explain

what is important for the paradigm shift in architecture. Theories in architecture usually

like to borrow concepts and explanations form other disciplines. In this sense, for forcingthe limits of Euclid/Newtonian perspective, the geometric and mathematical notions of

complexity have became highly significant. In fact, Newtonian physics can be considered

as an abstraction of quantum physics, since Newtonian physics neglects a number offactors that are certainly insignificant in worldly scale of space and time. Through the

developments of new geometries, nth

-dimension systems, splines instead of curves, and

integral calculus; architecture can force the limits of its classical notions and establish a

new geometrical system of analyzing the form. Through these techniques, architecturecan design relational systems that are not static and singular, but dynamic and multiple.

Self-organization is another key concept developed through the chaos and complexity

theories, trying to explain the inner dynamics of a system which cannot be managed withdeterminant rules and power organizations. A self-organizing system can be analyzed

through its inner dynamics and potentials which are continuously under a certain way of

evolution. Such a system can be conducted through designing the macro mechanismscontrolling the inner relations on a higher level. For the point of architecture, design can

be seen as not the design of architectural components, but the design of the general

principles that generate and re-generate these components and construct theirinterrelations.

Thus, the transformation of architectural space, or with a more pretentious claim, the

paradigm shift in architecture have been a debate that had begun in the turn of the centurywith avant-garde modern and nourished with the complexity theories flowingly. This

shift alters primarily the classical space understanding as a passive container of objects

and events, but instead offers an understanding of an active field of forms and vectors or

relationships of any kind. Instead of Euclid Geometry, more complex and differentialgeometries; instead of points and lines, splines and complex curves take place. Resistance

to the physical environment and change leaves itself to an inherit dynamic and evolution.

17Brodnick, Robert J., and Krafft, Larry J., Chaos and Complexity Theory: Implications For Research and

Planinng in Higher Education. Contributed Paper for Association for Institutional Research 37th Annual

Forum, May 1997, p. 3.


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III

Forms are alive in that they are never immobile.

Henri Focillon18

Reading the paradigm shift in architecture from the point of view of form, in this part Iwish to discuss the digital approach to form. In this sense, the beginning can be on the

required conditions for activity, or for a more actual approach, life. Complexity theory

offers a hypothesis that the real activity or life takes place in the in-between states ofmatter. Theoretical biologist Stuart Kaufmann explains as follows:

The wonderful possibility is that on many fronts, life evolves toward a

regime that is poised between order and chaos. The evocative phrase thatpoints to this working hypothesis is this: life exists at the edge of chaos.

19

He states that, one of these in-between states is somewhere about liquid state of water,since ice is too ordered and the gaseous is too chaotic. The edge of chaos is an active

state between order and chaos. His ideas have remembered me the Le Chateliers principle in basic chemistry, which is defined as follows in The Columbia Electronic

Encyclopedia,

Le Chtelier's principle, chemical principle that states that if a system in

equilibrium is disturbed by changes in determining factors, such astemperature, pressure, and concentration of components, the system will

tend to shift its equilibrium position so as to counteract the effect of the

disturbance.20

Combining these two ideas, it is possible to say that life occurs in the in-between states ofa system, where you are not in equilibrium, but a constant activity to counteract the

effect of the disturbance through the equilibrium. The disturbance never stops, since it is

a complex system of multiple agents in interaction. So in this state, the system gains acontinuous dynamism, an activity of continuous motion through the equilibrium, but

never equilibrium. Any activity, so the forms themselves, come into being in this state of

constant activity and transformation.

Such an activity in a system funds a continuous mode of exchange of energy orinformation. Turning back to the chemical metaphor, system constantly acts and reacts,

crating and using energy. Forms in a complex system continuously transfer energy or

information to each other, as long as they are in an interactive state. Mark Taylor stresses

that, words movement and moment come from the same root in Latin; momentum.21Moment holds a movement potential and movement occurs in a moment. This argument

18 Focillon, Henry, The Life of Forms in Art. New York: Zone Books, 1992.19 Kaufmann, Stuart,At Home in the Universe: The Search for the Laws of Self-Organization andComplexity. New York: Oxford University Press, 1995, p. 32.20

The Columbia Electronic Encyclopedia, 6th

ed., Columbia University Press, 2005. 05.01.2005, 01:51.21 Taylor, Mark C., The moment of complexity: emerging network culture. Chicago: The University of

Chicago Press, 2001, p. 23.


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puts notions of time and motion in a critical condition in the complexity theory.

Interrelations between these two notions are so strong and multiple, that their effects onforms can not be denied. These two concepts are continuous fluid forces, not acting

together, but acting blending into each other and evolving the other. Form can be

assumed under the effects of this couple force, which are the self of the whole activity in

a complex system.Thus making a comparison between space defined in Cartesian coordinates and space

defined through the tools of differential mathematics; Cartesian space is presumed to be a

passive container of agents and events resulting from the inter-relations of these agents.

Cartesian space is in a neutral equilibrium state in this sense, and opposing with it, spaceof vectors and energy transformation is an active one. It is a continuously active space,

near to the point of equilibrium, just on the edge line of equilibrium and not equilibrium,

but never equilibrium. It is like a man standing on the rope and trying to stay in balance,but never in balance, moving forwards and backwards continuously.

This kind of an energy transfer and continuous activity of multiple agents make the

complex systems holistic. The details can not be neglected in order to understand the

system. The whole can not be reduced to its fragments or components. Ray Kurzweilcites one of the most accepted theories about the origin of the universe, where he uses the

word emergence for process of formation of light, for it is the result of a very tiny,

conventionally neglectable advantage. For the theory, the universe has 10 billion and 1protons for each 10 billion antiprotons, and the confrontation of these resulted with the

emergence of light.22

Any slight advantage or distinction may be important and create an

unpredictable result in a complex system.

In modern chaos and complexity theories, irreducible character of complex systems iscritical. Through this statement, it is possible to conclude that it is not the way to examine

the pieces in order to understand a complex system. The proposal of complexity in its

place is the investigation of the system as a differential whole. In a complexmathematical system forms can be defined with differential equations where each

curvature is defined with parameters that are affected by the other curvatures, opposingEuclidean geometry where each element is statically determined independent from the

external factors.

This is why splines and NURBS curves are important for understanding the forms, re-

considered under the light of modern chaos and complexity theories. I will cite Figure 4from Greg Lynn, where he compares an Euclidean curve with its, in a way,

correspondent constructed with spline geometry.

The degree of the curve depends on the number of its parameters and has no maximum

limit in getting more complex. In Figure 5, to cite from Lynn again, various degrees ofthe same curve is demonstrated. Lynn states the substitution of splines instead of lines

and describes splines as follows;

Unlike lines, splines are vectors defined with direction. These vectors

are suspended from lines with hanging weights similar to the geometry of

22 Kurzweil, Raymond, Chapter One: The Law of Time and Chaos in The Age of Spiritual Machines.

New York: Penguin Books, 2000, p. 10.


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a catenoidal curve. Yet unlike a catenoidal curve, a spline can

accommodate weights and gravities directed in free space. Althoughthe control vertices, hulls and weights are defined in a point-based.

Cartesian space, the splines are not defined as points but flows. The

spline curve is unlike a line or radius in that its shape is not reducable to

exact coordinates. The spline curve flows as a stream between aconstellation of weighted control vertices and any position along this

continous series can only be defined relative to its position in the

sequence.23

New digital vocabulary of forms employ complex curvatures of varying degrees forcreating forms, resulting in forms holding some kind of a dynamic information. This

information is inherited in the curvature, in the mathematical composition and

geometrical existence of the form itself. Even a simple vector holds the information ofdirection and magnitude as a level further than a simple line. Whats more is it holds the

information in relation to the other forms that it is in interaction with. The differential

composition of the form holds the information of the relational effects of the other forms.

Below statement by Jean Molino can be read as an interpretation of factors generating thecomposition of the form, as explained in the previous lines.

Nothing explains the genesis of forms, nothing, that is, except forms

themselves and their encounters with other forms.24

The information that a form carries is dynamic, under continuous evolution by otherforms. The weights and distances, namely the parameters of the differentiality is a

parameter in this interactive communication. It is just like a computer that again proves

why computers are necessary to work with complex geometry which incessantlycalculates the result of a certain operation with given new parameters. The computer

knows the rules of the operation, but the parameters are emerging through the interaction

of other forms. If the results of the operations accomplished by the computer were plotted by certain intervals of time, the result would be a complex curve of the degree of

interchanging parameters. For a spontaneous time on the graph, the complex curve holdsboth the information from its previous state (vectorial information), and the information

for the next state, additionally the similar information for the other interacting forms,

with a precision due to the definition of the relations.

Actually, Greg Lynn gives an example very similar to this curve-machine calculatingnew data continuously.

25He brings up the relational process of a dog chasing a Frisbee.

At the initial time, dog does not know any of the necessary information about the flight of

the Frisbee such as direction, velocity, weight, wind and gravity. However, after the

Frisbee is launched, the dog begins to perform successive operations using any vectorial

information he acquires about both the Frisbee and itself.26 In each new operation, he

23 Lynn, Greg,Animate Form. New York: Princeton Architectural Press, 1998, pp. 21-22.24 Molino, Jean, Introduction,inFocillon, Henry, The Life of Forms in Art. New York: Zone Books,

1992, p. 14.25

Lynn, 1998, pp. 23-24.26 It is not clearly known what dog performs in this situation, since we do not know how his brain and

bodily actions work in this sense. I am not insisting about the dog performing certain operations or making


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uses more accurate or updated data added on the previous data. In each step of new time,

the weight of the past positions increase and the graph of the differential curve becomemore explicit. And finally, two distinct differential curves of various degrees meet at a

point, unless any new external parameter alters the curve. To cite from Lynn;

The path of the dog will inevitably be described by a curved line. The

inflections of this curved line indicate the velocities, directions and timingof each of the imbricated vectors. This situation cannot be described by a

straight line with endpoints because, mathematically, it is a differential

equation with more than two interacting components. Curvature is

mode of integrating complex interacting entities into a continuousform.

27

The capacity and ability of form holding extensive information and transferring it to the

other forms, proves its continuity in time. The complex curvature of the dogs path

running after the Frisbee can be extended infinitely on both points of, capture time andinitial time as well. The degree of the complexity of the curvature depends on its

definition or literally, dogs skill, here. It is necessary to note that, such a form holding

various levels of information, and open to interactions by other forms, clearly opposesEuclids fifth postulate of indeformability of figures in movement, which have been

mentioned in the previous part of this paper. Such a form can continuously be deformed

as seen in the differential curvatures.

Working on the continuity of forms, Scottish biologist DArcy Thompson have gainedreputation as one of the pioneer figures of modern chaos and complexity theories with his

famous work On Growth and Form.28

He compared the morphology of the form of

some animals, insects and plants, by utilizing deformable grids, on which he plotted theforms of his objects. Through these analysis, Thompson have realized a certain relation,

or in better words, continuation between forms of nature. His work figured out

curvilinear lines when the deformations of the deformable grids are plotted. Going onestep further, Thompson had been able to analyze certain forces acting on the forms of

nature, through the continuity relations, he had observed, between certain creatures.Gregg Lynn explains what can be concluded as his contribution to the modern chaos and

complexity theories in following lines:

Rather than thinking of deformation as a subset of the pure, the term

deformation can be understood as a system of regulation and order that proceeds through the integration and resolution of multiple interacting

forces and fields.29

As the interaction between the forms does not stop, which is impossible in the terms of

complexity defining space as an active and dynamic entity, every form is certainlycontinuous. Looking from this perspective, architectural form could no more be designed

calculations. My intention here is to express that the dog gathers information through its senses and

somehow processes that information resulting with an action of a complex curvature.27 Ibid, p. 24.28

Thomson, DArcy Wentworth, On Growth and Form. New York: Dover Publications Inc., 1992.29 Lynn, 1998, p. 26.


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in the conventional way, since it is impossible to design the form, which is a continuity in

time. Instead some tactics are being developed in order to produce form, as an integralelement of new vocabulary. Instead of designing form, some designers prefer the term

selecting form. In this sense, designer is aware of the continuous wholeness of form, as

understood in the chaos and complexity theories. This awareness is a potential for

analyzing, understanding and reflecting the information inherited in the form itself. Inthis way, it will be possible to uncover the flows, vectors, and other dynamical

parameters of forms.

Henceforth, position of the architect and the discipline of architecture have to be

questioned and discussed, concluding with a re-definition, at least, in terms of theirrelation with forms. Architecture seems to provide a new position for the architect, who

somehow leaves his position of satisfaction of urge of abstraction. Instead, architect

becomes an editor or designer of the designing sub-systems. Terms like form selectingor form capturing have been begun getting used, in order to define the process of

design. Architect becomes the designer of what works on form, either machine or human.

He is the designer of the rules of the game, the level and shape of interactivity, the weight

of the elements and all the other factors. Form production becomes form-selecting fromthe continuity of forms. Bernard Cache takes the statement on a closely related basis:

objects are no longer designed, but calculated allowing the design of

complex forms with surfaces of variable curvature and laying thefoundation for a non-standard mode of production.

Such a questioning seems to be started for a period of time, and going on spreading

through a vast territory. This process will redefine architecture and architects, repeating

again, at least in the sense that their relation with formal constitution. This redefinitionhas to produce a new formal vocabulary, examples of which are being applied in various

places of the world, by architects such as Greg Lynn. The new formal vocabulary is very

basically of motion and animation or complexity and curvature, or multiplicity andinteraction, non-linearity and emergence.

This new spatial and formal paradigm expands visual and plastic

repertoire by producing highly complex gestalten, augmented ininformation content, a thickness defying the limits of our perceptual and

mental abilities, and appealing for a similar augmentation of our

faculties.30

30 English original of Mennan, Zeynep, Des Formes Non Standard: Un Gestalt Switch ., in Migayrou,

Frederick and Zeynep Mennan (eds.), 2003,Architectures Non Standard(Paris: Editions du CentrePompidou), p. 34.


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Figure 1 - Umberto

Boccioni, Dynamism of aSoccer Player, 1913, Oil

on canvas

Figure 2 Marcel Duchamp, Nude Descending a

Staircase, No: 2, 1912, Oil on canvas

Figure 3 Giacomo Balla, Dynamism of a Dogon a Leash, 1912, Oil on canvas


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Original note: An example of

composite curve using thesame logic of regional

definition and tangency

Each section of thecomposite curve is defined

by a fixed radius. Theconnection between radial

curve segments occurs at

points of tangency that aredefined by a line connecting

the radii. Perpendicular to

these lines, straight linesegments can be inserted

between the radial curves.

Figure 4 Two similar curves, one of Euclidian geometry with radius, and other employing splines with weights.Soruce: Lynn, Greg, Animate Form. New York: Princeton Architectural Press, 1998, p. 21.

Original note: A similar

curve described using splinegeometry, in which the radii

are replaced by control

vertices with weights and

handles through which the

curved spline flows..

Figure 5 Same spline curve of varying degress. The first three images are three-degree, seven-degree and two-

degree splines. The fourth image displays a superimposed series of splines sharing the same control vertices withdifferent degrees of influence. The final image is a mesh surface produced using the splines. Soruce: Lynn, Greg,

Animate Form. New York: Princeton Architectural Press, 1998, pp. 24-25.


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BIBLIOGRAPHY

Brodnick, Robert J., and Krafft, Larry J., Chaos and Complexity Theory: Implications

For Research and Planinng in Higher Education. Contributed Paper for Association for

Institutional Research 37th

Annual Forum, May 1997.

Bury, Mark. Notes on the Non Standard: numerical and architectural productiontomorrow in Migayrou, Frdric and Zeynep Mennan (eds.).Architectures Non

Standard. Paris: Centre Pompidou, 2003, pp. 54-57.

Focillon, Henry, The Life of Forms in Art. New York: Zone Books, 1992.

Gombrich, Ernest Hans Josef, The Story of Art. New York: Phaidon, 1995.

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Organization and Complexity. New York: Oxford University Press, 1995.

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Kurzweil, Raymond, Chapter One: The Law of Time and Chaos in The Age of Spiritual

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Lynn, Greg,Animate Form. New York: Princeton Architectural Press, 1998.

(English original of:) Mennan, Zeynep. Des Formes Non Standard: Un Gestalt Switch

., Migayrou, Frdric and Zeynep Mennan (eds.).Architectures Non Standard. Paris:

Centre Pompidou, 2003, pp. 34-41.

Migayrou, Frdric and Zeynep Mennan (eds.).Architectures Non Standard. Paris:Centre Pompidou, 2003.

Molino, Jean, Introduction,inFocillon, Henry, The Life of Forms in Art. New York:

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Spuybroek, Lars, http://www.vividvormgeving.nl/vormgeverpagina/spuybroeknrc.htm,02

nd.01.2006, 00:17. This interview with Lars Spuybroek was done by Arjen Mulder and

Maaike Post for their book called 'Book for the electronic arts', published by de

balie/V2_Organisation (2000).

Taylor, Mark C., The moment of complexity: emerging network culture. Chicago: TheUniversity of Chicago Press, 2001.

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An Approach to Architectural Form Through the Complexity Theories [Kutay Karabag]

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