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Parametric Diagrammes,
Patrik Schumacher, London
Published in: Mark Garcia (editor), The Diagrams of Architecture, AD Reader, John Wiley&Sons, London 2010


The focus of avant-garde architectural design moves away from the design of individual buildings to the design of parametric diagrams that are capable of multi-various individuation.

Two distinctions concerning Diagrammes

A diagramme is a type of representation that is characterized by a high level of abstraction. The representation focuses on very specific aspects of the represented entity. These isolated aspects can then be grasped and manipulated with a high degree of efficiency. This abstraction works well if what has been abstracted from can be taken for granted, i.e. usually this high level of abstraction is granted on the basis of a clear understanding of what is omitted from the representation, and how the diagramme can be completed in order to obtain a more fully mimetic representation. I would like to talk of ordinary diagrammes if the relationship between the abstract diagramme and the concrete entity represented is unproblematic because it is fixed through built in routine assumptions.
Durand1 was perhaps the first to introduce a diagrammatic process within architecture. He proposed a “mechanics of composition”2 made easy and efficient by using gridded paper upon which a series of basic elements like walls and columns could be combined  - following the rules of alignment, regularity and symmetry -  to form standard building parts like porches, vestibules, and rooms which in turn could be combined into various whole buildings, again following the rules of alignment, regularity and symmetry. Both elements and parts were familiar. To further reign in the results of the compositional process from the very start Durand proposed in fact a procedure of decomposition or successive division starting from global geometric forms like squares or rectangles. Even with these top down restrictions the introduction of diagrammatic composition implied an unheard of variety of results: “there is no telling how many different compositions this host of combinations can produce.”3
From the results of this diagrammatic process the rest of the design (including all the familiar classical detail) followed automatically: “We have given a formula, in our discussion of the parts of the building, that will make it unnecessary even to look at the sections that we give of each ensemble. The elevations … must be nothing but the natural and necessary consequences of the plan and the section …”4
The advent of the 20th century saw a massive increase in building tasks. Architectural composition finally shook off the classical restrictions of global geometric prefiguration, symmetry and proportion. The compositional process could now proceed from inside out, with nearly total openness with respect to the final configuration. This was the true moment of the ordinary diagramme: isolating and freeing the aspect of lay-out configuration, but having a clear, new canon of translating diagrammes into buildings that had even less variety in section, elevation and detail than the neo-classical architecture of Durand: white walls, glass-walls, and flat roofs.
Since the refoundation of the discipline in the early 1920s the architect's design world has thus been a singular and stable system of hierarchically scaled line drawings. From the scale-less (topological) sketch to the working drawings this world distributes nothing but outlines and boundaries. Everything is about the distribution of horizontal and vertical planes. The meaning of each drawing resides in its position and role in the chain of translation from one drawing to the next (more detailed) drawing and from there to the construction process and the building itself. Within this routinised practise of translation, from the abstract to the concrete, it is habitually known how each drawing constraints the next set of decisions, until the detailed lines finally translate into physical edges. (And we all have learned to perceive and inhabit space along those edges.) Only within such an order of repetition can one speak of a well defined notational system. Within such a system the design process can efficiently operate with diagrammes, i.e. with ordinary diagrammes.

The concept of an ordinary diagramme that is firmly lodged in a routine practise is the model against which the extra-ordinary diagramme is defined. The extra-ordinary diagramme is a diagramme in the sense that Deleuze distinguishes diagrammes from representations. A Deleuzian (extra-ordinary) diagramme is an abstract machine that is valued precisely because its downstream implications are totally open. The crucial difference between ordinary and extra-ordinary diagrammes does not reside within the graphic or digital object itself, but in the patterns of its use. The question here is, whether or not it functions within a stable social practice of translation. For the extra-ordinary (Deleuzian) diagramme no defining routine practise has as yet crystallized. It is instead creatively engaged in the formation of such a (potentially reproducible) practise. It therefore is worked upon without stable interpretation, without predetermined consequences. We might thus say that extra-ordinary diagrammes are proto-representations.

Deleuzian Diagrammatic Processes:
Emergence via pixel-clustering, Patrik Schumacher 1995

Deleuzian Diagrammatic Processes: Emergence via
domain-interpenetration, Patrik Schumacher 1995

Deleuzian Diagrammatic Processes:
Field-directionalities, Zaha Hadid Architects 1996

At least from the mid-eighties to the late nineties virtually all avant-garde design efforts were conducted through such Deleuzian "diagrammatic" processes. Such design processes are as open-ended as they are unpredictable.  (They might be compared to the aleatoric process of figuratively interpreting “random” natural structures like the famous watermarks on the walls that inspired Leonardo (and later Max Ernst) to create fantastic landscapes from.) All that is initially given is the very basic premise that some kind of unusual spatial configuration should be discovered in the process. The architectural interpretation of the various graphic or digital primitives that are manipulated within the diagramme remains open – lines might be walls, beams, shifts in materiality or merely trajectories of movement etc. This kind of open ended formal experimentation is indicative of revolutionary transition periods between paradigms  - specifically the transition from modernism to the contemporary paradigm. Accordingly, I would like to distinguish revolutionary from cumulative periods of avant-garde design research. During revolutionary periods all premises and certainties of the previous paradigm are being questioned. Philosophical debates rage unresolved and Deleuzian diagrammes are the working tool of choice. This phenomenon was first observed during the transition from classical to modern architecture from about 1905 to 1925. During this time future architects and designers invented abstract art and utilized its non-figurative operations as abstract design machines. New viable formal repertoires were filtered out and fully routinized by 1925. Thereafter the extra-ordinary diagrammes stabilized into ordinary diagrammes.

The second distinction I would like to introduce is the distinction between metric and parametric diagrammes. Whereas the distinction between ordinary and extraordinary diagrammes concerns the external embedding of the diagramme within the rationality of an encompassing design process, the distinction between metric and parametric diagrammes concerns the internal constitution of the diagramme. While the attributes of the graphic/digital primitives that are manipulated within the metric diagramme are fully determined and fixed at any time, within the parametric diagramme they remain variable and are only constrained within a defined range. Parametric diagrammes might be compared to the way the evolution has produced the fantastic diversity of life based on a rather small number fundamental body plans5. A body plan is essentially the parametric diagramme for the way the body of an organism is laid out: its symmetry, its number of body segments and number of limbs etc. The same basic body-plan underlies an enormous manifold comprising the most diverse species.
Concerning the two distinctions  - ordinary vs. extra-ordinary and metric vs.parametric -  it is important to note that these two distinctions operate orthogonal to each other so that each side of each distinction can be combined with each side of the other distinction. Durand’s diagrammes as well as the diagrammes of modernism since 1925 are ordinary metric diagrammes. The abstract art of the 20th Century, as well as the diagrammes of deconstructivism and the “abstract machines” of early folding were extraordinary metric diagrammes. Since the mid-nineties parametric diagrammes started to emerge, first in the form of animations. These were extra-ordinary parametric diagrammes within open-ended design research explorations. Today most of us have switched to work with ordinary parametric diagrammes, i.e. we know in advance what we are aiming for.

The Emergence of Parametrics

Parametric diagrammes rely on digital technology. The first generation of parametric diagrammes entered architecture via the use of animation software allowing for versioning and intuitive form-finding by means of the continuous deformation of topologically defined surfaces or by means of inverse kinematic constructs. The animation of object transformations also lead to the desire to maintain a certain degree of transformability within the final architectural construct. At the AADRL we dedicated a whole 3 year research cycle  - Responsive Environments – to this potential of utilizing animation software to design kinetically active spaces. It was during this cycle of working with the action-reaction schema that we grasped the power of associative parametrics.

Kinetic Transformations: Lotus, Zaha Hadid & Patrik Schumacher, Venice Biennale 2008

The stability or recognizable self-identity of parametric diagrammes against the backdrop of shifting parameter inputs rests on the powerful possibility to “link” or “associate” parameters by defining correlations (dependencies) between them. This internal self-consistency of the parametric primitives offered by animation software is established by internal functions that remain hidden to the intuitive user. In principle any conceivable network of relations between a given set of element attributes can be constructed. Scripting languages started to open the hood and allowed us to be creative on the molecular and even atomic level. On the other hand, there is no principled limit (except computational limits) to take (or build) dynamic “primitives”, or complex components,  and build up complexity by associating whole swarms of them, then correlate different swarms etc.
The demiurge-like freedom to link any parameter/property of any object with arbitrary parameters/properties of any or all other objects within the model (as long as circularity is avoided).  The realization of this ability to set up whole chains of dependencies and the creative challenge to conceive such functions as the quasi laws of nature of a new artificial universe was the moment at which I was first struck by the enormous potential power of parametric design for the organization and articulation of social complexity – both as static and as dynamic condition.

Since the contemporary avant-garde has moved from a revolutionary stage to a cumulative stage of design research  - at least since 2000 -  the parametric diagrammes employed transformed from extra-ordinary to ordinary parametric diagrammes. This shift from extra-ordinary to ordinary parametrics often goes hand in hand with a more rigorous employment of computationally advanced design techniques like scripting (in Mel-script or Rhino-script) and parametric modeling (with tools like GC or DP). However, this is not a necessary connection. Extra-ordinary parametric diagramming is not obsolete, and it might continue to take place on the highest level of technical sophistication. It is precisely the richness of this new world of associative design that still demands and rewards open-ended (extra-ordinary) diagrammatic design explorations into the abstract world of relational logics without a preconceived path of translation into the design-world where parametric models offer concrete solutions to clearly stated design problems. To the extent to which the provision of new parametric tools  - which keep flowing into architecture from other domains and disciplines – continues, to this extent we might witness and welcome an oscillation, and cross-fertilization between ordinary and extra-ordinary efforts in parametric diagramming.


A New Style: Parametricism

That the parametric paradigm is becoming pervasive in contemporary architecture and design is evident. There has been talk about versioning, iteration and mass customization etc. for quite a while within the architectural avant-garde discourse.
The fundamental desire that has come to the fore in this tendency had already been formulated at the beginning of the 1990s with the key slogan of “continuous differentiation”. Since then there has been both a widespread, even hegemonic dissemination of this tendency as well as a cumulative build up of virtuosity, resolution and refinement within it. The shared concepts, computational techniques, formal repertoires, and tectonic logics that characterize this work are crystallizing into a solid new hegemonic paradigm for architecture.
There have even been various exhibitions like “Latent Utopias”6 in Graz, "Non-Standard Architectures”7 at the Centre Georges Pompidou in Paris, or more recently "Design and the Elastic Mind"8 at New York’s MOMA, which have brought this latest avant-garde tendency to the attention of the educated public.
Despite this long term, pervasive convergence of efforts nobody has as yet announced the formation of a new style. However, I would like to argue that there has not been such a persistent, long wave of collective architectural work since modernism (1920-1970). We are fully justified to talk about a new style. I would like to propose parametricism as the most appropriate label for the contemporary style in question. Parametricism is the great new style after modernism. Postmodernism and Deconstructivism have been transitional episodes that ushered in this new, long wave of research and innovation.

Elsewhere I have argued and explicated that architectural styles should be understood as design research programmes9.
A research programme/style consists of methodological rules: some tell us what paths of research to avoid (negative heuristics), and others what paths to pursue (positive heuristics). The negative heuristics formulates strictures that prevent the relapse into patterns that are not fully consistent with the core, and the positive heuristics offers guiding principles and preferred techniques that allow the work to fast-forward in one direction. The defining heuristics of parametricism are the taboos and dogmas of contemporary design culture:
Negative heuristics: avoid familiar typologies, avoid platonic/hermetic objects, avoid clear-cut zones/territories, avoid repetition, avoid straight lines, avoid right angles, avoid corners, …, avoid simple repetition of elements, avoid juxtaposition of unrelated elements or systems.
Positive heuristics: hybridize, morph, deterritorialize, deform, iterate, use splines, nurbs, generative components, script rather than model, …, consider all forms to be parametrically malleable, differentiate gradually (at variant rates), inflect and correlate systematically.
Finally, computationally advanced design techniques like scripting (in Mel-script or Rhino-script) and parametric modeling (with tools like GC or DP) are becoming a pervasive reality. Today it is impossible to compete within the contemporary avant-garde scene without mastering these techniques. Parametricism can only exist on the basis of sophisticated parametric techniques.

But new techniques are not enough to engender a whole new style. Styles are research programmes that redefine both form and function as well as the relationship between form and function in response to societal challenges. Contemporary architecture finds itself at the mid-point of an ongoing cycle of innovative adaptation – retooling the discipline and adapting the architectural and urban environment to the socio-economic era of post-fordism. The mass society that was characterized by a single, nearly universal consumption standard has evolved into the heterogenous society of the multitude.
The key issues that avant-garde architecture and urbanism are addressing can be summarized in the slogan: organising and articulating the increased complexity of post-fordist society. The task is to develop an architectural and urban repertoire that is geared up to create complex, polycentric urban fields which are densely layered and continuously differentiated. Contemporary avant-garde architecture is addressing the demand for an increased level of articulated complexity by means of retooling its methods on the basis of parametric design systems. Parametricism emerges from the creative exploitation of parametric design systems in view of articulating the multi-various processes and institutions of a complex and variegated society. The parametric design tools by themselves cannot account for this drastic stylistic shift from modernism to parametricism. This is evidenced by the fact that late modernist architects like Norman Foster are employing parametric tools in ways which result in the maintenance of a modernist aesthetics despite the increased geometrical complexity afforded by the tools in question. Foster is using the parametric set ups to absorb complexity with a minimum of inconspicuous differentiation. Parametricist sensibility pushes in the opposite direction and aims for a maximal emphasis on differentiation.

Network script accentuates undulated surface – Maren Klasing & Martin Krcha,
Masterclass Hadid, University of Applied Arts, Vienna

The distinction between the modernist and the parametricist deployment of parametric tools can be illustrated by the example shown here. The undulating surface itself displays an open-ended rhythm of convex and concave zones. But more than this – the differentiation of the surface in terms of its continuously shifting curvature values drives the differentiation of a second system.  In this diagramme a script translates the rather subtle differences of surface condition into highly differentiated network patterns. There is an amplification rather than amelioration of the initial differentiation. The result is a rather compelling accentuation of the surface by means of an expressive range of qualities that now differentiate the original surface – yet without tearing the surface apart or collapsing into a collage. The aesthetic effect is one of stunning, organic elegance10. The potential for the articulation of a significant programmatic differentiation is tangible here.
The same principle of amplified articulation via mutual accentuation between sub-systems can be applied to urban diagrammes. The differentiation of the urban massing might be scripted to accentuate the topography and is in turn accentuated by the differentiated circulation system etc. The exploration of the parametricist paradigm for the build-up of a complex urban order is just beginning.

Mutually accentuating systems: topography, massing, path-network
Masterplan Competition, Appur, India, Zaha Hadid Architects, 2008


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1 Jean-Nicolas-Louis Durand (1760 – 1834), architect, since 1796 lecturer at the Ecole Politechnique established by Napoleon in Paris 1794.

2 Jean-Nicolas-Louis Durand, Precis des lecons d’architecture donnes a la l’Ecole Royale Polytechnique, Paris 1802-1805, English translation by David Britt, published by The Getty Research Institute, Los Angeles, CA, 2000, p.196

3 Ibid., p.126

4 Ibid., p.196

5 There are only 36 different basic animal body plans, corresponding to the different phyla that have been distinguished in biological taxonomy. A phylum is a taxonomic rank at the level below Kingdom (Plantae, Animalia, Fungi, …) and above Class. The list of 36 phyla includes a.o. chordates (including vertebrates) and arthropods (including insects).
6 Curated by Zaha Hadid & Patrik Schumacher in 2002

7 Curated by Frederic Frederic Migayrou in 2004

8 Curated by Paola Antonelli in 2008

9Patrik Schumacher, Style as Research Programme, in: DRL TEN, AADRL Documents 2, AA Publications, Architectural Association, London 2008

10 For a pertinent concept of elegance that is related to the visual resolution of complexity see: Patrik Schumacher, Aguing for Elegance, in: Castle, H., Rahim, A. & Jamelle, H., (eds), Elegance, Architectural Design, January/February 2007, Vol.77, No.1, Wiley – Academy, London