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Parametric Order – Architectural Order via an Agent Based Parametric Semiology
Patrik Schumacher, London 2012
Published in: Adaptive Ecologies – Correlated Systems of Living by Theodore Spyropoulos, AA Publications, London 2013


THESIS: It has now become both possible and necessary to enhance architecture’s capacity to organize and articulate the increasing complexity of (the most advanced centres of) Post-fordist network society through the re-foundation of architectural semiology under the auspices of Parametricism.


As Theodore Spyropoulos points out in his introduction, architecture is challenged to cope with new social and cultural complexities that demand networked systems that are dynamic, flexible and participatory. According to Spyropoulos this implies a new model of the city as adaptive ecology. Spyropoulos also talks about correlated formations. The first task is thus to define the relevant ‘systems’ or urban ‘formations’ that are to be networked, correlated and adapted to each other. The question thus arises: What is  - in the context of contemporary urbanism -  the most pertinent conceptualisation and decomposition (into subsystems) of the contemporary city?
Guided by architecture’s lead distinction of form vs function we can distinguish the formal decomposition of the city (into its formal-spatial components/subsystems) from the functional decomposition/analysis of the city (into its functional components/subsystems). Each of these decompositions leads to a set of subsystems. The formal-spatial analysis of the city might deliver different fabric typologies. The functional-social analysis delivers different function types understood as typical patterns of communicative interaction (social institutions). The pendent of the concept of decomposition/analysis is the concept of composition/synthesis. Parametricism has transmuted the concept of synthesis understood as composition into the concept of synthesis understood as (scripted) correlation. Correlation has become the new fundamental base concept of architectural design. According to the above distinction of formal vs functional decomposition we thus must take care to distinguish three types of correlation: formal correlations, functional correlations, and form-function correlations. So far the discourse on Parametricism has primarily focussed on formal correlation, the correlation of formal-spatial subsystems.1 However, it is pertinent to expand the concept of correlation to include form-function relations, i.e. to the correlation of the patterned built environment with the patterns of social communications that unfold within it. This is meaningful because the same computational techniques that operationalize the concept of formal correlation can now be applied to form-function correlations. How is this possible?
The functional heuristics of Parametricism proposes to conceive of the functions of spaces in terms of dynamic patterns of social communications, i.e. as parametrically variable, dynamic event scenarios rather than in terms of static schedules of accommodation that list functional stereotypes. It has now become possible  -  for the first time in the history of architecture -  to model the functional layer of the city and thus incorporate it into a dynamic design process. This is made possible by computational crowd modelling techniques via agent based models. Such models reproduce/predict collective patterns of movement including the emergence of formations such as stop-and-go waves and the spontaneous separation of opposite flows of pedestrians in bidirectional traffic.

Crowds modelled as physical flows

(Left) Differentiated crowds. (Right) Cognitive crowds with perception based behavioural heuristics

Crowd modelling is also starting to program agents with rudimentary “perceptual” capacities. While most crowd simulation softwares are based on analogies with physical systems, such as Newtonnian repulsive forces between agents, cognitive science researchers Mehdi Moussaïd, Guy Theraulaz and Dirk Helbing, in contrast, have elaborated a new “cognitive” approach to crowd modelling, assuming that pedestrians try to minimize the coverage of their vision field, move through gaps between people while keeping a safe distance from others, and adjusting their walking speed accordingly2. (Although this kind of research is still in its infancy, relative to the challenge of phenomenal articulation, it ties in with the author’s own concern with observer parameters as a crucial parameter type to be incorporated into the tool set of Parametricism.)
Tools like ‘MiArmy’ or ‘AI.implant’ (available as plugins for Maya) now make behavioral modeling within designed environments accessible to architects. Agent modeling should not be limited to crowd circulation flows but should encompass all patterns of occupation and social interaction in space. In fact scientists are already engaged in the underlying research. Such research takes place e.g. at the Center for Human Modeling and Simulation, Department of Computer & Information Science at the University of Pennsylvania, as well as at the Department of Computer Science at George Mason University. Jan M. Allbeck (from George Mason University) emphasises this new departure away from mere crowd flow engineering to the programming of functional crowds: ”Most crowd simulation research either focuses on navigating characters through an environment while avoiding collisions or on simulating very large crowds. Our work focuses on creating populations that inhabit a space as opposed to passing through it. Characters exhibit behaviors that are typical for their setting. We term these populations functional crowds.  … We use roles and groups to help specify behaviors, we use a parameterized representation to add the semantics of actions and objects, and we implemented four types of actions (i.e. scheduled, reactive, opportunistic, and aleatoric) to ensure rich, emergent behaviors.”3 This research seems primarily to be intended for application within the game industry. However, architects should start appropriating this research, both in terms of the tools and the analytic intelligence it provides.

Functional crowds - Crowds with Aleatoric, Reactive, Opportunistic, and Scheduled Actions

The idea of functional crowds can be taken further: The agents’ behavior might be scripted so as to be correlated with the configurational and morphological features of the designed environment, i.e. programmed agents respond to environmental clues. Such clues/triggers might include furniture configurations as well as other artefacts. The idea is to build up dynamic actor-artefact networks. Colours, textures, stylistic features, together with ambient parameters (lighting conditions), might influence the behavioural mode (mood) of the agent. Since the ‘meaning’ of an architectural space is the (nuanced) type of event/social interaction to be expected within its territory, the new tools allow for the re-foundation of architectural semiology as parametric semiology. This implies that the meaning of the architectural language can enter the design medium (digital model). The semiological project implies that the design project systematizes all form-function correlations into a coherent system of signification. A system of signification is a system of mappings (correlations) that map distinctions/manifolds defined within the domain of the signified (here the domain of patterns of social interaction) onto distinctions/manifolds defined within the domain of the signifier (here the domain of spatial positions and morphological features) and vice versa.  The system of signification works if the programmed social agents consistently respond to the relevantly coded positional and morphological clues so that behaviours to be expected can be read off the articulated environmental configuration. The meaning of architecture, the prospective life processes it frames and sustains, is modelled and assessed within the design process, thus becoming a direct object of creative speculation and cumulative design elaboration.

The Semantic Dimension as Crucial Aspect of Architectural Order

That all architecture and urbanism has an inevitable semantic dimension is generally accepted. However, so far nobody seems to have succeeded in making architecture’s semantic dimension an arena of an explicit, strategic design effort. Earlier attempts to develop an architectural semiology (under the auspices of Postmodernism and Deconstructivism) failed to convince and were rejected in the early 1990s when ‘operativity’ was counter-posed to ‘representation’. This opposition was the expression of a necessary retreat from an unproductive engagement with architectural symbolism. However, this opposition is ultimately a false opposition. Architecture operates/functions via its semantic associations as much as it functions via physical separation/connection. The built environment functions through its visual appearance, via its legibility and its related capacity to frame and prime communication. The built environment is not just channelling bodies. It is orienting sentient, socialized beings who must actively comprehend and navigate ever more complex urban scenes. As a communicative frame, a designed space is itself a communication, a framing communication or premise for all communications that take place within its territory.
The theory of architectural autopoiesis4 posits the spatio-morphological framing of communicative interaction as the unique societal function of the design disciplines including architecture and urbanism. My attempt at formulating the axioms and heuristics of a viable architectural semiology is elaborated in the second Volume of my book ‘The Autopoiesis of Architecture’5. There I propose a definition of architectural order that poses organisation, phenomenological articulation and semiological articulation (signification) as three equally vital moments of a full-blown architectural/urban design project that can meet the most advanced contemporary societal challenges. I distinguish three agendas   - the organizational, the phenomenological, and the semiological agenda -  for the re-tooling of architecture’s expertise. The three dimensions that together procure architectural order are conceptually derived via two binary distinctions as follows:

architectural order   organization
                 articulation  phenomenology


Organisation is based upon the constitution/distribution of positions for spatial elements and their pattern of linkages. Articulation is based upon the constitution/distribution of morphological identities, similitudes and differences across the architectural elements to be organized. Organisation is instituted via the physical means of distancing, barring, as well as connecting via vistas and/or circulatory channelling. These physical mechanisms can operate independently of all nuanced perception and comprehension, and can thus in principle succeed without the efforts of articulation.  However, the restriction to mere organization without articulation, without facilitating the participants’ active navigation, severely constrains the level of complexity possible in the pattern of social communication thus framed. Articulation presupposes cognition. It enlists the participant’s perception and comprehension and thus facilitates the participants’ active orientation.  The distinction of organisation vs articulation is thus based on the difference between handling passive bodies versus enlisting active, cognitive agents. The two registers relate as follows: Articulation builds upon and reveals organisation. It makes the organization of functions apparent. In doing so it elevates organization into order.
The dimension of articulation includes two distinct sub-tasks: phenomenological articulation and semiological articulation. The distinction is between the enlistment of behavioral responses from cognitive agents and the communicative engagement of socialized actors. The phenomenological project enlists the users as cognitive agents, perceiving and decomposing their environment along the lines of the cognitive principles of pattern-recognition or Gestalt-perception. It is all about making organisational arrangements perceptually legible by making important points conspicuous, avoiding the visual overcrowding of the scene etc.  This is a necessary precondition for all semiological codings that can only attach to the visually discernable features of the environment. Users can only read/interpret/comprehend what they can discern. However, the comprehension of a social situation involves more than the distinction of conspicuous features. It is an act of interpretation, an act of reading a communication, namely the reading of the communication that the space itself constitutes as framing communication and premise for all communicative interactions to be expected within its ambit. (These situated communications are attributed to the institutions that host the respective communicative events, i.e. they are attributed to the clients rather than to the architects/designers.) Communication presupposes language, i.e. a system of signification. The built environment spontaneously evolves into such a (more or less vague and unreliable) system of signification. The task of architectural semiology as design agenda is to go beyond this spontaneous semiosis (that every talented designer navigates intutively) and to build up a more complex and more precise system of signification.  To summarize, we can thus distinguish the contributions that the three fundamental dimensions of architecture make (via their respective design projects) to architecture’s essential societal function:

task dimension

framing contribution

engagement  of users

solicited response

organisational project

as physical frame

as physical bodies

passive movement

phenomenological project

as perceptual frame

as cognitive beings

active behavior

semiological project

as communicative frame

as socialized actors

communicative action

Why is this important now?
The ability to navigate dense and complex urban environments is an important aspect of our overall productivity today. Post-Fordist network society demands that we keep continuously connected and informed. We cannot afford to beaver away in isolation when innovation accelerates all around. In order to remain relevant and productive we need to network all the time and coordinate our efforts with what everybody else is doing. Everything must communicate with everything. In terms of urban environments this implies that we should be able to see and participate in as many events as possible, always remaining exposed to many further choices to select our next move. This is facilitated best, if the visual field presents a rich, ordered scene of manifold offerings and also provides clues and anticipations about what lies behind the currently visible layers. The speed and confidence with which one can make new experiences and meaningful connections is decisive. The design of environments that facilitate such hyper-connectivity must be very dense and complex and yet highly ordered and legible. As urban complexity and density increase, effective articulation becomes more important.
Every talented/successful designer adapts to and intervenes intuitively within the spontaneous and historically evolving semiological system of the built environment. The aim of parametric semiology  is it to move from an intuitive participation within an evolving semiosis to an explicit design agenda that understands the design of a large scale architectural complex as an opportunity to design a new, coherent system of signification, a new artificial architectural language (without relying on the familiar codes found in the existing built environments). The maturing style of Parametricism is geared up  - in terms of its computational techniques and attendant formal-spatial repertoire -  to build up and order unprecedented levels of spatio-morphological complexity. Parametric Urbanism- the application of Parametricism to urban design  -  provides an accomplished point of departure for the parametric semiology (semiological project) yet to be accomplished.


Parametric Urbanism

Above we posed the question: How should contemporary urbanism analyse/decompose the city into subsystems?
The most general and abstract decomposition of the city is given with Frei Otto’s distinction of occupation vs movement, leading to the task of differentiating and correlating the fabric system and the circulation/street system of the built environment. This conceptualization already encapsulates architecture’s lead distinction of form (internal reference, self-reference) vs function (external reference, world-reference): The distinction of fabric vs streets is a distinction in the domain of form and the distinction of occupation vs movement is a distinction in the domain of function (social action). However, this conceptualization lacks richness or requisite variety in relation to the challenge architecture/urbanism faces with respect to contemporary society. This very basic conceptualization/decomposition would perhaps have been adequate with respect to early/primitive societies  - societies based on segmentary differentiation -  with their simple settlement structures build up from the agglomeration of undifferentiated units. The medieval city and the built environment of the era of Feudalism was characterized by a stratified order. Here the built environment was segregated according to the order of the estates: the nobility’s castle/palace, the clergy’s monasteries, the burgher’s walled city and the farmer’s village. Starting with the Renaissance (Modernity), the stratified order evolved into what Niklas Luhmann6 calls modern, functionally differentiated society. Functional differentiation (rather than segmentation or stratification) became the primary mode of societal differentiation. The Modernist city delivered the full blown urban expression of modern, functionally differentiated society. The city was differentiated according to the following basic function types: Production, administration, consumption, recreation, habitation. For each of these function-types (types of social interaction) the Modernist architect/urbanists developed functionally specialized urban typologies, instantiated as distinct, separate, specialized, internally repetitive zones. This approach is explicit in Le Corbusier’s Ville Radieuse, a generic design for the ideal modernist/functionalist city. The Modernist principles of separation, specialisation and repetition are clearly demonstrated. Zones are distinct and sharply set apart.

(Left) Le Corbusier, zoned plan of ‘Ville Radieuse’, 1925 (Right) Bernard Tschumi, Parc de La Vilette, Axonometry, 1983


Deconstructivism initiated a surprising, radical expansion of the compositional repertoire.  The synthesis of subsystems moved from the lay-out of separated, adjacent zones to the superposition of layers, as e.g. demonstrated by Bernard Tschumi’s competition winning entry for the Parc de La Vilette in 1983. The author took the basic Modernist function types as starting point for a studio at Columbia University in 19937. Rather than instantiating these functional subsystems as separate zones, the premise of the studio was to interpret them as interpenetrating layers. However, the intention was to go beyond Deconstructivist superposition/collage and allow the layers to mutually adapt to each other via mutual, dynamic distortion. However, the result remained rather chaotic.

Ubiquitous Urbanism, layering process with adaptative distortion (action-reaction)
Studio Hadid/Schumacher, Columbia University 1993

Ubiquitous Urbanism, generic masterplan, build up of multi-system complexity
Studio Hadid/Schumacher, Columbia University 1993


About 10 years later the author started to revisit the problem of urbanism, first with master-planning projects at Zaha Hadid Architects, and then more systematically with the AADRL research project “Parametric Urbanism”8. By this time we were equipped with new tools and techniques that allowed the earlier intentions to come to fruition in a much more convincing way. The intervening years had delivered the capacity to produce smooth, continuous differentiations. Now, the task of complex multi-system urbanism was once more posed in terms of layered subsystems whereby each subsystem displays its own ontology and internal logic of differentiation as the basis for scripted subsystem-to-subsystem correlations (rather than either zoning or collage). The project presented here used Maya fluid as tool for the initial generation of a basic urban geometry. The tool simulates the dynamic of fluids and makes a fluid’s typical characteristics subject to parametric control. The particle flow is sensitive to contextual features like boundaries and obstacles. Two fluids flowing into each other form complex patterns of nesting and intermixing. The field of particles or vectors might be analyzed in terms of particle directions, densities and velocities, thus producing a data-set delivering input parameters for the scripted definition of geometry (urban morphology). The most diverse transcoding scripts are imaginable here. The strategic choice was made to translate the different fluids rather differently. The model contained four types of fluids driving four spatio-morpophological systems. (The programmatic layers were stipulated as residential accommodation (two typologies), public/cultural facilities and landscape/park areas.) All transcodings display the fluidity of the original diagrams. This shared character assimilates the systems to each other despite their ontological difference. The shared, underlying fluid system thus insures that these four systems are able to participate in a single, coherent, multi-layer urban field.


Interaction of two fluids, Parametric Urbanism, AADRL 2008   Fluid deployed – simple geometric translation

Fluid 1 transcoded into courtyard morphology    -    Fluid 2 transcoded into tower morphology

Fluid integration of 4 urban morphologies, Parametric Urbanism, AADRL, London 2008, authors:
Ludovico Lombardi, Du Yu, Victoria Goldstein, Xingzhu Hu; tutor: Patrik Schumacher


Parametric Semiology

This brief excursion into parametric urbanism serves here only to set the scene to outline the task set for the semiological project under conditions of variety, density and complexity. The consistent mapping of four basic function types onto the four distinct morphological sub-systems is only a crude beginning. Each of the spatio-formal subsystems is internally differentiated. These morphological differentiations would have to be correlated to respective programmatic differentiations. An open-to-closed gradient in the domain of the signifier might be correlated to a public-to-private gradient in the domain of the signified. As Ferdinand de Saussure 9 has taught us, a system of signification can only be build up as a system of distinctions, not via the positing of positive terms. To be more precise a system of signification (language) is established through the correlation of two systems of distinctions: the systems of distinctions in the domain of the signifier (form) and the systems of distinctions in the domain of the signified (function). Through their correlation the two planes of distinction are mutually stabilizing. The correlation is established through association. As Wittgenstein taught us, this association/correlation is constituted and reproduced via use within the user’s social life process. Saussure emphasises that language structures thought (action) as much as thought (action) structures the formal medium of language. This medium is the world of sounds in the case of spoken languages and the world of spatial forms in the case of architectural languages. In the absence of their correlation both domains are rather amorphous and open ended. They only take shape via their mutual determination, as their mapped patterns of distinction find their stabilizing scaffold in each other. Saussure illustrates the way linguistic order emerges by means of a diagram and explains: “So we can envisage the linguistic phenomenon in its entirety  - the language that is -  as a series of adjoining subdivisions simultaneously imprinted both on the plane of vague, amorphous thought (A), and on the equally featureless plane of sound (B). This can be represented very approximately in the following sketch. … The combination of both a necessary and mutually complementary delimitation of units. Thought, chaotic by nature, is made precise by this process of segmentation.  … What takes place, is a somewhat mysterious process by which ‘thought-sound’ evolves divisions, and a language takes shape with its linguistic units in between these two amorphous masses. “10

Diagram from Ferdinand de Saussure’s Course in General Linguistics, 1916


As indicated by the above example of an open-to-closed gradient, distinctions might involve a smooth spectrum rather than being restricted to hard edged discrete concepts. Thus parametric semiology involves the move from discrete logic to fuzzy logic, i.e. involving the logic of ‘more or less’ and probability rather than merely the logic of ‘either/or’ and certainty. General distinctions like open-closed/public-private might be re-used across several function types. Thus distinction can co-operate by cutting across each other, thus multiplying (rather than merely adding) determinations.
Potential briefs for the semiological project must be sufficiently complex, so as to warrant and enable the design of a system of signification. The task is to design an information rich, dense built environment that orders and codes/reveals the manifold social interactions to be expected within its spaces. The types of information that are to be encoded are the function type (interaction types, what is going on here?), the social type (the various status groups of the institution, who is to expected here?), and the location type (facilitating navigation: How can I find the event I am looking for?). On the side of the signifier we can distinguish the following dimensions/registers of encoding: the positional dimension (distinction of relative positions), the spatial shape dimension (distinction of spatial shapes) and the dimension of surface treatment (materiality, relief/texture, colour, perforation etc.). These three dimensions are functionally equivalent and can substitute each other. (Shape and surface articulation might be drawn together under the heading of morphology.) The designed semiological system should be conceived as a parametric system, i.e. the various distinctions and their correlations are subject to parametric variation. The programme domain, the domain of the signified, is best understood in terms of interaction patterns or communicative activities. These patterns are always patterns of a certain type, i.e. they adhere to a certain function type, although subject to parametric variation and open to programmatic intermixing and hybridization. These patterns of communicative interaction can be modelled via programmed agents that respond to the coded environmental clues. Each function type involves a typical social institution or interaction type unfolding in its respectively pertinent spatial setting. For instance, a lecture differs from a seminar (or workshop, or individual learning) in terms of the number of participants, their spatial constellation, orientation and action pattern. A specific communicative interaction can only commence once the participants have been gathered, primed (mentally prepared) and ordered into the appropriate constellation. The specific spatial frames (organised and articulated territories) invite and structure such specific communicative situations. Frames allow participants to find each other and allow them to recognize and anticipate the communicative event. Architectural frames help to define the situation. Without a shared definition of the situation no communication is possible. This is the societal function of architecture: The provision of an ordered system of situational definitions via spatial framing. The semiological project is thus at the centre of architecture’s core competency.


1 Correlation is the 3rd principle of Parametricism’s formal heuristics. See: Patrik Schumacher, Parametricism - A New Global Style for Architecture and Urban Design, Published in: AD Architectural Design - Digital Cities, Vol 79, No 4, July/August 2009, guest editor: Neil Leach, general editor: Helen Castle. As example of formal-spatial correlation might serve the correlation between the subsystems of a tower: skeleton, floors and envelope.

2 Mehdi Moussaïd, Dirk Helbing & Guy Theraulaz, How simple rules determine pedestrian behavior and crowd disasters, Proceedings of the National Academy of Science, 2011; see also:
Mehdi Moussaïd, Dirk Helbing, Simon Garnier, Anders Johansson, Maud Combes & Guy Theraulaz, Experimental study of the behavioural mechanisms underlying self-organization in human crowds, Proceedings of the Royal Society B: Biological science, 2009

3 Allbeck, J.M., Functional Crowds. In Workshop on Crowd Simulation co-located with the 23rd Annual Conference on Computer Animation and Social Agents. Saint Malo, France, 2010. See also: Allbeck, J.M. and Kress-Gazit, H. Constraints-Based Complex Behavior in Rich Environments. In Proceedings of the 10th International Conference on Intelligent Virtual Agents, Springer, 2010, pages 1-14.

4 Patrik Schumacher, The Autopoiesis of Architecture, Volume 1: A New Framework for Architecture, John Wiley & Sons Ltd., London 2010

5 Patrik Schumacher, The Autopoiesis of Architecture, Volume 2: A New Agenda for Architecture, John Wiley & Sons Ltd., London 2012

6 Luhmann, Niklas, Social Systems, Stanford University Press, Stanford, California 1995

7 The author joined Zaha Hadid teaching an Avanced Architecture Studio at Columbia University in 1993. The result of the studio was published by Columbia University under the title ‘Ubiquitous Urbanism’.

8 Parametric Urbanism was the title of a three year design research agenda at the AADRL (Design Research Lab) from 2005 -2008.

9 Ferdinand de Saussure, Course in General Linguistics, 4th ed, London 1995, original French, Paris 1916, p.110

10 Ferdinand de Saussure, Course in General Linguistics, Duckworth, 4th ed, London 1995, original French: Cours de liguistique general, Paris 1916


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