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Design Parameters to Parametric Design
Patrik Schumacher, London 2014
Published in: The Routledge Companion for Architecture Design and Practice: Established and Emerging Trends
Edited by Mitra Kanaani and Dak Kopec, Routledge,Taylor and Francis, New York 2016

Parametric Design is a computer based design approach that treats the geometric properties of the design as variables. The dimensions, angles and geometric properties (like curvature) remain malleable as the design progresses. Although at any time the ‘parametric model’ displays a determinate shape according to the set of currently chosen values, the essential identity of the parametric design resides in the malleable object’s topology rather than its momentary determinate shape. This means that the design consists in the relationships that are maintained between the various elements of the composition. In fact the parametric design model is conceived as a network of relations or dependencies. This way of building up a design has the important advantage that the build-up of complexity and the detail resolution of the design can progress while simultaneously maintaining the malleability to adapt to changing requirements as new information is fed into the design process.  The generation of alternative options remains viable and economical deep into the detail design without requiring abortive modeling and drafting work. This parametric malleability is advantageous both for the sake of continuous design adjustments as the design progresses, and for the sake of the generation of options and variations. The parametric model can be conceived as general building plan or geno-type for the generation of many different versions or pheno-types that might co-exist (rather than substitute each other as options). Optioniering thus leads to versioning. Mechanical repetition is being replaced by mass customization. Versioning might also be applied within a single building design via the versioning of components, via ‘generative components’. The components adjust their individual shapes in relation to their placement within the encompassing model. These components are small parametric models, i.e. sets of interdependent parts with adjustable shapes. The component adapts to (and fits into) local constraints via the adjustment of its internal parameters. For instance an array of façade components  - complete with glazed openings, frames and fixing details -  might be made to populate the surface of a volume with changing curvature. The components are to be set up in such a way that they auto-fit to the surface. Each component will assume an individually fitted ‘phenol-typical’ shape, on the basis of the same underlying ‘geno-type’. Thus parametric design is a powerful methodology to achieve a new architectural morphology, namely a morphology of continuous differentiation. However, the potential for such differentiation is not confined to the achievement of scaling and geometric fit with respect to complex forms with continuously changing surface curvature. This kind of differentiation might also be driven by performance parameters like environmental or structural performance parameters, on the basis of external parameters like sun exposure or wind loads. For instance the opening within a façade panel or the shape of a shading element might vary according to the differential sun-exposure of a curved façade at each point of its surface. The parametric designer might set up the following dependency: the higher the sun-exposure of a certain surface patch, the smaller should be the opening of the façade component at this location. A sun-exposure map imported from an environmental analysis tool might then deliver the data input for the component differentiation. The sun-exposure map is thus being ‘transcoded’ into a differentiated field of façade panels that ‘optimizes’ the sunlight penetration within brackets set out by the parametric design. The resultant façade articulation is thus a function, mapping or indeed a representation of the façade’s differential exposure to the sun. Similarly, a designed architectural volume might be structurally articulated via the transcoding of structural analysis parameters into differentiated geometric components. For this purpose the results of a finite elements stress analysis might become the input for a framing pattern that differentiates either member density or member size or both. Again, the result achieves a relative structural optimization (if compared to an undifferentiated framing pattern) and a thus differentiated structure represents the underlying stress distribution. Thus in a tall building a parametrically designed skeleton responds to and displays the differentiation of structural forces.  Both compressive stresses due to the accumulating vertical loads as well as the moments due to horizontal wind-loads accumulate at the bottom of the tower which will thus be rather different from the middle and top of the tower respectively. The respective variation of performance parameters of the various subsystems of the building like envelope and skeleton thus translates into the morphological differentiation of these subsystems. The way performance parameters might be transcoded into morphologies is an open question that calls forth the creative designer. Further: These subsystems – each adaptively differentiated according to its own performance logic – also might adapt to each other’s differentiation. We might talk about sub-system ‘correlation’. To the extent that the envelope’s differentiation is responsive to the skeleton’s differentiation according to a rule it becomes its ‘mapping’ or ‘representation’. The particular rule or mode of correlation is again open to design invention. The same principles of adaptive system differentiation and multi-subsystem correlation might be applied to urbanism which thus becomes ‘parametric urbanism’. The initially considered subsystems here might be the circulation system (road network), the building fabric (massing) and the programmatic distribution (land use). The existing topography (topo-map) as well as the pre-existing roads might serve as underlying input data sets to be transcoded into a differentiated road network. The differentiation of the urban massing might initially follow its own logic of block differentiation, initially conceived as internal product variation without as yet responding to external data inputs. This internal differentiation could in a second step be ‘over-coded’ or correlated with the differentiation of the circulation network according to a certain rule. The fabric differentiation might be further adapted with respect to an agenda of morphological affiliation with the adjacent urban context. Each step requires the invention of a rule of differentiation or adaptive correlation. At the basis of these differentiations and correlations are the chosen geometric ‘primitives’ (or components buildup from those primitives) with their respective variables and respectively chosen degrees of freedom.
Parametric design thus delivers a new powerful adaptive capacity to architectural design. This new capacity opens up a new domain of creative design invention, namely the invention of transcoding rules and rules of sub-system correlation. Design thus becomes ‘rule-based’ design. Critics unfamiliar with this new world of parametric design sometimes presume that the new algorithmic design operations somehow replace or dis-empowers the designer’s creative freedom. The opposite is the case: a new realm of creative exploration with its new design challenges is opened up and calling for the designer’s creative ingenuity. The more computational design tools free the designer from the drudgery of drafting and modeling, the more does the creative essence of the design process as process of invention and decision making comes to the fore.

To design is to generate and to choose. All design is decision making, i.e. the making of choices. Choice presupposes a set of alternatives to choose from. The design process thus comprises two fundamental sub-processes: the generation of alternative solution candidates and the selection of an alternative according to test results on the basis of posited evaluation/selection criteria.  The overall rationality and effectiveness of a design process depends thus on two principally independent factors: its power to generate and its power to test/select. The design principle of ‘generate and test’ conducted in a design medium or model in advance of physical construction stands in as economic (rational) substitute for the physical ‘trial and error’ process that is the principle of the biological evolution as well as of all pre-architectural cultural evolution. Both powers and factors of design rationality are being massively enhanced by the computational aids that constitute parametric and algorithmic design in comparison with traditional design based on drawing according to precedent or intuition. The more the processes of generation and selection are themselves automated via algorithms , the more powerful does the design process become, as the designer’s creative choices shift to the meta-plane of choosing generative algorithms and evaluating selection criteria. These in turn might be looped into evolutionary algorithmic set ups. Parametric design and design via scripted rules is replacing design via the direct manipulation of individual forms. Computational processes can uniquely enhance both the design process's generative power and its analytical power. The techniques of variation and versioning as well as the differentiation on the basis of transcoding and correlation advance the parametric designer’s efficiency as well as the rationality of his design.
The generation of design options can be opened up much further than the mere versioning proliferation of phenol-types on the basis of a pre-established geno-type. A much more open ended, generative  technique of producing solution candidates is via agent based system whereby the elemental primitives (atoms) of a composition or multi-primitive components (molecules) are set free to roam within the modeling space where they aggregate and configure larger global structures according to local rules of attraction, repulsion, alignment, attachment etc. Many of the properties of the resultant configuration are emergent and un-anticipated. Prediction can only mean pattern prediction here in terms of general qualitative properties or in terms of quantitative brackets but hardly precise anticipation. Genuine surprise is possible. Some undesired properties might be prevented by giving the generation process respective constraints. Certain desired properties might be attainable in ways and to a degree that would have been difficult or impossible to attain via intuitive methods. Agent based processes open up a huge field of exploration and arena for the designer’s creative ingenuity. They can also be used in the agenda of multi-subsystem correlation described above. A structural skeleton or an urban path network might be configured via agent based aggregation processes. Urban fabric particles (agents) might interact and configure over the substrate of a topographic map that biases the migration and self-organisation process of the agent population in ways that produce a transcoding of the underlying topography not unlike the more direct transcoding via a simple rule of correlation. The result of the agent based model might display many unexpected variants and properties that might or might not be advantageous upon further analysis. The general advantage of these less predictable processes is that they might deliver in-built criteria in new, unexpected ways and offer up unusual properties that might stimulate the designer’s formulation of altogether new desires and criteria. However, the legibility of the transcoding as representation might be compromised relative to the technique with direct rules of correlation.


Parametric Software

By far the most widely used parametric design software is ‘Grasshopper’ developed by the David Rutten for Robert McNeel Associates1 and first released in 2008. Grasshopper is a freely available graphical associative logic modeler and algorithm editor closely integrated with McNeel’s 3-D modeling tool ‘Rhinoceros’. Grasshopper is a pertinent tool for the set up parametric models as described here as networks of interdependent elements. The network of relations is set up and visualized graphically so that the designer can keep track of and intervene in the relational network he is designing. The parametric designer usually opens two programmes/windows: the 3D modeling space of Rhinoceros and Grasshopper’s graphical algorithm editor. The designer can now move between the modeling and the scripting environment to build up the parametric design, e.g. creating objects in Rhino, make them interdependent in Grasshopper and then manipulate the interdependent configuration in Rhino etc. Grasshopper might become the primary medium and site of the design work while the 3D geometric model visible in Rhinoceros (passive visual control) is driven or executed by the active definition/script visualized and manipulated in the grasshopper window. That the design is all about the set-up of topological parametric geno-types defined via networks of relations (both internal to the building/artefact and external in relation to context parameters) is thus evident in the constitution of the primary design medium. That indeed most parameters/values are treated as variables is evident in the ubiquitous use of sliders (with designated ranges of values).
Rhino/Grasshopper has also become the preferred platform for scripted plug-ins and for a new powerful set of integrated tools that push architecture’s design intelligence beyond the mere handling of geometry to include engineering logics and real time access to physics simulations that allow for sophisticated form-finding and optimization processes to be seamlessly folded into the design process. Kangeroo is a physics engine created by Daniel Piker as a tool for interactive real time structural form-finding simulations like surface-relaxations. These simulations are implemented via particle-spring systems. With this particular tool Frei Otto’s seminal physical form finding experiments with tensile structures and shells via inverted catenary systems as well as his famous wool-thread models can be recreated in the much more versatile digital domain. Frei Otto’s models represent but a small corner of the new space of possibilities that is put at the fingertips of parametric designers in a very intuitive, playful way that equals the intuitive play with real physical materials, however now unleashed from the narrow parametric bounds given by any chosen physical material. Karamba and Milipede are structural analysis and optimization tools for grasshopper. They are interactive, parametric finite element analysis programs that display stress distributions and deformations of any geometric form under any imaginable load.  Karamba was (and continues to be) developed by Clemens Preisinger and Robert Vierlinger a.o. within the structural engineering office Bollinger- Grohmann-Schneider. Millipede was (and continues to be) developed by Panagiotis Michalatos. These tools are allowing architects to design intuitively with immediate engineering feedback and intelligence. They also allow the articulation and characterization of spaces and elements to be guided by structural logics, i.e. they are tools for the architectural project of ‘tectonic articulation’2. For instance, both programs deliver vector-fields that depict the principle stress lines of any surface under specific load conditions. These principle stress lines (or moment lines) can then be used to generate beautifully adapted rib-patterns beyond the usual default grids. These might be used to articulate skeletons, waffle-slabs or grid-shells etc. In addition millipede also offers structural form-generation via so called topology optimization, i.e. the iterative erosion of a solid form placed between any loads and support points to reveal an optimized truss-like dematerialization or framing pattern that might be substituted for the solid form.
Octopus is a multi-objective optimization tool for Grasshopper using genetic algorithms developed by Robert Vierlinger (from the Karamba team). Objectives might include both structural and environmental parameters at the same time, or any other further parameters. The program searches for the best trade-offs between the different potentially conflicting fitness criteria that need to be addressed. Or the designer sets a single fitness criterion but imposes diversity as a second objective to generate a multitude of possible approaches and solutions. Octopus displays the various (pareto-optimal3) solutions within a 3D possibility matrix. In a multiple objectives search (within a multi-dimensional parameter space) that searches trade-offs between several goals a full range or spectrum of options is produced that spans between the extremes of each separate goal. This tool is based on David Rutten's Galapagos User Interface. Galapagos is a general evolutionary solver that David Rutten has developed for the Rhino/Grasshopper design world. The computational harnessing of the principles of evolution  - variation (mutation, recombination), selection (according to fitness criteria), reproduction (as a basis for further variation) – is one of the most exciting new frontiers in computationally augmented design. The work with evolutionary algorithms accelerates the design process. Some worry about where the designer is in such a process. However, like all enhancements that are implied in the move from manual design to computational design, the use of evolutionary algorithms does empowers rather than dis-empowers the designer and enhances the designer’s explicit design intelligence. All design might be construed as a trial and error quasi-evolution. With evolutionary algorithms the fitness criteria for design decisions have to be clearly stated. This enhances the clarity of design thinking. The author does not expect that the totality of the design process for a complex product like a (contextually embedded) building can be solved via a single evolutionary set up. This is so because it is virtually impossible to state in advance all the criteria that might become relevant during the project development. The design process is a discovery process not only in terms of solutions but also in terms of the goals and potentials of the project. Computational design processes augment the designer’s capacity of discovery in both dimensions. The proliferation of (intelligently pre-constrained) options boosts selection according to set criteria and stimulates the setting of new criteria. To summarize the advantages of augmenting the design process with the computational tools described above:
Contemporary, parametric and scripting-based design techniques allow for the establishment of a powerful design process/method. The unique power of this process/method lies in its ability to combine otherwise conflicting trajectories:
1. The combination and simultaneous increase in both the generative power and the constraining power of each design cycle.
2. The combination and simultaneous increase in both the breadth and depth of the solution search in each design cycle.
3. The combination and simultaneous increase in both the power of creative surprise discovery and analytic selective rationality.

Parametric Style

Is there a parametric style? Parametric design is a design methodology based on parametric modeling and scripting techniques. This methodology might be productively employed on any architectural design, independent of the architectural style the designer might be adhering to. All styles can benefit from the advantage of maintaining design malleability during the design’s progressive resolution. Parametric design is thus equally applicable to all architectural styles and in this sense stylistically neutral.
Parametricism is the contemporary style that is most vigorously advancing its design agenda on the basis of parametric design techniques.
Conceptual and Operational Definition of Parametricism:
As conceptual definition of parametricism one might offer the following formula: Parametricism implies that all architectural elements and compositions are parametrically malleable.  This implies a fundamental ontological shift within the basic, constituent elements of architecture. Instead of the classical and modern reliance on ideal (hermetic, rigid) geometrical figures  - straight lines, rectangles, as well as cubes, cylinders, pyramids, and (semi-)spheres -  the new primitives of parametricism are animate (dynamic, adaptive, interactive) geometrical entities   - splines, nurbs, subdivs, particle-spring systems, agent based systems ect.  -  as fundamental ‘geometrical’ building blocks for dynamical compositions that react to “attractors” and that can be made to resonate with each other via scripts.

In principle every property of every element or complex is subject to parametric variation. The key technique for handling this variability is the scripting of functions that establish associations between the properties of the various elements. However, although the new style is to a large extent dependent upon these new design techniques the style cannot be reduced to the mere introduction of new tools and techniques. What characterizes the new style are new ambitions and new values  - both in terms of form and in terms of function -  that are to be pursued with the aid of the new tools and techniques. Parametricism pursues the very general aim to organize and articulate the increasing diversity and complexity of social institutions and life processes within the most advanced centre of post-fordist network society. For this task parametricism aims to establish a complex variegated spatial order. It uses scripting to lawfully differentiate and correlate all elements and subsystems of a design. The goal is to intensify the internal interdependencies within an architectural design as well as the external affiliations and continuities within complex, urban contexts. Parametricism offers a new, complex order via the principles of differentiation and correlation.

This general verbal and motivational definition of parametricism can and must be complemented by an operational definition. It is necessary to operationalise the intuitive values of a style in order to make its hypotheses testable, to make its dissemination systematic, to be exposed to constructive criticism, including self-critique of the parametricist design work etc.
The operational definition of a style must formulate general instructions that guide the creative process in line with the general ambitions and expected qualities of the style. A style is not only concerned with the elaboration and evaluation of architectural form. Each style poses a specific way of understanding and handling functions. Accordingly, the operational definition of parametricism comprises both a formal heuristics  -  establishing rules and principles that guide the elaboration and evaluation of the design’s formal development and resolution – as well as a functional heuristics - establishing rules and principles that guide the elaboration and evaluation of the design’s social functionality.
For each of these two dimensions the operational definition formulates the heuristics of the design process in terms of operational taboos and dogmas specifying what to avoid and what to pursue. At the same time these heuristic design guidelines provide criteria of self-critique and continuous design enhancement.

Operational definition of Parametricism:

Formal heuristics:

Negative principles (taboos):     
avoid rigid forms (lack of malleability)
avoid simple repetition (lack of variety)
avoid collage of isolated, unrelated elements (lack of order)

Positive principles (dogmas):     
all forms must be soft (intelligent: deformation = information)
all systems must be differentiated (gradients)
all systems must be interdependent (correlations)

Functional heuristics:

Negative principles (taboos):     
avoid rigid functional stereotypes
avoid segregative functional zoning

Positive principles (dogmas):     
all functions are parametric activity/event scenarios
all activities/events communicate with each other

The avoidance of the taboos and the adherence to the dogmas delivers complex, variegated order for complex social institutions. These principles outline pathways for the continuous critique and improvement of the design. The designer can always increase the coherence and intricacy of his/her design by inventing further variables (degrees of freedom) for the compositions’ primitive components. There is always scope for the further differentiation of the arrays or subsystems that are made up by the elemental primitives. This differentiation can be increased with respect to the number of variables at play, with respect to the range of differences it encompasses and with respect to the fineness and differential rhythm of its gradients. There is always further scope for the correlation of the various subsystems at play in the multi-system set up. Ultimately every subsystem will be in a relation of mutual dependency with every other subsystem, directly or indirectly. The number of aspects or properties of each subsystem that are involved in the network of correlation might be increased with each design step. Further there is always the possibility (and often the necessity) to add further subsystems or layers to the (ever more complex and intricate) composition. Also: it is always possible to identify further aspects or features of the (principally unlimited) urban context that might become an occasion for the design to register and respond to. Thus the context sensitivity of the design can be increased with every design step. Thus the heuristics of parametricism direct a trajectory of design intensification that is in principle an infinite task and trajectory. There is always a further possibility pushing up the intensity, coherence, intricacy, and beauty of the design. As the network of relations tightens, each further step becomes more elaborate, more involved as all the prior subsystems and their trajectories of differentiation should ideally be taken into account. Arbitrary additions show up conspicuously as alien disruption of the intricate order elaborated so far. Each additional element or subsystem that enters the composition at a late, highly evolved stage challenges the ingenuity of the designer, and more so the more the design advances. The complex, highly evolved design assumes more and more the awesome air of necessity or quasi-nature. However, the design remains open ended. There can be no closure. The classical concepts of completeness and perfection do not apply to parametricism. Parametricism’s complex variegated order does not rely on the completion of a figure. It remains an inherently open composition.


Parametric Society

In the perspective of architecture, and specifically in the perspective of contemporary parametric design, contemporary society is a vast panoply of parametrically variable event scenarios. (This formula spells the program dimension of the built environment.) But is parametric design really concerned with society?
Many critics of parametric design and parametricism ask: What is the societal relevance of the complex geometries and intricate spatial compositions made possible by parametric design? Is this not an expensive, indulgent and self-serving narcissism on the part of designers that distracts from the social task of architecture? This question must be answered. In order to answer this question we need to clarify the specific social task (societal function) of architecture: the spatial ordering of social processes. The increasing density, diversity and complexity of contemporary social life processes requires complex spatial configurations that allow a diversity of event scenarios to unfold in close proximity and awareness of each other. The required complex spatial organizations can only function if the participants that need to come together in the various event scenarios can successfully orient and navigate the spaces they encounter. This requires architectural articulation. The stylistic characteristics of parametricism like curvelinearity, gradients and correlative resonances are potentially more effective in the legible articulation of complex relations  - clustering, nesting, interpenetration - between multiple different spaces. Without curves, smooth transitions and gradients the complex urban scene quickly degenerates into visual chaos. Above the correlative transcoding of external parameters into subsystem differentiations, and then the correlative resonances between different subsystem differentiations was introduced as a key concept and technique of parametric design. The urban subsystems that might be correlated via rule-based associative set ups or scripts might include the differentiated urban massing, topography, vehicular circulation, and pedestrian circulation. It is important to note here that establishment of systematic dependencies via transcodings – and indeed all associative logics – increase the information density of the built environment because every dependency chain can be traced back via inferences. The designer might choose and calibrate the adaptive correlations between the subsystems so that the different system do indeed become “representations” of each other in the sense that users navigating the urban environment can not only follow the gradients or vectors of transformation in each of the subsystems but that whatever is visible from one of the subsystems gives clues about the other systems even if they are not directly visible, e.g. the silhouette of the urban massing will “represent” the topography and allow the street- and path-network to be inferred. Similarly, within a complex mixed-use complex the differentially articulated structural system might represent or indicate the circulation path and the program distribution etc. This powerful enhancement of the communicative capacity of the built environment via rule-based parametric design goes to the heart of architecture’s societal function of ordering the multitude social interaction scenarios that make up contemporary society. Architecture is in charge of the social functionality of the designed/built environment. (Its technical functionality can become the responsibility of various engineering specialisms. However, here too the concept of parameter based differentiation is relevant in the delivery of optimized solutions with respect to structural and environmental engineering.)
Here we can only point towards the promising potential of parametric design techniques – employed under the auspices of the heuristics of parametricism – for the organization and articulation of contemporary societal complexity. The actual proof can only be delivered via individual designs and buildings. There are successful built examples of parametricism. (The attempt to deliver this proof via the documentation of these designs and their ordering work would go beyond the scope of this article.) However, the parametric design community is still flexing its muscles rather than going to work with a clear social purpose. In many young design studios and schools of architecture the playful exploration of new parametric tools results in designs that cannot yet stand up to the critical scrutiny of the skeptics that demand to see the societal relevance and social performance of design efforts. The strategic social instrumentalization of parametric design becomes an urgent agenda that must be explicitly posed and addressed now with the parametric design movement. The credibility of parametricism is at stake. However, we must also protect the need for continued playfulness in the exploration of new tools, techniques and repertoires. Innovation requires the oscillation between open ended exploration and determinate testing. The explicit formulation of the key task is crucial: the ordering of the complexity of social life processes via complex, legible, information-rich spatial orders.
A Post-Fordist network society demands that we continuously browse and scan as much of the social world as possible, in order to remain continuously connected and informed. We cannot afford to withdraw and beaver away in isolation when innovation accelerates all around. We must continuously recalibrate what we are doing in line with what everybody else is doing. We must be networked all the time, so as to continuously ascertain the relevancy of our own efforts. Telecommunication only via mobile devices may help, but it does not suffice. Rapid and effective face-to-face communication remains a crucial component of our daily productivity. The whole built environment must become an interface of multi-modal communication, as the ability to navigate dense and complex urban environments has become a crucial aspect of today’s overall productivity.


Parametric Semiology

In the agenda of parametric semiology architecture’s conception of society as the panoply of parametrically variable event scenarios that need to be ordered spatially comes together with of parametricism’s conception of the built environment as a complex system built up from correlated subsystems that represent each other in the following rather compelling way: The event scenarios  - simulated via agent based crowd modeling techniques – are treated as one more subsystem in the multi-system parametric design model. However, this system of differentiated crowds should be the central, decisive system around which all the architectural sub-systems revolve as so many contributing inputs to its patterned functioning. The principle of correlation, i.e. the establishment of rule-based dependencies also encompasses the relationship of the crowd-behavior relative to its surrounding architectural subsystems, albeit with the additional complication that the pattern displayed by the crowds emerge bottom up via the behaviors of the individual agents.4 These agents’ behaviors are made dependent on where they are, guided by the encoded environmental clues presumed to be accessible to the agents’ cognition. The space communicates its designation with its implied rules of behavior and interaction.
All design is communication design. The built environment, with its complex matrix of territorial distinctions, is a giant, navigable, information-rich interface of communication. Each territory is a communication. It gives potential social actors information about the communicative interactions to be expected within its bounds. It communicates an invitation to participate in the framed social situation. Designed spaces are spatial communications that frame and order further communications. They place the participants into specific constellations that are pertinent with respect to the anticipated communication situations. Like any communication, a spatial communication can be accepted or rejected, i.e. – the space can be entered or exited. Entry implies accepting the communication as the premise for all further communication taking place within its boundaries. Crossing a territorial threshold makes a difference in terms of behavioural dispositions. Entry implies submission to the specific rules of conduct that the type of social situation inscribed within the territory prescribes. In this way, the designed-built environment orders social processes. This spells the unique, societal function of architecture: to order and frame communicative interaction.

Parametric design is able to increase the information density of the built environment. Everything must resonate with everything else. This should result in an overall intensification of relations, which gives the urban field a performative density, informational richness, and cognitive coherence that makes for quick navigation and effective participation in a complex social arena. Our increasing ability to scan an ever-increasing simultaneity of events, and to move through a rapid succession of communicative encounters, constitutes the essential, contemporary form of cultural advancement. Further advancement of this vital capacity requires a new built environment with an unprecedented level of complexity, a complexity that is organized and articulated into a complex, variegated order of the kind we admire in natural, self-organized systems.
The more free and the more complex a society, the more it must spatially order and orient its participants via perceived thresholds and semiotic clues – rather than via physical barriers and channels. The city is a complex text and a permanent broadcast. Therefore, our ambition as architects and urban designers must be to spatially unfold more simultaneous choices of communicative situations in dense, perceptually palpable, and legible arrangements. The visual field must be dense with offerings and information about what lies behind the immediate field of vision. The parametricist logics of rule-based variation, differentiation, and correlation establish order within the built environment, giving those who must navigate it the crucial possibility of making inferences. Employing associative logics correlates the different urban and architectural subsystems in ways that make them representations of each other. Everything communicates with everything. This is not a metaphysical assertion about the world, but a heuristic principle for parametric design under the auspices of parametricism. The rule-based design processes that inform all forms on the basis of informational transcoding imply the possibility of information retrieval through the user, as long as human cognitive capacities are reflected.

Architecture’s societal function – the framing of communicative interaction – can be broken down and concretized into three related subtasks: organisation, articulation, and signification.  Organization is based on the distribution of positions for spatial elements and their pattern of linkages. Articulation is based upon the constitution of morphological identities, similitudes, and differences across the architectural elements to be organized. Organization is instituted via the physical means of distancing, barring, and connecting via circulatory channeling. These physical mechanisms can, in theory, 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, and 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 thereby facilitates the participants’ active orientation. The distinction of organization versus articulation is then based on the difference between handling passive bodies and enlisting active, cognitive agents. These two registers relate in this way: articulation builds upon, and reveals, organization. It makes the organization of functions apparent. In so doing, it elevates organization into order.
The dimension of articulation includes two distinct sub-tasks: phenomenological and semiological articulation (signification). Their distinction is between the enlistment of behavioral responses from cognitive agents, on the one hand, and the communicative engagement of socialized actors, on the other. The phenomenological project enlists users as cognitive agents, perceiving and decomposing their environment along the lines of the principles of pattern-recognition or Gestalt-perception. It makes organizational arrangements perceptually legible by making important points conspicuous, avoiding the visual overcrowding of the scene, and so on. This is a necessary precondition for all semiological encodings that can only attach to the visually discernible features of the environment. In other words, users can only read, interpret, or 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 that presupposes socialization. It is an act of reading a communication: namely, the reading of space as both framing communication and the premise for all further communications to be expected within its ambit. (These framing communications are attributed to the institutions hosting the respective communicative events, i.e. – they are attributed to the clients, rather than to the architects or designers.) Communication presupposes language, that is, 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, therefore, is to go beyond this spontaneous semiosis (that every talented designer navigates intuitively), and build up a more complex and precise system of signification.

Architectural semiology needs to be re-inaugurated as architecture’s core competency under the auspices of Parametricism. After the failed attempts of the 1970s and 1980s, architectural semiology can now be effectively theorized and operationalized as parametric semiology. It is important to note that a semiotic system can neither be reduced to syntax nor to semantics. This was the mistake of the attempts in the 1970s. Eisenman’s work had no sematic dimension, and Jencks had no syntax. The postmodern architects tried to build on the spontaneous semiosis of architectural history and were thus restricted to the recycling of clichés, and without the chance to build up a more complex syntax. Instead the refoundation of architectural semiology promoted here suggests a radical severance from all historical semiotic material, promoting the construction of a new, artificial spatio-visual language in analogy to the creation of artificial programming languages, taking full advantage of the radical arbitrariness of all languages. The construction of this language must proceed step by step, oscillating between syntactical and semantic advances. This is made possible via parametric agen-based modelling that realizes the signifying relations as associative functions that systematically make agent behaviours dependent on architectural features. At the same time the pragmatic layer is anticipated as the (never fully predictable) social appropriation process that commences when the design spaces are finally utilized and re-utilized.
In the second volume of the author’s treatise, The Autopoiesis of Architecture5, a set of axioms and heuristic principles are formulated that outline strategies for semiological projects conceived as complex architectural designs – for instance, the design of a university campus – as the design of a coherent visual language or system of signification. The first axiom restricts the domain of architecture’s signified to the social events that are expected to happen within the respective buildings or spaces, defined along the three dimensions of function type, social type and location type. The second axiom states that the relevant unit of architectural communication, the architectural sign, is the designed/designated territory (just like the sentence is the minimal relevant unit of speech). Territorial thresholds mark differences that make a difference in terms of social situation. These differences in use constitute the meaning of architectural signs/communications.
Architectural semiology can be operationalized via agent-based crowd modelling. The scripting of the agents’ specific behavioural dispositions, in relation to specific spatial and/or morphological features of the designed environment, allows designers to model and work on the signification relation. The domain of the signified – the patterns of social interaction expected within designed territories, can thus be brought into architecture’s design medium as one more subsystem (the crucial subsystem) in the set of correlated subsystems constituting the parametric model.It therefore becomes possible, for the first time in the history of architecture, to model this life-process, thus incorporating it into design speculation. This was made possible by the use of computational crowd modelling techniques, via agent-based models. General tools like “Processing”, or specific tools like “MiArmy” and “AI.implant” (available as plugins for Maya), and “Massive” now make behavioural modelling within designed environments accessible to architects. Agent modelling should not be limited to crowd circulation flows, but should encompass all patterns of occupation and social interaction in space. The agents’ behaviour might be scripted so as to correlate with the configurational and morphological features of the designed environment, i.e. – programmed agents responding to environmental clues. Such clues or triggers might include furniture configurations, as well as other artefacts. The idea, then, is to build dynamic action-artefact networks.
Morphological features, as well as colours and textures that, together with ambient parameters (lighting conditions), constitute and characterize a certain territory can now influence the behavioural mode of the agent. Since the ‘meaning’ of an architectural space is the (nuanced) type of event or social interaction to be expected within its territory, these new tools allow for the re-foundation of architectural semiology as parametric semiology. The semiological project therefore implies that the design project systematizes all form-function correlations into a coherent system of signification. A system of signification, in turn, is a system of mappings (correlations) that map distinctions or manifolds, defined within the domain of the signified (here the domain of patterns of social interaction), onto the distinctions or manifolds, which are defined within the domain of the signifier (here, the domain of spatial positions and morphological features defining and characterizing a given territory) and vice-versa. This system of signification works if the programmed social agents consistently respond to the relevantly coded positional and morphological clues in such a way that expected behaviours can be read off the articulated environmental configuration. However, rather than modelling scenarios frame by frame, agent based modelling works by defining the agents’ behavioural dispositions and biases relative to environmental features. The event itself then becomes an emergent global pattern resulting from the local interactions of agents with each other inside the environment. If this succeeds, architecture will have done its job of ordering the event scenario. That is, the meaning of architecture, the prospective life processes it frames and sustains, will have been modelled and assessed within the design process as an object of direct creative speculation and cumulative design elaboration. In this way, architectural semiology can finally be operationalized; in this way, it will have a real chance of succeeding as a promising, rigorous design-research project.



Parametric design starts with parametric variation. Variation can be employed for the differentiation of a field, layer or subsystem. To the extent to which this differentiation is rule-based (and gradual) rather than random, it establishes an order that might allow for orientation and navigation along its vector of transformation. Gradients as well as more complex rule-based differentiations allow for inferences from what is visible to what is not yet visible. A differentiated field or subsystem might become the substrate upon which the differentiation of further subsystems might be made dependent via functions or transcoding rules. As rule-based mappings these subsystems are representations6 of each other that allow inferences from one to the other. The technique of associative modelling allows the crucial programme layer to be treated as one more correlated subsystem in the multi-system parametric set up, via a programme distribution rule that correlates with the spatio-morphological (typological) differentiation of the design. However, the heuristics of parametricism interpret program as parametrically variable event scenarios whereby the number, type, density and configuration of participants are pertinent variables that make a difference. This conception allows for gradual variation as well as inbetweening or hybridization of programs or event scenarios. This program layer is thus much more pertinently displayed and elaborated via crowd modelling than via the usual labelling or colour coding of areas.
The ordered pattern of crowd behaviour and interaction, i.e. the social life process, will be a correlate of the spatio-morphological built environment. This built environment in turn becomes a function and representation of the life processes it accommodates. And its functioning as a legible representation that becomes a communication is part and parcel of its very functioning, i.e. of the functioning of the accommodated life processes themselves. These life-processes indeed require the organized and articulated system of spatial frames as necessary precondition of their very formation and regular reproduction. Parametric design can enhance the density, intensity, complexity and thus productivity of contemporary life-processes via the systematic enhancement of the built environment as a well-ordered, information rich, perceptually tractable, and intuitively legible system of signification.


1 Founded in 1980, McNeel is a privately-held, employee-owned company based in Seattle with sales and support offices and affiliates in Seattle, Boston, Miami, Buenos Aires, Barcelona, Rome, Tokyo, Taipei, Seoul, Kuala Lumpur, and Shanghai.

2 Patrik Schumacher, Tectonics - The Differentiation and Collaboration of Architecture and Engineering, in: ‘Stefan Polonyi – Bearing Lines – Bearing Surfaces’, Ed. Ursula Kleefisch-Jobst et al., Edition Axel Menges, Stuttgart/London 2012

3 A solution is in a multi-objective optimization is called ‘Pareto optimal’ if none of the addressed fitness values can be increased without decreasing some of the other fitness values. The set of Pareto optimal solutions is called the ‘pareto front’.

4 Crowd modelling must follow the principle of ‘methodological individualism’.

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

6 The German word for mathematical function  - Abbildung -  literally means pictorial representation.



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