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Parametricism  -  A New Global Style for Architecture and Urban Design
Patrik Schumacher, London 2008
Published in: AD Architectural Design - Digital Cities, Vol 79, No 4, July/August 2009,
guest editor: Neil Leach, general editor: Helen Castle


Abstract: Though parametricism has its roots in the digital animation techniques of the mid-1990s, it has only fully emerged in recent years with the development of advanced parametric design systems. Parametricism has become the dominant, single style for avant-garde practice today. It is particularly suited to large-scale urbanism as exemplified by a series of competition-winning master-plans by Zaha Hadid Architects.


There is a global convergence in recent avant-garde architecture that justifies the enunciation of a new style: Parametricism. The style is rooted in digital animation techniques. Its latest refinements are based on advanced parametric design systems and scripting techniques. This style has been developed over the last 15 years and is now claiming hegemony within avant-garde architecture. It succeeds modernism as a new long wave of systematic innovation. The style finally closes the transitional period of uncertainty that was engendered by the crisis of modernism and that was marked by a series of short lived episodes including Postmodernism, Deconstructivism, and Minimalism.
Parametricism is the great new style after modernism. The new style claims relevance on all scales from architecture and interior design to large scale urban design. The larger the scale of the project the more pronounced is parametricism’s superior capacity to articulate programmatic complexity. The urbanist potential of parametricism has been explored in a three year research agenda at the AADRL  - Parametric Urbanism – and demonstrated by a series of competition winning masterplans by Zaha Hadid Architects.

Zaha Hadid Archiects, Kartal-Pendik Masterplan, Istanbul, Turkey, 2006
Fabric study. The urban fabric comprises both cross towers and perimeter blocks. The image shows the morphological range of the perimeter block type. Blocks are split into four quadrants allowing for a secondary, pedestrian path system. At certain network crossing points the block system is assimilated to the tower system: each block sponsors one of the quadrants to form a pseudo tower around a network crossing point.


One North Masterplan, Network – Fabric – Buildings, Singapore, Zaha Hadid Architects 2001-2003
Fabric and network. This masterplan for a new mixed-used urban business district in Singapore was the first of a series of radical masterplans that led to the concept of parametric urbanism and then to the general concept of parametricism.


I. Parametricism as Style

Avant-garde architecture and urbanism are going through a cycle of innovative adaptation – retooling and adapting the discipline to the demands of the socio-economic era of post-fordism. The mass society that was characterized by a universal consumption standard has evolved into the heterogenous society of the multitude, marked by a proliferating life-style and career differentiation. Architecture and urbanism are called upon to organize and articulate the increased complexity of post-fordist society.

Contemporary avant-garde architecture and urbanism is addressing this societal demand via a rich panoply of parametric design techniques. However, we are confronted with a new style rather than just with a new set of techniques. The techniques in questions – the employment of animation, simulation and form-finding tools, as well as parametric modelling and scripting  -  have inspired a new collective movement with radically new ambitions and values. This has lead to many new, systematically connected design problems that are being worked on competitively within a global network of design researchers.1  Over and above aesthetic recognisability, it is this wide-spread, long-term consistency of shared design ambitions/problems that justifies the enunciation of a style in the sense of an epochal phenomenon.2 We propose to call this style: Parametricism.
Parametricism is a mature style. There has been talk about “continuous differentiation”3, versioning, iteration and mass customization etc. for quite a while within the architectural avant-garde discourse.
Recently we witnessed an accelerated, cumulative build up of virtuosity, resolution and refinement, facilitated by the attendant development of parametric design tools and scripts that allow the precise formulation and execution of intricate correlations between elements and subsystems. The shared concepts, computational techniques, formal repertoires, and tectonic logics that characterize this work are crystallizing into a solid new hegemonic paradigm for architecture.
Parametricism emerges from the creative exploitation of parametric design systems in view of articulating increasingly complex social processes and institutions. The parametric design tools themselves cannot account for this profound shift in style from modernism to parametricism. This is evidenced by the fact that late modernist architects are employing parametric tools in ways which result in the maintenance of a modernist aesthetics, i.e. using parametric modelling to inconspicuously absorb complexity. The parametricist sensibility pushes in the opposite direction and aims for a maximal emphasis on conspicuous differentiation and the visual amplification differentiating logics. Aesthetically it is the elegance4 of ordered complexity and the sense of seamless fluidity, akin to natural systems, that is the hallmark of parametricism.


II. Styles as Design Research Programmes

Avant-garde styles might be interpreted and evaluated in analogy to new scientific paradigms, affording a new conceptual framework, and formulating new aims, methods and values. Thus a new direction for concerted research work is established.5 My thesis is therefore: Styles are design research programmes.6
Innovation in architecture proceeds via the progression of styles so understood. This implies the alternation between periods of cumulative advancement within a style and revolutionary periods of transition between styles. Styles represent cycles of innovation, gathering the design research efforts into a collective endeavor. Stable self-identity is here as much a necessary precondition of evolution as it is in the case of organic life. To hold on to the new principles in the face of difficulties is crucial for the chance of eventual success. This is incompatible with an understanding of styles as transient fashions. Basic principles and methodologies need to be preserved and defended with tenacity in the face of initial difficulties and setbacks. Each style has its hard core of principles and a characteristic way of tackling design problems/tasks.
The 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 old 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.

III. Defining Heuristics and Pertinent Agendas

The defining heuristics of parametricism are fully reflected in the taboos and dogmas of contemporary avant-gared design culture:

Negative heuristics (taboos): avoid rigid geometric primitives like squares, triangles and circles, avoid simple repetition of elements, avoid juxtaposition of unrelated elements or systems.

Positive heuristics (dogmas): consider all forms to be parametrically malleable, differentiate gradually (at variant rates), inflect and correlate systematically.


The current stage of advancement within parametricism relates as much to the continuous advancement of the attendant computational design processes as it is due to the designer’s realization of the unique formal and organizational opportunities that are afforded by these processes. Parametricism can only exist via the continuous advancement and sophisticated appropriation of computational geometry. 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 and advancing these techniques. However, the advancement of techniques should go hand in hand with the formulation of further ambitions and agendas. The following 5 agendas are to inject new aspects into the parametric paradigm and to push parametricism further:

1.Parametric Inter-articulation of Sub-systems:
The ambition is to move from single system differentiation – e.g. a swarm of façade components - to the scripted association of multiple subsystems – envelope, structure, internal subdivision, navigation void. The differentiation in any one systems is correlated with differentions in the other systems.6.

2.Parametric Accentuation:
The ambition is to enhance the overall sense of organic integration through correlations that favour deviation amplification rather than compensatory adaptations. The associated system should accentuate the initial differentiation. Thus a far richer articulation can be achieved and more orienting visual information can be made available.

3.Parametric Figuration7:
We propose that complex configurations that are latent with multiple readings can be constructed as a parametric model with extremely figuration-sensitive variables. Parametric variations trigger “gestalt-catastrophes”, i.e. the quantitative modification of these parameters trigger qualitative shifts in the perceived configuration. Beyond object parameters, ambient parameters and observer parameters have to be integrated into the parametric system.

4.Parametric Responsiveness8:
Urban and architectural environments receive an inbuilt kinetic capacity that allows those environments to reconfigure and adapt themselves in response to prevalent occupation patterns. The real time registration of use-patterns drives the real time kinetic adaptation. The built environment thus acquires responsive agency at different time scales.

5.Parametric Urbanism9 - Deep Relationality:
The assumption is that the urban massing describes a swarm-formation of many buildings whereby lawful continuities cohere this manifold of buildings. The systematic modulation of morphologies produces powerful urban effects and facilitates field orientation. Our ambition is deep relationality, i.e. to integrate the building morphology - all the way to the detailed tectonic articulation and the interior organisation. Parametric Urbanism might involve parametric accentuation, parametric figuration, and parametric responsiveness as registers to fulfill its ambition of deep relationality.


IV. Parametricist vs. Modernist Urbanism

Le Corbusier’s first theoretical statement on Urbanism starts with a eulogy of the straight line and the right angle as means by which man conquers nature. The first two paragraphs of The City of Tomorrow contrast man’s way with the pack-donkey’s way:
“Man walks in a straight line because he has a goal and knows where he is going; he has made up his mind to reach some particular place and he goes straight to it. The pack-donkey meanders along, meditates a little in his scatter-brained and distracted fashion, he zig-zags in order to avoid larger stones, or to ease the climb, or to gain a little shade; he takes the line of least resistance.”10 Le Corbusier admires the urban order of the Romans and rejects our sentimental attachment to the picturesque irregularity of the medieval cities: “The curve is ruinous, difficult and dangerous; it is a paralyzing thing.”11 Le Corbusier insists that “the house, the street, the town … should be ordered; … if they are not ordered, they oppose themselves to us.”12  Le Corbusier’s limitation is not his insistence upon order but his limited concept of order in terms of classical geometry. Complexity theory in general, and the research of Frei Otto13 in particular, have since taught us to recognize, measure and simulate the complex patterns that emerge from processes of self-organisation. Phenomena like the “donkey’s path” and the urban patterns resulting from unplanned settlement processes can now be analyzed and appreciated in terms of their underlying logic and rationality, i.e. in terms of their hidden regularity and related performative power.
Le Corbusier realized that although “nature presents itself to us as a chaos … the spirit which animates Nature is a spirit of order ”14. However, his understanding of nature’s order was limited by the science of his day. Today we can reveal the complex order of those apparently chaotic patterns by means of simulating their lawful “material computation”.
Our parametricist sensibility gives more credit to the “pack-donkey’s path” as a form of recursive material computation than to the simplicity of clear geometries that can be imposed in one sweeping move.

Frei Otto’s pioneering work on natural structures included work on settlement patterns. He starts with the distinction/relation of occupying and connecting as the two fundamental processes that are involved in all processes of urbanisation.15 His analysis of existing patterns was paralleled by analogue experiments modelling crucial features of the settlement process. He distinguished distancing and attractive occupations. For distancing occupation he used magnets floating in water and for attractive occupation he used floating polystyrene chips. A more complex model integrates both distancing and attractive occupation whereby the polystyrene chips cluster around the floating magnetic needles that maintain distance among themselves16. The result closely resembles the typical settlement patterns found in our real urban landscapes.17

Frei Otto, Occupation with simultaneous distancing and attracting forces,
Institute for Lightweight Structures (ILEK), Stuttgart, Germany, 1992
Analogue models for the material computation of structural building forms (form-finding) are the hallmark of Frei Otto’s research institute. The same methodology has been applied to his urban simulation work. The model shown integrates both distancing and attractive occupations by using polystyrene chips that cluster around the floating magnetic needles that maintain distance among themselves.


With respect to processes of connection Frei Otto empirically distinguishes three scalar levels of path networks – each with its own typical configuration: settlement path networks, territory path networks, and long-distance path networks. All start as forking systems that eventually close into continuous networks. Frei Otto distinguishes three fundamental types of configuration: direct path networks, minimal path networks and minimizing detour networks. Again he conceives material analogues that are able to self-organise into relatively optimized solutions. For minimal path networks Frei Otto devised the soap bubble skin apparatus where a glass plate is held over a water surface and the minimal path system forms itself from needles.18 For the optimized detour networks the famous wool-thread models19 are able to compute a network solution between given points that optimize the relationship of total network length and the average detour factor imposed. For each set of points, and for each adopted sur-length over the theoretical direct path, an optimizing solution is produced. Although no unique optimal solution exists, and each computation is different, characteristic patterns emerge in different regions of the parametric space.

Frei Otto, Apparatus for computing minimal path systems,
Institute for Lightweight Structures (ILEK), Stuttgart, 1988
The analogue model finds the minimal path system, that is, the system connects a distributed set of given points, thus the overall length of the path system is minimised. Each point is reached but there is a considerable imposition of detours between some pairs of points. The system is a tree (branching system) without any redundant connections.


Marek Kolodziejczyk, Wool-thread model to compute optimised detour path networks,
Institute for Lightweight Structures (ILEK), Stuttgart, 1991
Depending on the adjustable parameter of the thread’s sur-length, the apparatus – through the fusion of threads – computes a solution that significantly reduces the overall length of the path system while maintaining a low average detour factor.


Frei Otto’s form-finding models bring a large number of components into a simultaneous organising force-field. Any variation of the parametric profile of any of the elements is being lawfully responded to by all other elements within the system. Such quantitative adaptations often cross tresholds into emergent qualities.
If such an associative sensitivity holds sway within a system we can talk about relational fields. Relational fields comprise mutually correlated sub-layers, for instance the correlation of patterns of occupation with patterns of connection. The growth-process of unplanned settlement patterns does indeed continuously oscillate between moments when points of occupation spawn paths and paths in turn attract occupation. The continuous differentiation of the path-network - linear stretches, forks, crossing points –  lawfully correlates with the continuous differentiation of the occupying fabric in terms of its density, programmatic type and morphology. The organising/articulating capacity of such relational fields is striking, e.g. in comparison with the grid of the American city. This modern grid is undifferentiated and therefore non-adaptive. Its “freedom” is now limiting: It leads to arbitrary juxtapositions that result in visual chaos.
Modernism was founded on the concept of universal space. Parametricism differentiates fields. Space is empty. Fields are full, as if filled with a fluid medium. We might think of liquids in motion, structured by radiating waves, laminal flows, and spiraling eddies. Swarms have also served as paradigmatic analogues for the field-concept: swarms of buildings that drift across the landscape. There are no platonic, discrete figures or zones with sharp outlines. Within fields only regional field qualities matter: biases, drifts, gradients, and perhaps conspicuous singularities like radiating centres. Deformation does no longer spell the breakdown of order but the lawful inscription of information. Orientation in a complex, lawfully differentiated field affords navigation along vectors of transformation .The contemporary condition of arriving in a metropolis for the first time, without prior hotel arrangements, without a map, might instigate this kind of field-navigation. Imagine there are no more landmarks to hold on, no axis to follow and no more boundaries to cross.
Parametricist urbanism aims to construct new field logics that operate via the mutually accentuating correlation of multiple urban systems: fabric modulation, street systems, system of open spaces etc. The agenda of deep relationality implies that the fabric modulation also extends to the tectonic articulation. Both massing and fenestration might   - each in its own way – be driven by sunlight orientation, producing a mutual enhancement of the visual orienting effect. Thus local perceptions (of the facade) can give clues about the relative position within the global system of the urban massing. The location and articulation of building entrances might be correlated with the differentiated urban navigation system20. This correlation might even extend to the internal circulation. This concept of deep relationality might also operate in reverse so that e.g. the internal organisation of a major institutional building might lead to multiple entrances that in turn trigger adaptations within the urban navigation system. It is important that such laws of correlation are adhered to across sufficiently large stretches.


V. Implementing Parametricist Urbanism

The urban implementation of parametricism is still in its infancy. However, ZHA was able to win a series of international masterplanning competitions with schemes that embody the key features of parametricism. The projects include the 200 hectar One-North Masterplan for a mixed-use business park in Singapore, Soho City in Beijing comprising 2.5 million squaremeter of residential and retail programme, the mixed use masterplan for Bilbao including the river island and both opposing embankments, and the Kartal-Pendik masterplan21, a mixed use urban field of 55 hectar with 6 million squaremeter of gross buildable area comprising all programmatic components of a city.

The project is to constitute a sub-center on Istanbul’s Asian side to release the pressure on the historic centre. The site is being reclaimed from industrial estates and is flanked with the small grain fabric of sub-urban towns. The parametricist taboo of unmediated juxtapositions implied that we took the adjacent context  - in particular the incoming lines of circulation - as an important input for the generation of the urban geometry. Maya’s hair dynamic tool achieved a parametrically tuned bundling of the incoming paths into larger roads enclosing larger sites. The resultant lateral path system that exhibits the basic properties of Frei Otto’s minimizing detour network. The longitudinal direction was imposed via a primary artery with a series of subsidiary roads running in parallel. The result was is a hybrid between minimizing detour network and deformed grid. In parallel we worked with two primary fabric typologies, towers and perimeter blocks, each conceived as generative component or geno-type that allows for wide range of pheno-typical variation. The towers, conceived as cross towers, placed on the crossing points accentuating the path network. The perimeter block inversely correlates height with parcel area so that courtyards morph into internal atria as sites get smaller and blocks get taller. Blocks split along the lines of the secondary path-network. This move, together with the accentuating height differentiation, allows the block type to be assimilated to the cross-tower type. “pseudo-towers” are formed at some crossing points by pulling up the four corners of the four blocks that meet at such a corner. Thus an overall sense of continuity is being achieved in spite of starting with two rather distinct urban typologies. In terms of the global height regulation – besides the local dependency of height upon parcel size – we are trying to correlate the conspicuous build up of height with the lateral width of the overall field. Thus the rhythm of urban peaks indexes the rhythm of widening and narrowing of the urban stretch.

Zaha Hadid Archiects, Kartal-Pendik Masterplan, Istanbul, Turkey, 2006
Maya hair-dynamic simulates minimised detour net. The path network was thus generated with a digital woolthread model. The set-up registers the multitude of incoming streets and bundles them into larger roads affording larger parcels.

Zaha Hadid Archiects, Kartal-Pendik Masterplan, Istanbul, Turkey, 2006
Masterplan: Hybrid detour net & deformed grid, Final Urban lay-out of streets and urban fabric     


Fabric studies 2: split block variations

Fabric studies 4: calligraphy block variation

Global Maya model. The model features the interarticulation between cross towers and perimeter blocks as well as the affiliation to the surrounding fabric. The correlation of global width to global height can also be observed.

Scripting calligraphy block patterns. Various scripts were developed that configure the perimeter blocks depending on parcel size, proportion and orientation. The script also allowed for random variations regarding the introduction of openings within blocks.

New cityscape. The Kartal-Penkik plan incorporates a vast quarry that becomes the largest item in a system of parks that are spread throughout the urban field. The rhythmic flow of the urban fabric gives a sense of organic cohesion.


The result is an elegant, coherently differentiated city-scape that facilitates navigation through its lawful constitution and through the architectural accentuation of both global and local field properties.
This much might be possible to institute with the imposition of strict planning guidelines using building lines and height regulation. Political and private buy-in is required. All constituencies need to be convinced that the individual restrictions placed upon all sites really deliver a worth-while collective value: the unique character and coherent order of the urban field that all players benefit from if adherence can be enforced. Ordered complexity here replaces the monotony of older planned developments and the disorienting visual chaos that marks virtually all unregulated contemporary city expansions.
To go further yet, in terms of our concept of deep relationality, we have to extend our involvement from urbanism to architecture. Only then we can further intensify the accentuating correlations, involving the systematic modulation of tectonic features. For instance, in terms of the calligraphy blocks  - a third perimeter block variation that has been designed to both open up the interior of parcels and to cross parcels – we use a continuous facade differentiation that leads from the street-side to the courtyard on the basis of an initial distinction of external and internal facades. Another moment of deep articulation is the coordination of landscape and public spaces, and the correlation of the secondary path-system with the disposition of internal navigation systems.

Calligraphy blocks – tectonic detail. The articulation of the facades is a function of the location within the urban field. The exterior of the blocks is given a heavier relief than the interior. Where a block opens up and the public space flows into the private courtyard, a semi-private zone is articulated via the gradient transformation between the outer and inner articulation.

Close-up of cross towers. The cross towers produce the urban peaks. Through their ground-level articulation these tower complexes participate in the creation of a continuous urban fabric that frames the streets and occasionally widens the street space into semi-public plazas. This is achieved while maintaining total continuity between the podium-like ground fabric and the shafts of the towers.


Doubts might be felt when confronted with the possibility of designing an urban field of up to 6 million squaremeter gross area with a single design team. Are we overstretching our capacity here? The more we are confronted with large scale development of this kind the more confident we grow that the tools and strategies we are deploying under the banner of parametricism can indeed deliver something that produces a decisive surplus value if compared with the usual alternative of uncoordinated, arbitrary juxtapositions. The contemporary choice of typologies, construction options and styles is simply too large to expect the underlying pragmatic logics to become legible. The result is a cacophony of pure difference. Parametricism is able to further coordinate pragmatic concerns and articulate them with all their rich differentiations and relevant associations. The danger of overriding real-life richness is minimized because variety and adaptiveness are written into the very genetic make-up of parametricism.



1 ZHA and AADRL together form just one node within this fast growing network.

2 Also, we should not forget that the desire for an architecture marked by a complex, fluid, nature-like continuity was clearly expressed before the new digital tools had entered the arena: Zaha Hadid’s work of the late eighties and Eisenman/Lynn’s folding projects of the early nineties. (This point also indicates that we are confronted with a new style and not only new techniques.) Since then we witnessed a conceptual radicalisation and increased formal sophistication along the lines set out then, leading to the emergence of a powerful new style.

3 The credit for coining this key slogan goes to Greg Lynn and Jeff Kipnis.

4 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

5 This interpretation of styles is valid only with respect to the avant-garde phase of any style.

6 It is important to distinguish between research programmes in the literal sense of institutional research plans from the meta-scientific conception of research programmes that has been introduced into the philosophy of science: whole new research traditions that are directed by a new fundamental theoretical framework. It is this latter concept that is utilized here for the reinterpretation of the concept of style. See: Imre Lakatos, The Methodology of Scientific Research Programmes, Cambridge 1978

7 Parametricism involves the conceptual shift from part-to-whole relationships to component-system relationships, system-to-system relationships, and system-subsystem relationships. Parametricism prefers open systems that always remain incomplete. As the density of associations increases components might be associated into multiple systems. The correlation of initially independent system implies the formation of a new encompassing system etc.

8 “Parametric Figuration” featured in our teachings at Yale and at the University of Applied Arts, Vienna. It also featured in my studio at the AADRL.

9 Parametric Responsiveness was at the heart of our 3 year design research agenda “Responsive Environments” at the AADRL in London from 2001-2004.

10 “Parametric Urbanism” is the title of our recently completed design research cycle at the AADRL, from 2005 – 2008.

11 Le Corbusier, The City of Tomorrow and its Planning, Dover Publications, New York 1987, translated from French original Urbanisme, Paris 1925, p.5

12 Le Corbusier, The City of Tomorrow and its Planning, Dover Publications, New York 1987, translated from French original Urbanisme, Paris 1925, p.8

13 Le Corbusier, The City of Tomorrow and its Planning, Dover Publications, New York 1987, translated from French original Urbanisme, Paris 1925, p.15

14 Frei Otto might be considered as the sole true precursor of parametricism.

15 Le Corbusier, The City of Tomorrow and its Planning, Dover Publications, New York 1987, translated from French original Urbanisme, Paris 1925, p.18

16 Frei Otto, Occupying and Connecting – Thoughts on Territories and Spheres of Influence with Particular Reference to Human Settlement, Edition Axel Menges, Stuttgart/London 2009

17 Frei Otto, Occupying and Connecting – Thoughts on Territories and Spheres of Influence with Particular Reference to Human Settlement, Edition Axel Menges, Stuttgart/London 2009, p.45

18 Within the AADRL research agenda of “Parametric Urbanism” we also always started with material analogues that were then transposed into the domain of digitally simulated  self-organisation.

19 Ibid. p.64

20 Marek Kolodziejczyk,Thread Model, Natural – spontaneous Formation of Branches, in: SFB 230, Natural Structures – Principles, Strategies, and Models in Architecture and Nature, Proceedings of the II. International Symposium of the Sonderforschungsbereich 230, Stuttgartr 1991, p.139

21 This is what we at ZHA imposed within the urban guidelines for our Singapore masterplan.

22 Zaha Hadid Architects, design team: Zaha Hadid, Patrik Schumacher, Saffet Bekiroglu, Daewa Kang, Daniel Widrig, Bozana Komljenovic, Sevil Yazici, Vigneswaran Ramaraju, Brian Dale, Jordan Darnell, Elif Erdine, Melike Altinisik, Ceyhun Baskin, Inanc Eray, Fluvio Wirz, Gonzalo Carbajo, Susanne Lettau, Amit Gupta, Marie-Perrine Placais, Jimena Araiza.


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