Oz
Volume 36 Article 4
1-1-2014
Complexity in Architecture and Design
Nikos Salingaros University of Texas at San Antonio
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Recommended Citation Salingaros, Nikos (2014) "Complexity in Architecture and Design," Oz: Vol. 36. https://doi.org/10.4148/ 2378-5853.1527
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Nikos Salingaros
Architecture is successful by con- necting visually, emotionally, and viscerally with the observer/user through its complexity. For this reason, complexity is a generative tool. All traditional societies devel- oped an individual architectural form language, transitioning into the complex design language of artifacts and the arts. Internation- Figure 1. This system’s organized complexity is Figure 2. Verbal descriptions of complexity. Left: “Circle of radius 1 in center”. Right: “Circle of radius alization in the early twentieth cen- hidden behind a misleadingly simplistic cover. 1 centered at point A, circle of radius 1 centered at point B, circle of radius 1 centered at point C, …” tury erased all of those traditions, with a vast concomitant reduction in design complexity. How do we re-embody complexity into archi- Defining Complexity A useful but limited measure of com- buildings needed more description, tectural form, space, and surface? plexity is the Kolmogorov-Chaitin giving a higher word count. Intelligent guidelines come from Complexity represents intricacy of complexity: how many words science. First, we can distinguish structure, stored information on are needed for a fairly accurate Two Types of Complexity: between different types of com- how the system actually works and description.2 For example, on a Disorganized Versus Organized plexity, something that few people its own makeup. This internal com- blank or uniform computer screen, have been clear about. Second, we plexity is independent of whether where all the pixels are exactly the Having established the two oppo- estimate the degree of complexity the system “looks” complex or not. same color, the complexity is zero, sites of low versus high complexity using a simple model. Organized Something empty, excessively plain, since the whole can be specified according to the word count of their complexity elicits a harmonious containing no structural informa- by a single word (the color of the description, it’s time to clarify a long- response; versus disorganized com- tion, is not complex. The system screen). I have taught this model standing enigma of complexity the- plexity that is perceived as random- itself would not exist without a in Architecture Class, asking my ory. There exist two entirely distinct ness. Only the former produces an sufficient internal complexity to students to catalogue the elements types of complexity: disorganized emotionally nourishing state in make it run or stand up structurally. of a form language that was used to and organized.4 Both types require human beings, whereas random- Disguising complexity is not really construct their favorite building.3 a high word count when describing ness increases anxiety. An architect being honest about the design, yet Descriptions varied from one to examples, but have distinct internal needs to understand complexity: the visual surface information of four pages, since students chose mathematical structure. They repre- its intentional generation, and how some man-made architectural and very different buildings. The stu- sent departures from low-complexity to manage emergent complexity as design objects is kept low for stylistic dents then did a word count of minimalist structures, yet the way a design tool. It is essential to stop reasons.1 As architects place an in- their description. The raw word their respective complexity is gener- using complexity as a metaphor ordinate emphasis on visual appear- count measured the degree of com- ated is very different. detached from reality, in a random ance, a confusion about superficial plexity of their building. Clearly, process without any underlying “look” versus substance permeates minimalist buildings required only We can describe a complex structure, reasoning, and adopt instead a and disorients many discussions of a very brief description, hence a but only up to a point, beyond which 18 practitioner’s perspective. complexity in architecture. low word count; whereas complex a complete description exceeds our Figure 3. Disorganized versus organized. Left: seven circles centered on different points. Right: seven circles Figure 4. Organization economizes description. Left: each subunit has to be individually specified. arranged in a rotationally-symmetric pattern. The same raw complexity, but different organization. Right: one basic subunit repeated vertically and horizontally.
capacity. Take a computer screen There exist many ways of doing this, measured by using entirely different All of these methods help to or- for example. The most complex case involving continuity, different types tools. We need to determine—and ganize visual complexity through would show a perceivable random of symmetries, scaling, correlations, somehow measure—the organization symmetry mechanisms acting on pattern: to describe this requires harmony, etc. All of these have been of a complex structure. Specific design different scales. Moreover, our per- specifying each and every distinct invented and applied at some time and structural features organize design ceptive system is designed (evolved!) portion of the image. That’s a lot of in the past in creating traditional components, and distinguish ordered to recognize the above symmetries information. Organized complexity art, artifacts, and architecture. They from disordered forms. We can count automatically. Objects lacking such avoids informational overload. Any form an essential part of the human the organizing features, or estimate organizing mechanisms are per- image that has organized patterns, creative heritage. And they also cor- their number as either low or high. ceived as random, disordered, not regularity, or represents some cogni- respond directly to how complexity is Those tools include the following: stably put together. This impression tively graspable information needs organized in natural settings, includ- most often causes alarm. a far shorter informational descrip- ing in organisms. Since our percep- A. Linear continuity among different tion. (But be careful, since if every tive systems evolved to interpret our pieces: forms flow into their neigh- pixel on the screen is random, we natural surroundings and other life bors and do not break off abruptly. cannot distinguish it from its neigh- forms, we resonate with organized bors, and only see the overall screen complexity but are alarmed by dis- B. Different symmetries on the same as uniformly gray, which has zero organized complexity. scale: translational (moving along complexity). a single line); reflectional (mirror); The Organization of Complexity rotational; glide reflections (move Organizing complexity reduces the along some distance then reflect). raw amount of information that is The Kolmogorov-Chaitin complexity needed to specify an object or sys- (i.e., the length of its description) is C. Scaling symmetry: the same or tem. The human cognitive system a first step in measuring a system’s similar form repeats at a higher or is able to comprehend complexity complexity. To what extent existing lower magnification, which links two Figure 5. Scaling symmetry relates similar only if it’s organized in some way. complexity is organized still has to be or more scales together visually. shapes at different sizes. 19 Monotonous Repetition and of complexity defined on the large repeating blocks of social housing, ing, or a cluster of buildings sur- Informational Collapse scales: complexity could exist on the to the vertically-repeating stories rounding an urban space should pay smaller scale (the scale of a unit), of a rectangular glass skyscraper, to attention to human sensibilities to Symmetries in structures and designs which is repeated to generate the the repeating cookie-cutter houses spaces, circulation realms, pedestrian repeat portions that are “symmetric.” larger scale, but nothing intrinsic to in suburban sprawl, our environment movement, the physical fit to the hu- Translational symmetry repeats units the large scale. Worst of all is when gi- suffers from complexity deficit on man scale, etc. These design forces along a line; rotational symmetry ant structures monotonously repeat some levels, and complexity over- acting together on different scales repeats units after a rotation by some an empty module. Complexity that load on others. Consequently, the guarantee that the result will exhibit angle; reflectional symmetry uses the is most psychologically satisfying industrial large-scale has no intrinsic complexity on every distinct scale mirror image to complete the other exhibits information on each and complexity: any complexity (or not) of the structure, and this is what we half of the design; etc. Generating every scale. is contained in the repeating unit. find in traditional architecture and larger structures via symmetries is urban design, and also in the layout a useful tool for creating complex The twentieth century’s fascination Adaptive design responds to differ- of informal settlements. objects from smaller units. with industrial mass-production ent forces acting on many different celebrates a design complexity for scales; therefore, by definition, it is The industrialization of design Nevertheless, a careless use of sym- architectural and city form that incapable of generating monotonous does not permit such a multiplicity metries to generate larger-scale embodies monotonous repetition repetition. Designing a doorframe, a of scales, nor the differentiation forms leads to informational collapse: and informational collapse. From room, a house, an apartment build- of complexity on each scale. The when the information contained in industrial practice in fact suppresses the whole is no more than that con- the natural response to adaptive tained in the repeating unit used to design forces, in order to make a generate it5. Then, the information formal geometrical statement. Such of the whole collapses into that of mechanical typologies exhibiting the single unit. Say that a repeating informational collapse have become unit has information content X. Ac- standard in the twentieth century. cording to the Kolmogorov-Chaitin Consequently, students find this complexity, the description of the discussion disturbing because it whole would be “repeat X a number Figure 6. Monotonous repetition of a unit without any variation is subject to informational collapse. forces them to reconsider design of times in this direction”, which is no principles that were presented as more complex than the original unit. fundamental.
The phenomenon of “monotonous Symmetry Breaking: repetition” affects human percep- Variation within Symmetry tion responding to designs and structures in the built environment. How then do we build up a larger- Confronted with objects that repeat scale complex whole using repeating without variation, we feel that they individual units? The answer is again are boring, uninteresting, depressing, to be found in cultural artifacts and and even oppressive if large enough. Figure 7. Variation of a repeating unit prevents informational collapse and helps to stably define traditional methods of design. We 20 This is simply a reaction to the lack the larger scale. simply vary the repeating units suffi- ciently to distinguish them from each exhibit requisite variety: e.g., individ- ism. The encoding of the structural less pronounced, with surrogate other, but not enough so as to remove ualized Byzantine and Romanesque complexity had better be efficient; natural settings. Thus, a particular their basic similarity.6 That is, we capitals; imperfectly symmetrical otherwise the genetic blueprint could type of organized complexity pres- make small changes among units that Gothic façades; architectural ele- not be transmitted. We know that ent in our environment is essential are the same on a particular scale. ments repeated with variations; etc. patterns of organized complexity for our health. Use the convenience of repeating (rather than disorganized random the same unit, but then distinguish And symmetry breaking also makes patterns) are more efficiently trans- Three Factors Estimate units through variations on differ- sense from an informational point of mitted. Thus, complex blueprints the Degree of Organized ent scales. This is called “breaking view. One intuitively expects that a can be coded, but not if every single Complexity the large-scale symmetry,” since an large-scale complex whole will have molecule has to be independently otherwise perfect symmetry (trans- much more information content than specified. For this reason, we see the First, there is the raw information lational, rotational, reflectional, etc.) a single unit used to generate it: there same types of regularity and symme- content: how many things are hap- is no longer strictly valid, although should be a match between amount tries in living forms as are found in pening, such as internal differentia- it obviously still dominates. of complexity corresponding to the traditional art and artifacts (albeit in tions, number and variety of com- size of the system. By breaking the more sophisticated yet approximate ponents, contrasting elements, etc. Limited variation on a smaller or symmetry through the injection of versions in Nature). Elsewhere, I have termed this aspect larger scale (symmetry breaking) additional information on smaller of systems the “architectural temper- prevents informational collapse. If scales, there is indeed more infor- Discovered complexity is also cultur- a tu re .” 4, 8 Second, organization arises we break the repetition symmetry, mation contained in the large-scale ally transmitted, mimicking the ge- from symmetries and connections of then we require additional informa- system than was present in an iso- netic transmission of biological com- all types, and this other quality of a tion to specify the whole structure, lated unit. plexity. Patterns represent repeating coherent system is measured by the more than was necessary when per- groups of codified information. number of such organizing mecha- fect symmetry was present. It is still Complexity and Life: Non-visual patterns are recurring nisms. We can estimate whether a much more economical to build up Biophilic Patterns socio-geometrical solutions found system has a small or large number complex structures through combina- across different regions, climates, of internal symmetries that tie all its tions and ordering rather than to have Life is the transformation of en- and cultures. Traditional practices components together into an easily- an entirely random structure, since ergy into information. Organisms discovered invariant design solutions graspable whole. the approximate symmetry saves an developed a means of preserving for how human beings live better, enormous amount of information their discovered/evolved structure whose biological basis is now being This aspect of form I call “architectur- specifying the overall complexity. by means of genetic information. discovered in the new discipline of al harmony.” 4, 8 The simplest measure Otherwise, each life form would be Biophilia.7 Biophilia privileges an of organized complexity is to esti- Traditional artifacts from all over the accidental, extremely primitive, and environment rich in complex pat- mate both “architectural tempera- world such as pottery, carvings, tex- exist only briefly. Life as we know it, terns over plain industrial surfaces, ture” and “architectural harmony” on tiles, and oriental carpets show, upon with its continuity and evolutionary independently of style. a scale of 0 to 10, then multiply those closer inspection, that every repeat- mechanisms striving towards greater two numbers together. This gives a ing unit has been made slightly differ- complexity and systemic sophistica- Biophilic patterns have been shown number corresponding to how much ent in order to prevent informational tion, would not exist. to be clinically healing: exposure to complexity there is, and how well it is collapse. Vernacular architectures are the patterns of living forms helps ac- organized. A complex but disordered replete with approximate symmetries A lot of information needs to be speci- celerate post-operative recovery.7 The form will score low in this model. So and more formal architectures often fied when constructing a living organ- measured effect is noticeable, though will an empty, minimalist form. Only 21 structures with evident complexity It’s no accident that well-loved arti- any way, visually or structurally. A serves a stylistic agenda and does that is well organized will score high. facts and architectural interiors are complex whole in which the parts not help to understand a form’s com- Countless examples from historical made from natural materials such are unrelated would not hold to- plexity. and vernacular architectures all score as polished stone and wood, which gether. And this is just for the static high on this scale.4, 8 show fine-grained natural patterns. structure: disorganization is totally What interests us here is the de- Unlike industrial materials, these nonsensical in a dynamic system pendence of distinct scales upon Third, the degree of organized com- continue the scaling hierarchy down- that has to work through multiple one-another. We discussed above plexity increases as the number of wards into the microscopic scales. mechanisms. Therefore, the organiza- how larger-scale structures could distinct structural scales increase. Glass, steel, titanium, and concrete, tion of structural complexity is a pre- arise from combining smaller-scale This is yet another independent fac- in contradistinction, show no ordered requisite of all complex structures. units in a coherent manner. The gen- tor. It relates to scaling symmetry, microstructure. erating symmetries are determined which can act to make a form more It happened through historical ac- by adapting to the design forces. coherent only if there exists a suf- The “machine aesthetic” that came cident that architects in the late This is an essential mechanism for ficient number of scales. Therefore, to dominate design in the twentieth twentieth century began to celebrate building organized complexity that an additional question to ask is: century eliminates multiple scales disconnected forms, following an is valid across all scales. Formal de- how many different recurrent sizes in structures. The typical number earlier cue from fine artists who had sign could be useful for reducing are well defined in a structure?9 In of scales in a “designed” object or abandoned all attempts at “natural- randomness through ordering, but nature (both in biological and in- contemporary building tends to be looking” art. So, now we are used to should not be imposed (as was the animate forms), structure is clearly closer to two rather than the number seeing buildings without internal case during much of the twentieth defined on all scales, from the size ten for traditional structures and coherence, in which the structural century). The larger scales in a hier- of an object down to its microstruc- artifacts. The more natural subdivi- engineer uses a contortionist’s toolkit archy thus invent new information ture. We keep seeing more organized sion of a form into its components of tricks to make the design stand not present in the smaller units, so (not random) structure the more on a hierarchy of decreasing scales is up without revealing its structural that the structure shows emergent we magnify it. The more scales we avoided. Nevertheless, human beings system. This clever feat nevertheless properties. perceive, the higher the complexity. perceive the machine aesthetic as If, in addition, the distinct scales are unnatural, precisely because it lacks related by scaling symmetry, then the the hierarchy of scales common with form has an additional dimension of natural structures. Regardless of the organization. dominant aesthetic, which influences individual taste, our neurophysiol- For example, a house or two-storey ogy is tuned to recognize a natural building from before the twentieth scaling hierarchy.10 century will show up to ten differ- ent scales, as defined by its forms, Hierarchy of Structural Scales subdivisions, materials, construction components, etc. A traditional arti- There is a structural reason for why fact—whether a utilitarian tool or a complexity should be organized. In strictly ornamental object—will also random, disordered structures each exhibit up to 10 scales if we examine part is independent, and certainly Figure 8. LEFT: minimalist design exhibits only one scale. RIGHT: traditional artifact shows 6 obvi- 22 it up close with a magnifying glass. does not support the other parts in ous scales, with 3 more if examined more closely. At the same time, large-scale units by founding principles of modernism, which are objects that repeat similar yet there is no mention of them any- themselves cannot define a coherent but there is no way to deny it. patterns on increasing and decreas- where. My answer will surprise some. design. Adapting to forces acting ing scales. The idea here is to situ- Designers and architects have indeed on all scales (a necessity for natural How Can Architects Use ate scaling symmetry at the heart of developed an intuitive grasp of the forms as well as in traditional and Organized Complexity? design, but only in an approximate, fifteen properties, but only in order vernacular architectures), units have Fractals and Alexander’s adaptive manner. Introduce many to violate them. The reason is that to accommodate a variety of forces 15 Properties different scales in a structure—as innovation in design has for the past acting on scales both smaller and required to make it more adaptive many decades been judged by how far larger than themselves. This requires Ever since the early twentieth cen- to the users—and strive for coher- it deviates from and opposes natu- plasticity and adaptation of larger tury, the overwhelming influence ence across different scales. Practical ral order. Thus, anybody wishing to forms so as to create a supportive of industrialization and mass-pro- design tools using fractals can make distinguish their designs from nature framework on a smaller scale. Thus, duction (and its associated way of a design healthier for the user, since necessarily does the opposite of the adaptation necessarily generates thought) imposed changes on de- they generate biophilic patterns. 7, 11 fifteen properties, whose cumulative smaller scales. sign that marked world architecture. effect is organized complexity.14 This determining phenomenon of Another, related set of methods was The corollary is also true: ruling the architectural profession is best developed by Christopher Alexander Having worked with Alexander for out the smaller scales for stylistic understood from the point of view when he discovered what geometri- years, I have tried to relate his 15 or dogmatically ideological reasons of complexity. cal properties characterize organized properties to organizing concepts in guarantees that the forms can never complexity in all systems. He has mathematics and physics to get a bet- adapt to all the design forces of the If an architect is convinced to try and distilled a working toolkit into his ter grasp of their universal nature. An problem. You either adapt to the use organized complexity again in “Fifteen Fundamental Properties,” interested reader can follow those con- system’s needs, or ignore them to architecture, there are several handy which are essential features of both nections with my own “Three Laws of impose your own design idea. This tools available. One set of methods natural and man-made coherent Architecture.”13, 14 Those postulate the conclusion contradicts one of the comes from mathematical fractals, systems.12, 13 One property is scaling essential need for a scaling hierarchy, hierarchy; another is the need for how units couple through contrast, and contrast; yet another is the pres- how large-scale order is established ence of abundant local symmetries through symmetries and alignment. but the relative insignificance of an overall symmetry; etc. A designer All of these ideas—Alexander’s “fif- can use these either as tools to help teen properties,” my “three laws,” guide the project towards increasing biophilic patterns, scaling coming coherence; or as a check to see that from mathematical fractals, rules for competing design forces are properly the generation and organization of accommodated. complexity—are mutually-support- ing, complementary aspects of a new A student might well ask: where have and comprehensive design method. these fifteen morphological proper- New in that it differs from both the ties been all along for the past cen- early twentieth-century modern- Figure 9. In order to adapt to forces acting on all scales, large-scale units partially break themselves tury of architectural training? They ist and the late twentieth-century up and generate supportive smaller-scale components. seem too important to be ignored; postmodernist and deconstructivist 23 design typologies, yet not really new small scale, and hence from intimate When we instead see complexity im- tires us, because we try to find mean- since it relates strongly to traditional human experience. posed for reasons of fashion, having ing where none is present. There is design methods. Nevertheless, these nothing to do with the multiple design an additional danger with injected new design tools are not meant to re- Irrelevant and Possibly forces, something is not right. The random complexity, because it easily produce traditional buildings, but to Damaging Complexity built configuration will always be at creates disturbing imbalances. Our create new, innovative structures that odds with the normal forces of the experience of symmetries depends adapt to human use and sensibilities. Every design problem has to organize situation, which can never be satisfied. upon physiology: the vertical axis is competing forces acting on many dif- Form contradicts function. This much tied to our inner-ear mechanism, so Fractal patterns and cellular au- ferent scales: adapting the design to may be suspected from the homo- that leaning, unbalanced, or twist- tomata are capable of generating a them generates emergent solutions in- geneous forms of excessively formal ed buildings can generate nausea, new type of mathematical ornament. corporating a high degree of organized design. Some contemporary build- alarm, and physiological distress. Biophilic information is mimicked complexity. This complexity evolves ings have a more subtle contradiction using color, detail, variation (sym- from the process of adaptation. While because there is clearly complexity in Conclusion metry breaking), curves, and variety there is no unique end-result, there the built form, yet this complexity is of materials within adaptive design are only a relative handful of optimal just as arbitrary for function as in the Recent years have produced a re- rules. Lacking this range of scales in designs, which could however look very minimalist case. But now it’s deceptive markable development in under- organized complexity from 1 millime- different. They all have in common a because it “looks” complex. standing complexity, and in translat- ter–20 centimeters, even the more high degree of organized complexity ing results from mathematics and interesting buildings of the past few that accommodates structural integrity, Disorganized complexity tends to science into practical design tools. decades are disconnected from the activities, and sustainability of the form. be arbitrary, random, and willful. It Natural structure suggests the neces- sity for differentiation, followed by collective organization marked by a high degree of multiple symmetries. Architectural evidence reveals the principle of broken symmetry as a key feature of buildings that mimic living structure.
It’s of course up to the individual architect to decide whether to ap- ply these methods or not. Many stu- dents, teachers, and practitioners are unfortunately still tied to dictates of “style,” even as it is becoming in- creasingly obvious that such an ap- proach does not lead to adaptive, long-term sustainable architecture. Hopefully, the younger generation is becoming aware of the tremendous opportunities for new design think- ing made possible by this input from Figure 10. LEFT: disorganized complexity injected into a design for stylistic effect conflicts with the system’s forces. RIGHT: design that evolves from the sciences. 24 adapting to the system’s forces generates organized complexity. Image credits 10. Nikos Salingaros, “The Sensory Value of All line drawings are by the author. Ornament,” Chapter 4 of A Theory of Archi- tecture, Sustasis Press, 2006. Notes 11. Nikos Salingaros, “Fractal Art and Archi- (Further Reading from the tecture Reduce Physiological Stress,” Journal Author’s Books) of Biourbanism, Volume II, No. 2 (2012) pages 1. Michael Mehaffy & Nikos Salingaros, “Geo- 11-28. Reprinted as Chapter 26 of Unified metrical Fundamentalism”, Chapter 9 of A Architectural Theory, Sustasis Press, 2013. See Theory of Architecture, Sustasis Press, 2006. also Chapters 24 and 25.
2. Nikos Salingaros, “Kolmogorov-Chaitin 12. Nikos Salingaros, “Alexander’s Fifteen Complexity,” Meandering Through Mathemat- Fundamental Properties,” Chapter 19 of Uni- ics, September 2012. Reprinted as Chapter fied Architectural Theory, Sustasis Press, 2013. 9 of Unified Architectural Theory, Sustasis Press, 2013. 13. Nikos Salingaros, “Universal Morphological Rules,” Lecture 6 of Algorithmic Sustainable De- 3. Nikos Salingaros, “Documenting a Form sign: Twelve Lectures on Architecture, Sustasis Language and Estimating Its Complexity,” Press, 2010. Online video lecture
5. Nikos Salingaros, “Why Monotonous Rep- etition is Unsatisfying”, Meandering Through Mathematics, September 2011. Reprinted in the Cornell University Library Arxiv, Septem- ber 2011.
6. Nikos Salingaros, “Symmetries and the Value of Ornament,” Lecture 9 of Algorithmic Sustainable Design: Twelve Lectures on Ar- chitecture, Sustasis Press, 2010. Online video lecture
7. Nikos Salingaros, “Biophilia”, Chapters 16 & 17 of Unified Architectural Theory, Sustasis Press, 2013.
8. Nikos Salingaros, “Organized Complexity and a Model That Estimates Life in Archi- tecture”, Chapter 21 of Unified Architectural Theory, Sustasis Press, 2013.
9. Nikos Salingaros, “Hierarchical Coopera- tion in Architecture”, Chapter 3 of A Theory of Architecture, Sustasis Press, 2006. 25