Exploratory Science Museum of Unicamp, Corsi Hirano Architecture Office

The ornament has been an element in architectural design, since the pre-historical times (1). The concepts for ornamentation patterns were usually inspired by natural forms and applied to architecture to show the dominance of humans over nature (2). However, due to the industrialization and changes in culture during the beginning of the 20th century, ornament almost disappeared, mostly in architecture.

Ornament and Crime, a text first published in 1908 by Adolf Loos, greatly influenced architects' prejudice against ornament. Loos criticizes the exploitation of human labor in the production of ornament, the amount of time used to produce an object and how quickly ornamented objects became outdated (3). This criticism, combined with the fact that society demanded a fast reconstruction of the cities in Europe and the advances in the construction industry (metal structures, large glass panels), changed dramatically the role of ornament in Modern architecture (4). Loveridge and Strehlke explain that the main reason why the ornament disappeared was industrialized mass production:

“Ornament and Crime can certainly be seen as a crucial contribution in the architectural discussion about the exclusion of ornament. This modernist emphasis on unadorned form, combined with the upcoming international style and the replacement of craftsmanship by the rise of mass production yielded a systematic elimination of ornament” (5).

In the beginning of the 1980s, architecture was in the middle of a new movement, Post-modernism. Ornament and complexity, once put aside by modernist architects, were returning due to the establishment of new concepts in the natural sciences, mathematics and philosophy (6). Chaos Theory and Complexity Theory, which aroused in the 1970s (7), played a major role on the interest of architects in complexity. At the beginning this appropriation was a way to criticize Modernism, a will to change from purism, in which architects proposed buildings covered with ornaments and symbolic meanings (8).

Ornament in contemporary architecture emerges with a new meaning, as the result of the application of new methods and technologies in the design process. This technological shift allowed a new perception of ornament by architects. Picon describes the relation of ornament and technologies:

“The widespread return of ornament that can be observed today is actually inseparable from the massive diffusion of the computer in architectural profession that had started by the mid-1990s. […] It is possible to generate textures and patterns with previously unknown ease. Complex geometries have become accessible to anyone who knows how to use a computer. In this regard, 3D printers, laser cutters, mills and routers have simplified the realization of intricate ornamental elements” (9).

Since the 1980s, with the introduction of CAD systems, which are accessible and easy to be used, and the development of scripting languages (10), architects have been generating more complex shapes. First the production of designs was limited by the available construction techniques, but recently the digital fabrication techniques are allowing architects to produce a new type of aesthetics.

Architectural elements can now be partially fabricated by programmable machines. However, the contemporary complexity is not simply a reproduction or copy of a handmade design. The new design and fabrication methods allow the production of ornamented surfaces with new types of textures and patterns that could never be made by hand. Nowadays, complex forms – which may be also seen as ornaments by some – may serve a purpose, such as stiffening a surface or creating a progressive shade. This does not necessarily imply higher costs, but oftentimes results in better performance. The recent shift in the means of production, with the new flexible manufacturing machines and the possibility of mass-customization at competitive costs, inverts the whole logic according to which any unnecessary twist in the material, any overdone detail that looks frivolous, is immoral because it must be the result of work exploitation.

Fractals as ornaments

A typical generative system which can be easily automated by recursive function is fractal geometry. The application of fractal geometry in architectural design has been explored in the last decades by many researchers, such as Yessios (11), Garcia (12), Bovill (13), Lorenz (14), Moisset (15), Edïz and Çagdas (16), Haggard, Cooper and Gyovai (17), Ostwald (18), Salingaros (19), Joye (20), Harris (21) and Sedrez and Pereira (22), to name a few.

Many are the reasons to use fractal geometry in a design, for instance, to comprehend different scales, to generate recursive patterns or self-similar patterns, to understand the building as an urban element (whole and parts), to generate complexity or structure. Other reasons include geometrical application such as the generation of shapes with similar value of area but with extremely different values for the border (perimeter). Furthermore, the human mind appreciates fractals, as it can be observed throughout the history of architecture and urbanism. Another motivation is the close relation of fractal geometry and computational generative process, since the computer is essential to generate fractals.

The discussion about the theory and practice of using fractals in architecture is new and important as a consequence of the introduction of two new variables in the design process: computational tools and digital fabrication (23). We believe that the use of fractal geometry must go further than simple convenience, as Salingaros explains: “There is no reason why contemporary architects should not use fractals in their designs, but those should be more than just motifs” (24).

The interest in complexity and in computational design and the desire to actually realize complex shapes with the aid of digital fabrication has brought ornament back to the architectural discourse. But the meaning of this new ornament that results from complexity is different from Adolf Loos' ornament ideas. This study aims at showing evidence of this new direction in architecture, looking at this reality specifically through the point of view of fractals, as an example of a generative design method. Finally, it will discuss the technical aspects and the new challenges that it poses to architectural education.

This research starts with a literature review of texts recently published by the most prominent authors on complexity in architecture and the use of digital resources in contemporary architecture. Next, in order to understand the return of the ornament in architecture, nine architects and one engineer were interviewed, in which their personal experience on research and practice bring light to the discussion. The questions are divided into four categories: fractals, computational design, digital fabrication, and new ornament. The interviewed people are authors of theoretical study on the topic, as well as practitioners whose recent work incorporates fractals, complexity, algorithmic design, digital fabrication or all the above: Michael Ostwald, Inés Moisset, James Harris, Daniel Corsi, Caroline Bos, Pieter Schreurs, Milos Dimcic, Florian Gauss, Michael Hansmeyer.

Complexity and ornament

Architects became interested in complexity in the past decades (25), especially on how to design and solve the problems that arise from it. It is difficult to define the term “complexity” in architecture, an approach that borrows concepts from Complexity Theory; however, its scope certainly involves the design of complex shapes. Jencks states:

“In this process [, of working with complexity,] quality emerges spontaneously as self-organisation, meaning, value, openness, fractal patterns, attractor formations and (often) increasing complexity (a greater degree of freedom)” (26).

Jencks puts together several concepts in an attempt to understand complexity in post-modern architecture. Recently the design of complex shapes usually comes with singular patterns on the surfaces, which is a result of the fabrication process possibilities (27).

New ornament or contemporary ornament is a term that has started being used in architecture in the last few years; one of the most important references is the work of Picon. His book is a discussion about the evolution of ornament in architecture and the changes of its conception more recently, especially on how architects put together ornamented designs that have a function on the building.

Gleiter explains that the new ornament would not be possible to be built without algorithmic procedures. It is important to notice that this assumption changes both the design process and the resulting architecture aesthetics:

“Today the potential for the new ornament and its double ontological definition lies in the “interactive linkage” between design and construction procedures that are no longer determined mechanically but are calculated algorithmically by computer. The digital-constructional and the anthropological sides are thus interlaced via algorithmic, digital conceptualization of the design” (28).

A strong linkage is observed between the aesthetics and new technologies. Gleiter reaffirms the role of computation for the design process and the contemporary architecture’s production:

“With computational design, mass customisation and scripting software, the ornaments have become separate from paper, walls or electronic screens and now penetrate the material and structure of things. […] Under the influence of digital processes, material, structure and ornament enter into a new interrelation” (29).

Complexity suggests fundamental directions for architecture: the ornamented building envelope, the discussion about the ornament function and its meaning. The first direction is a characteristic of contemporary architecture: buildings with no windows generate an envelope that becomes an opportunity for architects to apply patterns on the surfaces (30). The second direction is that ornament can be more than aesthetic decoration and can have a functional role in the building (31). Patterns may have many functions, such as creating perforations for the air to pass through, giving structure to an otherwise crinkled surface, or simply disguising seams if the material used is not large enough to cover the whole façade. The third is a discussion in architecture theory about the meaning of the building and how the ornament might be able to give symbolic value to architecture (32).

A final direction would be to think about ornament as a human psychological necessity. Carl Jung studied the effects of complex images on humans, the symbols, or what he calls archetypes, interpretations of the brain. This appreciation for complexity “can act as creative or destructive forces in our mind: creative when they inspire new ideas, destructive when these same ideas stiffen into conscious prejudices that inhibit further discoveries” (33). In other words, decorative patterns, when correctly used in the built space, can be relaxing and help organizing one’s complex mind. While the modern “detailless” aesthetics is widespread, the “complexity” aesthetics produce a dilemma for contemporary architects, who are trying to constantly escape from the symbology of its own work. It is important to consider that humans have been “marking” architecture surfaces for a long time in a way that conscious or unconscious aspects of perceptions of reality are always present. Fractals can provide a strong aesthetic result from its iterations, and this must be considered when working with this geometry.

Considering these aspects, we can go to some key points on the interviews. Initially, we perceive that architects are excited with the possibilities of the new ornament, however, still in an experimental level. Caroline Bos, who is co-founder and director of UNStudio, explains one of their designs, in which the ornament assumes an important function in the design: “For instance, the acoustic paneling in our project in Graz is an example of that, which is really a sort of experimentation of new ornament. […] Because it is possible, we want to explore and experiment” (34).

Music Theatre, UNStudio

Michael Hansmeyer is creating and printing complex shapes using additive technologies as sand-printing. When asked about the reappearance of ornament in architecture, Hansmeyer ponders about the mass fabrication, one of the modernists premise: “People are naturally curious to discover and explore new possibilities. But also because mass fabrication has been very homogenizing, and many people appreciate heterogeneity, diversity, etc.” (35). Milos Dimcic director of Programming Architecture is responsible for the solution of complex shaped buildings using advanced coding. Dimcic believes that ornament should return, and more than that, he already works on a solution for ornamentation of surfaces: “I think that ornament should come back. That means more work for us, because ornament is something that you can program and parameterize. I actually did a plug-in for ornament” (36).

When it comes to fractal geometry, Harris has a vision about fractals generating ornament, he considers:

“Ornament can be obtained as the end product of a number of iterations. This ornament’s value is reflected on its ability to reflect the whole in its structure. […] In a fractal sense the ornament has to be a part of the fractal model and if developed in this manner could provide a tangible methodology of experiencing the whole structure by the user. I think this provides richness to the user’s experience” (37).

Harris generates fractal architecture using scripting; his designs usually are composed of very ornamented surfaces. Despite the fact that his experiments are not built, still is an example of how architects could appropriate fractal geometry.

Fractal façade #1, James Harris

Another example of fractals used as ornament in architecture is the project of the architecture office Corsi Hirano. Corsi explains his idea of ornament for the Exploratory Science Museum of Unicamp, a building in which the façade panels are designed based on fractal geometry:

“A surface involving the building doesn’t function as mere ornament, rather it means something, but also will perform a key technical role. The idea of constructive elements, which constitute a building, perform a series of roles, one of these roles is what the building means, represents, expresses. But also in this case [, the science museum,] what the building communicates in its design by its form” (38).

Exploratory Science Museum of Unicamp, Corsi Hirano Architecture Office

We can recall the discussion of Picon about the meaning of ornament in architecture, in which ornamented surfaces are expressing social connotations (39). The ornament is not only carrying out a function as Moussavi and Kubo affirm, but has a symbolic meaning, something to express, like Jung explains. Bos also talks about the ornamental surfaces of other UNStudio designs:

“What we tried with the ceramics tridimensional tile in Qatar [railstation (Figure 4)] is very much the example of it. It is very double, it is sort of a play with the logo, with the logo of Qatar rail, making it tridimensional in sort of a flower. It really gives these vaults a tactile experience; I think it is fantastic that we can really bring the ornament. Again it requires very skillful handing” (40).

Qatar Railstation, UNStudio

ONL is another Dutch architecture office with very complex solutions for architecture. In their case, the parametric and algorithmic design is very sophisticated in terms of the control of the fabrication process. Pieter Schreurs, architect at ONL, talks about how ornament should be designed in his opinion:

“As I would see it, it shouldn’t become additive. When it becomes an integrated strategy then actually I think it becomes really aesthetically pleasing, the detail becomes the ornament. […] The detail or the design becomes the ornament” (41).

It is interesting to know that the architect Sullivan had a very similar opinion, almost at the same time of Loos’ studies: “It must be manifest that an ornamental design will be more beautiful if it seems a part of the surface or substance that receives it than if it looks “stuck on,” so to speak” (42).

Schreurs expresses how they understand ornament at ONL in the design of the A2 Cockpit for instance, which can be considered a very contemporary and computational approach:

“That also is very different in the way we approach to as other offices do, then the ornament often becomes an overlay or addition. Of course, digital techniques always allow you to do that, but then it is merely functional as a façade layer or a dress. The full integration of that, the actual detail becomes the ornament itself and you get a full integrated aesthetics as well in terms of structure skin” (43).

A2 Cockpit, ONL

Schreurs questions what some architects are doing: using technology to create superficial compositions detached from the actual building itself, or just producing complexity because it is possible.

Fractals

As expressed before, the fractals are being applied to architectural design since the 1980s, but a true definition of “fractal architecture” is not consensus. Albeit architects are using fractals to generate or justify projects, there is still confusion or unfamiliarity with its concepts. For instance, Hansmeyer does not believe his work is self-similar, a true characteristic of fractal geometry, although it is possible to identify words like L-system appearing in his design descriptions. Hansmeyer states:

“Many people claim self-similarity as a key element of a fractal. None of the designs [I made] exhibit any self-similarity, so at least according to that definition they aren’t fractals. What they have in common with fractals is the possibility of multiple scales, with fluid transitions between them” (44).

L-System using three leaves as system, Michael Hansmeyer

Hansmeyer explains that he uses subdivision processes derivate of the Catmull-Clark and Doo-Sabin algorithms, which are recursive methods to smooth surfaces. It is important to state: 1. it is not possible to build a fractal per se, because of its infinite recursiveness, however fractals can inspire a design with a limited number of iterations; 2. self-similarity is a characteristic of fractal geometry, but not all fractals are similar in each and every scale; 3. a fractal algorithm uses substitutive, additive or subtractive rules combined with recursion and a infinite number of iterations. The iterations are limited in the case of architecture design. These definitions might help to explain what could be considered fractal architecture.

Architect Guto Requena states he never used fractals in any design before. He gives an answer about his thoughts of fractal geometry, which is a disarray of what actually is surface triangulation subdivision. Architects and computational designers use the triangulation of a surface as a method to produce curved surfaces, because the three vertices of the triangle always generate a plane, therefore flat panels which are cheaper to be produced. Requena comments about the new aesthetics: “The main question is, we are entering this moment of digital age in which everything became fractal, and things tend to have this aesthetics of lapidary and the triangle” (45).

These confusing and sometimes contradictory approaches on fractals and architecture can be a result of lost of interest by the fractal geometry by architects in the 1990s (46). Alternatively the increasing number of recent “fractal architecture” projects could be explained by the introduction of computational thinking in architecture schools, for instance. Salingaros affirms: “computer-generated fractals are now common in our everyday environment because of our pervasive digital technology” (47).

When asked about the increase number of architecture with fractals compositions in the last years, Ostwald agrees, but makes an interesting remark: “While the number of seemingly fractalesque designs being produced each year has grown, and that might be a sign of heightened levels of interest, the way in which these designs use geometry has not changed” (48). However the possible solutions to produce complexity have changed, so one must pay attention to not repeat same approaches. On one hand the use of fractals by architects is growing, but on the other hand the resulting designs are still very limited; what is missing to generate a design with better quality?

Computation has an important role on the learning of fractal geometry by architects, and the generation of complex shapes. Both Inés Moisset and James Harris experimented with fractals using programming in their careers. Moisset explains why she approached fractals:

“I was interested in the generative process and started to experiment in the computer with the help of my brothers who know how to program. We scripted a small software in which we included variables such as dimensions, angles and colors. In the beginning it was only two-dimensional drawing” (49).

Moisset also uses the fractals in her classes by working the design in different scales. She talks about her design teaching method: “The comprehension of the complexity of the site is part of the formalization of architecture itself. The fractals allow [the designer] to see the landscape and the architecture as part of the same system” (50).

Scales superposition, Inés Moisset

Harris also learned how to program fractals in a very basic software:

“When I first started experimenting with fractal geometry I utilized a DOS based program that had a relatively easy user interface that did not require any programming. Eventually the operating systems moved past using DOS making that program obsolete. During this time I started using 3D Max (although it was called something else then) and learned that it had a scripting language called Maxscript. I taught myself how to use it and have used it ever since to generate fractal structures” (51).

In both cases the architects taught themselves how to program fractals. In Brazil also architects face difficulties imposed by the limited knowledge of fractals and computational design. Corsi explains their design for the Exploratory Science Museum, in which they had the intention to create their own fractal instead of just copying a fractal like the Koch’s curve:

“This would be a literal application of von Koch [curve], so how do we create our own interpretation over it? An architectonic interpretation. Then we started a second step which was from the diagram [of Koch’s curve] to draw a new geometry that is consistent with the same criteria of scale, modulation, generation” (52).

The proposed design by the architects is not based on the Koch’s curve, but on the Minkowski’s curve using a single iteration, then they select points to create three different squares and reproduce this pattern in four different scales. His explanation to what they designed lacks concepts of generative systems and fractal geometry. They miss the opportunity to explore computational solutions, since the design was made by hand.

Generative design rules, Corsi Hirano

Another example of how architects can take advantage of fractal is the Grand Egyptian Museum, project of the architects Heneghan Peng. The project is near the great pyramids, so the architects choose the Sierpinski triangle as a façade pattern. Florian Gauss talks about his participation in the design of the façade of the project. Gauss explains the concept and how fractals are a good structural solution for this case:

“This is a simple fractal, the Sierpinski Sieve which is of course a very nice and rational principle, creates a reciprocal grid adaptable to any triangle. It is quite a strong simple approach. I wouldn’t say this is a very complex shape, is not really complex. It is rigorous and generates interesting visual form. Structurally you can say it is sensible, it is not something which is optimized; however it has a fairly useable internal organization for a structure. One beam spanning on the other one. Probably not the most efficient one, if you do it out of flat steel. However it is always a trade-off, it needs to be a balance between your design inspirations, the methods which you have available for fabrication, of course structural and other impacts which are relative to your aspirations” (53).

Grand Egyptian Museum, Heneghan Peng

Because Gauss was much involved in the detail of the façade and not so much in the design process, his answers are more technical on how to design complexity. One of the challenges of design using fractals is the fabrication and construction, because fractals generative system creates small parts every iteration. So if the use of fractals is for structural purposes this might need an attention to details, production and costs. Gauss has a clear opinion about the use of fractal geometry in architectural design, it might generate many small pieces which can be a problem to produce and to assemble, beside of costs.

Fabrication of complexity

In this section we explore some alternatives for the fabrication of complexity which can be generated with fractals or other generative systems. Digital fabrication and computational design are key concepts for the fabrication of complex shapes. CNC machines, 3D printers or even robotic arms are on the top of the list of technologies for architecture, although still need a lot of research on practical uses. Schreurs has a design process entirely digital; he explains ONL’s view: “We use digital tools and scripting to inform our design and allow for a rich complexity and design freedom, while integrating all boundary conditions” (54). The only way of creating such complex buildings, within the time-frame and restricted budget, is dominating programming language, and in the case of ONL, they also master the fabrication process. Schreurs states:

“All our designs are about file-to-factory production, so we integrate the thinking about production process from the very first stages of design. I would say that is essential, if you create more complex shapes and different geometries. […] We had to set up a complete chain from the design to the production facility to be able to do that. So we directly generate the information for CNC cutting machines to produce all the steel lengths and nodes” (55).

Only in recent years sophisticated machines started to be incorporated in the architecture schools, giving an opportunity for young architects to know the machineries and to take advantage of the fabrication process. It is not smart to design complex structures using traditional methods and hand-drawing, automation must be part of the tools. At ONL, the industrialization of the fabrication process is one of the most prominent, and they even control the CNC machines instead of using a person to control it (56).

The conflicts between the work done by a human and the attempts to fabricate digitally can also be observed at the Heydar Aliyev Cultural Center, a design from Zaha Hadid. Gauss explains the fabrication phase: “The surface was not rationalized. The surface was giving. It was not optimized. It was set by the architects; also the seams of the panels were given” (57). The surface definition caused a complication for the design of the substructure to support the façade panels, although the structure of nodes and arcs was generated automatically by a scripting.

Hansmeyer, who is dedicating a lot of research to 3D printing large scale elements, talks about the new options in the fabrication process:

“It was challenging to find a method to produce such a geometrically complex form without any loss of detail. […] Sand-printing technology was previously used mostly for disposable casting parts. We're now using it to create durable architectural elements. We thus had to do research on the material's structural strength, and on its surface properties. Pieces weighing 11 tons in total had to be assembled and adjoined at the precision of millimeters” (58).

In this case the 3D printer works by spraying a binder over a layer of sand, like the common powder 3D printer works. To 3D print architecture or parts of a building is absolutely new. The 3D Print Canal House in Amsterdam, which is being printed with a large scale 3D printer using recycled plastics, is an example of this technology. And the Chinese 3D Print house, in this case using a large scale 3D printer of concrete. In both cases the extrusion of material prints the object layer by layer.

In Brazil there are some difficulties such as the lack of large scale equipment (3D printers), the high costs of printing and the uneven diffusion of small scale equipment (59). This might be connected with the low demand for new technologies, where the construction industry is heavily based on handwork. On the other hand we have a set of equipment which is not being used yet in architecture. Silva states:

“We believe that the difficulty to incorporate digital fabrication in the production of Brazilian architecture is not anymore a result of a possible absence of such resources in this country. It is fundamental to highlight that these [resources] are available and being used by the aeronautics’ and automobile’s national industries. It is important to stress that digital fabrication systems are already available, for instance, in structural and frame metal factories of this country. We believe that the reasons why digital fabrication is not being incorporated in the design and construction of buildings in Brazil, in this moment, essentially are: the misinformation more than the allegedly technological unavailability, also the lack of formal education and training in the context of the teaching of architectural design and the lack of connections between the architecture schools and the construction industry” (60).

A similar statement was done by Kolarevic:

“Architects might be ignorant of digital fabrication, and I don´t really blame them. But I think you would be surprised with how much of this technology is actually accessible almost universally. I´ve discovered that in various parts of the US and Europe the folks who are involved in metal sheet fabrication – aluminum, steel, any kind of metal – they do have CNC capabilities. I bet that if you were to go around Campinas you would find a lot of metal shops and all of them can have some CNC capacity” (61).

Here lies an opportunity for architecture professors in Brazil; to make use of the industrial technology available connecting the design studio and the production.

Conclusion: the new ornament and architectural education

The prejudice against ornament is difficult to overcome, especially because during Modernism it was reasonable to argue against the exploitation of human labor and high costs of the production of complexity. Also, a lot of cities needed to be rebuilt after the World Wars, and during these times there were other priorities. After a long period of being avoided or even disregarded by architects, ornament slowly became an important element in design again. The new digital technologies to design and fabricate architecture are allowing new methods to produce complexity, which is regarded as a new type of ornament. However, with all these transformations, few changes on architect’s education were made in order to provide knowledge on how to design with new technologies. In many schools CAAD is still considered simply a drafting tool.

Programming abilities and fabrication techniques could be included in architectural education to help a new generation of architects rethink the limits of architecture. Bos agrees with this idea: “you also have to learn all these tools [digital fabrication]. We see for instance, Germans in the 90’s, a lot of them did that. And it worked really well for them. They are very good. And they also have a very thorough training in, as you said, geometry and construction and so on” (62).

The new ornament in architecture is an important element of the contemporary building, and an approach in education can connect technology, design, construction and aesthetics. We believe that architects must acquire a set of skills which includes programming and fabrication technologies. This knowledge is important to produce coherent results, and to avoid problems in the design fabrication. Programming, for example, is the way Moisset and Harris found to explore complex shapes, they taught themselves how to program and the concepts of fractal geometry.

Harris states: “I think it is fundamental for any architect wishing to explore generative forms to understand and utilize programming” (63). Hansmeyer  also believes that computation is the key element for complex architecture: “Yet architects have always been quick to adopt and explore any new tools available to them. And computation is arguably one of the most interesting tools of our times” (64). It seems, by the conversation with Schreurs (65) and Dimcic (66), that the architects must master one or more programming languages, it is the right way to overcome the challenges of digital fabrication.

More than thirty years after Mandelbrot wrote his book about fractals, it is conceivable that this knowledge have been diffused among architects (67). This new wave of “fractal architecture” might be associated to the use of new technologies for the design, such as shape grammars and generative systems. Also, the use of scripting to generation of shapes recently became focus of a large number of architects, which includes concepts such as recursion and fractals.

The new technologies available to create architecture could help designers use fractals, for example, in a more inventive way. Although Ostwald considers:

“My feeling is that the rise of parametric modeling generally undermined the potential for a deeper application of fractal form in architecture. There are exceptions, but any review of the examples provided in the parametric design literature shows that these are in the minority” (68).

On one hand parametric modeling is becoming very popular amongst architects with the new and easy to use programming languages, on the other hand we believe that computational design has increased the interest of architects in fractals and recursive algorithms. However, the motivation to use fractals in architecture and the association of them with more sustainable design, as expressed by Ostwald, can only be truly productive if more information about fractal geometry is available to architects, and it only makes sense if one has a clear objective for using it.

notes

1
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2
JONES, O. The grammar of ornament (op. cit.).

3
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4
PICON, A. Ornament: the politics of architecture and subjectivity. AD Primer, London, Wiley, 2013; TRILLING, J. The language of ornament (op. cit.).

5
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6
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8
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9
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10
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11
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12
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14
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15
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19
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26
JENCKS, C. Nonlinear architecture (op. cit.).

27
BURRY, J., BURRY, M. The new mathematics of architecture. New York, Thames and Hudson, 2010; PICON, A. Digital Culture in Architecture. Basel, Birkhäuser Architecture, 2010; PICON, A. Ornament: the politics of architecture and subjectivity (op. cit.); MOUSSAVI F., KUBO, M. The function of ornament. Barcelona, Actar, 2006.

28
GLEITER, J. H. Ornament: the battleground theory. Zona #4, Ornament Return of the repressed. Abitare, n. 494, 2009.

29
GLEITER, J. H. Synopsis for the conference. Ornament Today, Bolzano, 2009.

30
LEE, S., HOLZHEU, S. Building envelope as surface. In: LEE, S. Aesthetics of sustainable architecture. Rotterdam, 010 Publishers, 2011; MOUSSAVI F., KUBO, M. The function of ornament (op. cit.)

31
MOUSSAVI F., KUBO, M. The function of ornament (op. cit.)

32
PICON, A. Ornament: the politics of architecture and subjectivity (op. cit.).

33
JUNG, Carl G. Man and his symbols. New York, Anchor Press, 1988, p. 304.

34
BOS, Caroline. The design methods of UNStudio [July 2015], Interviewer: Maycon Sedrez, São Paulo, Recorded at Blue Tree Hotel, 2015. Not published.

35
HANSMEYER, M. Fabricating complex shapes [March 2015], Interviewer: Maycon Sedrez, Kyoto/Eindhoven, 2015. Not published.

36
CELANI, Gabriela. Learning from other people's mistakes. Interview with Milos Dimcic. Entrevista, São Paulo, year 16, n. 064.05, Vitruvius, dec. 2015 <www.vitruvius.com.br/revistas/read/entrevista/16.064/5824/en>.

37
HARRIS, J. Programming fractals and architecture [February 2015], Interviewer: Maycon Sedrez. New York/Campinas, 2015. Not published.

38
CORSI, D. Fractals in the architecture of the Unicamps’s Science Museum [May 2014], Interviewer: Maycon Sedrez, São Paulo, Recorded at Corsi Hirano’s office, 2014. Not published. Our translation.

39
PICON, A. Ornament: the politics of architecture and subjectivity (op. cit.).

40
BOS, Caroline. The design methods of UNStudio (op. cit.). Our emphasis.

41
SEDREZ, Maycon. One building, one detail. Interview with the architect Pieter Schreurs, ONL. Entrevista, São Paulo, year 16, n. 064.04, Vitruvius, nov. 2015 <www.vitruvius.com.br/revistas/read/entrevista/16.064/5821/en_US>.

42
SULLIVAN, L. H. Ornament in architecture. In: Kindergarten chats and others writings, 1918. First Published: The engineering magazine, vol. 3, n. 5, 1892, 633-644.

43
SCHREURS, P. One building, one detail (op. cit).

44
HANSMEYER, M. Fabricating complex shapes (op. cit.).

45
REQUENA, G. Computational design and digital fabrication in Brazil [October 2014], Interviewer: Maycon Sedrez, São Paulo, 2014. Not published. Our translation.

46
OSTWALD, M. J. “Fractal architecture”: late twentieth century connections between architecture and fractal geometry. Nexus Network Journal, 2001, vol. 3, n. 1.

47
SALINGAROS, N. A. Fractal art and architecture reduce physiological stress (op. cit.).

48
OSTWALD, M. J. Issues about Fractal Architecture [July 2014], Interviewer: Maycon Sedrez, Newcastle/Campinas, 2014. Not Published.

49
MOISSET, I. E. Fractals and architecture [December 2014], Interviewer: Maycon Seddrez, Córdoba/Campinas, 2014. Not published. Our translation.

50
Idem, ibidem, our translation.

51
HARRIS, J. Programming fractals and architecture (op. cit.).

52
CORSI, D. Fractals in the architecture of the Unicamps’s Science Museum (op. cit.). Our translation

53
SEDREZ, Maycon. Designing and fabricating complexity. Interview with Florian Gauss. Entrevista, São Paulo, year 17, n. 065.01, Vitruvius, jan. 2016 <www.vitruvius.com.br/revistas/read/entrevista/17.065/5878/en>.

54
SCHREURS, P. One building, one detail (op. cit).

55
Idem, ibidem.

56
Idem, ibidem.

57
SEDREZ, Maycon. Designing and fabricating complexity (op. cit.).

58
HANSMEYER, M. Fabricating complex shapes (op. cit.).

59
REQUENA, G. Computational design and digital fabrication in Brazil (op. cit.).

60
SILVA, N. F., BRIDGES, A. H., LIMA, E. M., MORAIS, H. R. A., JUNIOR, F. A S. A indústria da construção civil está pronta para a fabricação digital e a customização em massa? Uma pesquisa sobre um caso brasileiro. In: SIGraDI, 2009, São Paulo, 430-432. Our translation.

61
KOLAREVIC, B. Chat with Branko Kolarevic [December 2013], Interviewer: Gabriela Celani, Campinas, 2016, Parc, v. 4, n. 2, Campinas, p. 38-44.

62
BOS, Caroline. The design methods of UNStudio (op. cit.). Our emphasis.

63
HARRIS, J. Programming fractals and architecture (op. cit.).

64
HANSMEYER, M. Fabricating complex shapes (op. cit.).

65
SCHREURS, P. One building, one detail (op. cit).

66
CELANI, Gabriela. Learning from other people's mistakes. Interview with Milos Dimcic (op. cit.).

67
MANDELBROT, B. B. The fractal geometry of nature. New York, W. H. Freeman, 1983.

68
OSTWALD, M. J. Issues about Fractal Architecture (op. cit).

about the authors

Maycon Sedrez is a Bachelor in Architecture and Urban Design from the University of Blumenau (2002), a Master in Architecture and Urbanism from the Federal University of Santa Catarina (2009) and a PhD in Architecture, Technology and the City from the University of Campinas (2016). In 2015, he did a research internship at the Eindhoven University of Technology – Netherlands – funded by the Science Without Borders scholarship. He is a researcher at the Institute for Sustainable Urbanism in Braunschweig. The author thanks CNPq, the Brazilian National Council for Scientific and Technological Development (grant 203267/2014-1) and the São Paulo Research Foundation (grant 2014/13572-5).

Gabriela Celani is a Bachelor (1989) and a Master (2007) in Architecture and Urban Design from the University of São Paulo (USP), and a PhD (2002) in Architecture: Design & Computation from the Massachusetts Institute of Technology (MIT). She is currently an Associate Professor at the School of Civil Engineering, Architecture and Urban Design at the University of Campinas (Unicamp), Brazil. She is the founder of LAPAC, the Laboratory of Automation and Prototyping for Architecture and Construction. Her work focuses on generative design, rapid prototyping, digital fabrication, 3D digitation and automation of the architectural design process. She is vice president of institutional relations of SIGRADI, the Iberoamerican Society for Digital Graphics, and belongs to the scientific committees of various CAAD conferences, such as eCAADe, CAADRIA and DCC, and journals such as IJAC, Automation in Construction, AIEDAM and Design Studies.