Science for Designers: Scaling and Fractals
With apologies to real estate agents, we’d like to say that the three most important factors in design are scale, scale, and scale. One reason is that many of the worst environmental design blunders of the 20th century have been mistakes of scale — especially our failures to come to terms with the linked nature of scales, ranging from small to large. The cumulative consequence of these failures is that the scales of the built environment have become highly fragmented, and (for reasons we detail here) this is not a good thing. Can we correct this shortcoming?
Most designers know something about “fractals,” those beautiful patterns that mathematicians like Benoît Mandelbrot have described in precise structural detail. In essence, fractals are patterns of elements that are “self-similar” at different scales. They repeat a similar geometric pattern in many different sizes. We see fractal patterns almost everywhere in nature: in the graceful repetition at different scales of the fronds of ferns, or the branching patterns of veins, or the more random-appearing (but repetitive at different scales) patterns of clouds or coastlines.
Figure 1. The beautiful structure of fractals, patterns that are repeated and sometimes rotated or otherwise transformed at different scales. Left, a natural example of ice crystals (Photo: Schnobby@wikimediacommons). Right, a computer-generated fractal coral reef that, helped by color and shading effects, could be mistaken for a natural scene (Photo: Prokofiev@wikimediacommons).
We can also reproduce fractal patterns in a computer, often with strangely beautiful results. Some graphic designers use fractal methods to reproduce very realistic-looking landscapes and other natural phenomena. These, too, seem to trigger something in our perception. We somehow recognize them as being “natural” and connect with them emotionally.
We seem to be wired to “read” fractals in our environment, probably for two key reasons. One is that biological structures are largely fractal in their patterning, and we are innately interested in other biological structures because they might be food, or predators, or other people, or just a key component of the biologically supportive environment.
The other reason goes deeper into geometry. When we look at a long vista, structures that repeat (trees for example), repeat at smaller apparent scales when they are farther away. This fractal information helps us read distances and depth in the environment. Doing so gives us an effortless understanding of the geometrical order of our environment. We’re aware of this only as a pleasurable sense and not, coincidentally, as an important survival need, from an evolutionary point of view.
Fractal structures also give us other kinds of useful information, like complex relationships among environmental elements. The order of an essential but non-graspable structure, like an ecosystem, is more intelligible to us because we can detect the symmetrical fractal patterns of its plants and animals — another important evolutionary need. In modern times we have a greater need for urban environments to be legible to us, and there is evidence that we do this by reading fractal relationships in buildings and details (after all, we have evolved with this sense).
From an evolutionary point of view, it’s evident that we perceive these relationships because they are supremely useful to us. They help us understand the structure of choices that our environments present, and how the different alternatives might offer us different benefits. It is an innate skill.
Importantly, fractal urban structures typically provide multiple combinations of benefits that work in synergy. And our pleasurable perception of fractals is probably related to this too. For example, the branching, layered, fractal-like paths we can take within a city help us carry out many different tasks simultaneously. People moving along such paths for the purpose of higher-level information exchange (going to a business meeting) can thus carry out lower-level information exchange (having informal “spillover” exchanges with other people, or perceiving pleasurable scenes). The time required for higher-level exchange is therefore used more effectively, and the net effect is a synergy of activities that often translate into economic, social, and other benefits.
Figure 2. The fractal pattern of self-organizing urbanism. On the left is a simple fractal pattern called a “Cantor Gasket” (Drawing by Nikos Salingaros). On the right is a much more complex and irregular pattern with recognizably similar fractal properties, a traditional urban neighborhood in Baghdad, Iraq. Notice the similar patterning at different scales of bordering spaces and alternating patterns of indoor-outdoor space (Photo: G. Eric and Edith Matson Photograph Collection, Library of Congress).
This “fractal loading” means that each high-level exchange carries with it simultaneous exchanges on many smaller levels. An ensemble of exchanges on different scales is supported by a physical infrastructure that permits mixed information exchanges, but does not let other competing exchanges squeeze out the weaker or lower-level exchanges.
Fractal loading is important at all scales. But it becomes especially important at the scale of a human being. For instance at the scale of a region there are not that many structural choices that are relevant to an individual going about his daily activities. But as we approach the scale of a human being (in fact, a group of scales ranging from 1mm to 10m), more and more structural choices begin to crowd into the picture, so that by the time we are at that scale, the environment often presents a rich set of structural choices that a person might make on a daily, hourly, and even instantaneous basis.
At this scale, the fractal loading of our environment vastly expands the structural options, and builds synergies between them. If I am in a well-connected, fractal-loaded spot at this human scale, I can read the newspaper, I can talk to a friend, I can say hello to a passerby, or I can run one errand or more. And I can easily connect these activities into a web of choices.
This is very likely a key reason that, within urban systems, well-structured pedestrian networks are so important. As our work has shown, there is reason to believe that there are important synergies of economics, resource conservation, psychological health, and other benefits, which are only provided by pedestrian networks that have this key property of fractal loading.
Figure 3. The pedestrian networks of medieval Rome have a fractal structure, extending into the buildings and even the rich ornamental details of the buildings themselves. These “place networks” offer pedestrians a dense and overlapping set of choices of movement, views, and other enriching experiences (Drawings/Photos: Michael Mehaffy).
Fractal loading is one example of a “scaling phenomenon” in complex network structures like cities, and an active area of urban research. Another related phenomenon is that as the scale of a structure like a network increases, the phenomena that happen at a smaller scale often do not increase at a linear (proportional) rate. Often they are “super-linear” (they increase more than proportionally) or “sub-linear” (they increase less than proportionally).
These phenomena, such as economic growth and resource use per person, are very important to us. If we get more economic growth per person at a larger scale, or less resource use per person, then our quality of life can improve. This may be one important reason why people are attracted to large cities. Dense settlements really do offer more quality of life for proportionally less cost than sprawl does. And by understanding scaling, we can deal better with challenges like resource depletion and climate change.
But notice that this phenomenon occurs as a result of the specific network structure of the city, and its “metabolic” interactions and synergies (such as fractal loading). A collection of entirely separate individuals all “doing their own thing” would likely not benefit from such scaling phenomena. It is in the multi-scale interactions that these phenomena, and the synergetic benefits they bring, come about.
Interestingly, this characteristic of fractal loading tends to emerge spontaneously within urban systems that are allowed to self-organize within the natural processes of human culture — that is, within traditional urban environments. We all recognize this intuitively in the fractal-rich environments of popular tourist destinations like Bruges or Edinburgh. (And we recognize its absence in engineered environments that are decidedly not tourist destinations, like London’s Docklands, or Paris’ La Defense.)
Figure 4. On the left is the highly fractal structure of urbanism in Bruges, Belgium. On the right, a much more sparse, fractal-free environment in the modern suburbs of Bruges — which is also far less walkable, and has other negative impacts (Photos: Michael Mehaffy).
What does this tell us? Are fractal urban structures just nostalgic remnants of an obsolete pre-modern era? Or do they offer crucial lessons for designers today?
While there are certainly ideologically dogmatic theories of style and history that support the nostalgic remnant proposition, they are unsupported by real scientific evidence. And, critically, there is important evidence for the crucial lessons for today’s designers proposition. To see what these lessons might be, we will discuss how fractal structures are formed in nature — and, it appears, in human nature — and why they might be such important attributes of a well-functioning environment.
Fractals have two related characteristics: They show complexity at every magnification. Their edges and interfaces are not smooth, but are either crinkled or perforated.
Figure 5. Some essential properties of fractals. (a) Fractal loading uses a basic scale as a carrier for other successively smaller mechanisms and structures. Far from being monofunctional and simplistic, every structure becomes richly complex and carries information on several distinct scales. (b) Longitudinal compression forms a “folded” fractal, creating a crinkled line that then generates crinkles on its crinkles. This interface can catalyze urban interactions, mimicking the non-smooth surface of a chemical catalyst. (c) Longitudinal tension and breaking along the entire line form a “perforated” fractal, here shown at its first stage. This is a natural mechanism for defining an urban colonnade and any semi-permeable urban boundary, such as a row of bollards that protect pedestrian from vehicular traffic (Drawings by Nikos Salingaros).
Fractal patterns tend to form naturally for one simple reason: there is a “generative process” that creates the geometric pattern, and it does so at more than one scale. For example, in a blooming flower, the genetic code that creates the pattern does so in a time sequence, while the previously generated patterns grow larger.
In a computer-generated fractal, the generative process is called an “algorithm,” a bit of code that generates the pattern from a complex interaction with what has been generated previously. In a city the generative processes are carried out by people doing what people do in making cities. They articulate spaces with boundaries that are shared to varying degrees. They create spaces that have degrees of publicness, somewhere along the spectrum ranging from public to private, from the most public streets and squares to the most private bedrooms and baths.
The boundaries of living spaces are not simple structures either, but complex membrane-like structures offering their own set of structural choices, either to maximize privacy (by closing a curtain) or publicness (by opening a door). These boundaries are wonderfully complex structures in themselves and self-organize into larger patterns (doors or windows that become shared types over time, and neighborhoods that develop characteristic interface patterns of porches or colonnades).
How are the different scales linked? Just as biological structures and computer algorithms spontaneously repeat their geometric patterns at different scales, so do we, unless we’re forced to do otherwise either by legislation or by ideology. Individuals might make small repetitions of a pattern (a rectangular room shape) while groups might make larger versions of the same pattern (a courtyard) and larger groups might make a still larger one (an urban plaza).
But as with biological and computer structures, the story does not end at any particular scale. The boundary of a room is perforated with smaller structures like rectangular doors and windows. The boundary of larger spaces might be perforated with colonnades (we are talking about living spaces and not the dead spaces characteristic of post-war architecture and urbanism).
These repetitive perforations at smaller scales — the fractal loading that results from the characteristic “generative algorithm” of fractal structure — will often continue on down to the scales of detail and ornament. Why is this? It seems likely that we, the users, making our way through these places find such complex environments (complex in a very precisely ordered sense) easier to comprehend, more intelligible, more usefully organized, and more beautiful. We are very good at reading the multiple scales of these “place networks”.
But there is a serious problem. If we are not users, but designers educated in our industrial/artistic culture, we might have another agenda: to impose another kind of order on the built environment. And that agenda might come from a very different set of criteria than the environmental experience of humans.
Such is indeed the case. To put it simply, our current methods of making cities are over-reliant on economies of repetition and scale, which do offer narrow advantages but are also extremely limited, and from a human perspective, very crude and destructive. Natural systems never use those strategies in isolation, but are always combined with economies of differentiation and adaptation. Surprisingly, we haven’t really figured out how to employ these in our current strategies (though many people are working on this problem, and our own work takes up this challenge).
Choosing to work with a severe technological limitation, modernist designers argued that a more sophisticated approach was to strip down buildings into “minimalist” compositions, much easier and cheaper to produce under the crude industrial processes of the early 20th century. It was the compositions of these elementary “Platonic” solids that were most beautiful, postulated architects like Le Corbusier, because they were “pure” expressions of form. The old Gothic cathedrals, with their fractal tracery, were “not very beautiful,” he said infamously. Nor were the lively streets that he despised! Indeed, Corb and other designers made a strong ideological case (still persuasive today) that the old ornamented designs were bourgeois, contemptible, even (in the famous words of Adolf Loos) “a crime”.
In this ideologically driven design movement, we have come to accept the incorrect idea that fractals are somehow primitive, whereas smooth, undifferentiated “Platonic” forms are “modern” and sophisticated. Ironically, the opposite is the case: The most advanced theories of today’s science are all about complexity, differentiation, networks, and fractals — a dramatic contrast with the straight, smooth industrial geometries of early modernism.
Recognizing this, many architects and urban designers are speaking in terms of fractals, scaling laws, and “morphogenetic design.” But the question remains: Are these individuals really engaging such principles to create human-adaptive structure? Or are they only using them to create attention-getting aesthetic schemes, tacked onto what is essentially the same failing industrial model of design? These questions are at the heart of the debate on the future of the built environment.
What, then, are the lessons to be drawn? Fractal structure is not just an aesthetic gimmick. It is an important characteristic of sustainable human environments. And this structure does not arise from the well-meaning top-down schemes of old-mode art-designers, but from those with a skilled application of processes of self-organization, as part of a new way of thinking about what it is to design.
And yet, we designers have been exceedingly stubborn in taking on this lesson. Under a misguided theory of environmental structure that confuses simplicity with order, we have been stripping away the critical connected scales and fractal relationships within our environment. We have replaced a world of richly connected urbanism with a disordered geography of artfully packaged, catastrophically failing art-products.
More posts from Michael and Nikos -
Science for Designers: The Transformation of Wholes
Science for Designers: The Meaning of Complexity
Science for Designers: Intelligence and the Information Environment
Frontiers of Design Science: Computational Irreducibility
Frontiers of Design Science: The Network City
Frontiers of Design Science: Biophilia
Frontiers of Design Science: Evidence-based Design
Frontiers of Design Science: Self Organization
The Radical Technology of Christopher Alexender
The Sustainable Technology of Christopher Alexander
The Pattern Technology of Christopher Alexander
The Living Technology of Christopher Alexander
Michael Mehaffy is an urbanist and critical thinker in complexity and the built environment. He is a practicing planner and builder, and is known for his many projects as well as his writings. He has been a close associate of the architect and software pioneer Christopher Alexander. Currently he is a Sir David Anderson Fellow at the University of Strathclyde in Glasgow, a Visiting Faculty Associate at Arizona State University; a Research Associate with the Center for Environmental Structure, Chris Alexander’s research center founded in 1967; and a strategic consultant on international projects, currently in Europe, North America and South America.
Nikos A. Salingaros is a mathematician and polymath known for his work on urban theory, architectural theory, complexity theory, and design philosophy. He has been a close collaborator of the architect and computer software pioneer Christopher Alexander. Salingaros published substantive research on Algebras, Mathematical Physics, Electromagnetic Fields, and Thermonuclear Fusion before turning his attention to Architecture and Urbanism. He still is Professor of Mathematics at the University of Texas at San Antonioand is also on the Architecture faculties of universities in Italy, Mexico, and The Netherlands.
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Wow, talk about naive. How can anyone who understands architecture talk about Le Corbusier as if all he had to offer were straight smooth surfaces? That’s extremely revealing. The way he developed his simple set of rules and the way those simple rules were implemented to achieve highly complex designs is in fact the essence of fractal logic. Yet, shockingly these authors aren’t able to perceive it. I’m not sure if that’s because they’re ignorant when it comes to architecture or simply because they have New Urbanist biases that prevent them from really understanding their subject matter.
But whatever the case, if they can’t understand Le Corbusier, then I can’t see how they’re fit to say much about Modernism or architecture in general. Whether or not a “space” becomes a healthy “place” for humans to live out their daily lives depends on a whole host of factors. Sometimes out of scale places work. Sometimes places at scale fail miserably. And in the end, the grandfather of fractal logic in architecture (Bucky Fuller) ultimately failed to realize buildings that were humane. There is no magic bullet.
The naivety in suggesting that fractals are such a magic bullet harkens back to the worst aspects of Modernism - i.e. the naivety in thinking that there’s some magic secret essence that once unearthed can guarantee success in placemaking. Most architects have evolved past that limited way of thinking. Unfortunately the authors here haven’t. But that’s the way it is with many New Urbanists. They cloak their traditionalism in a lot of fancy talk, but in the end it’s really just an aesthetic fear of modernity and a dishonest attempt to corral society into returning to failed outdated ways of life that are largely paternalistic in nature. Some urban spaces work for some people. But not everyone wants to or could live in Manhattan. And not everyone wants to or could live the type of rural life that Thomas Jefferson talked about.
I agree that fractals can be a very compelling way to generate various types of geometric logic. I also believe they can create great urban, suburban, and exurban spaces. But the way the authors denigrate Modernism reveals that their intentions aren’t honest.
Much of Modernism is rooted in the types of logic they’re discussing here. And much of the New Urbanism that they support (but don’t mention in their article) does not. Ultimately it’s not the logic they care about, it’s the aesthetic and the politics behind the logic. And that’s what I find disturbing - the lack of honesty and sincerity masquerading behind this series on science. Science can be used to legitimize a lot of wrongheaded neo-traditionalist ideas - if we let those who would use it for such ends get away with it.
Comment by Alice — May 28, 2012, @ 9:45 pm
Reply to Alice:
“The way [Le Corbusier] developed his simple set of rules and the way those simple rules were implemented to achieve highly complex designs is in fact the essence of fractal logic.”
I would beg to differ, in that Le Corbusier did not understand fractals, or any other mathematics for that matter. Yet this comment sheds light beyond leading a defense of Corbu. Whenever Michael and I propose what we believe is a useful design tool, inevitably some person reacts with polemics and rather nasty personal attacks. We seem to have touched a nerve.
And since when is belonging to the CNU a punishable offense? This is not the first response to our essays in this forum that accuses us of terrible things simply because we are associated with New Urbanism. The Annual Conference CNU 20 was just held in West Palm Beach — openly — it’s not a secret organization.
“If they can’t understand Le Corbusier, then I can’t see how they’re fit to say much about Modernism or architecture in general.”
The problem is, I suspect, that we understand Corbu only too well, and have published our conclusions elsewhere. But here is not the place to argue about Corbu or any other individual architect. We simply wish to provide tools for young designers, and for all those who wish to create a more humanly-adapted environment.
Applications of the Golden Mean to Architecture
The End of the Modern World
and especially our chapter 9 “Geometrical Fundamentalism” in A Theory of Architecture
With best wishes,
Nikos
Comment by Nikos Salingaros — May 29, 2012, @ 9:27 am
I am an urban planner. And, I think that your opening thought about scale is right on target. Bull’s eye.
In my planning blog, I have been attempting to deconstruct human settlements and figure out what they need to include in order for them to be optimal habitats for human beings.
I had not thought about fractals…but, it makes sense, and I am going to look into this further.
Thanks for a really thought-provoking article!
Comment by Libby — May 29, 2012, @ 11:29 am
If this wasn’t the place to argue about Corbusier, then you shouldn’t have used him as an example of the problem.
Feel free to delete that entire part of your text, and then you can lecture people about whether it’s appropriate to discuss him. I’ll wait for you to delete it.
If you type in “Corbusier and fractals” at Google, you can find quite a few people who see such logic in his methodology and in his geometry. But beyond that, his uses a logic of scaling (the main topic in your article and the reason you look to fractals) that always ties his projects to the human being. Corbusier was probably the absolute worst figure in Modernism you could have chosen to try and prove your point.
If you can honestly say that you’ve visited La Tourette in person and didn’t see fractal logic and supreme examples of a humanizing attention to scale and detail at every single turn, then again - you simply don’t have the capability to analyze Corbusier, and therefore any other type of architecture - in my opinion.
If you can’t get Corbusier right, then you’re missing a fundamental sense of what good contemporary architecture is.
And that might explain why you’re a New Urbanist.
And no, of course it’s not a secret that you’re a New Urbanist. It’s just fascinating that you never bring it up unless you get called out on it.
And most people reading Metropolis would know that it’s because you would undermine your ‘wolf in sheep’s clothing’ attempts to get people to embrace traditionalism if they knew where you were really coming from.
Comment by Alice — May 29, 2012, @ 4:57 pm
“Le Corbusier did not understand … mathematics for that matter.” - Nikos Salingaros
LOL
Wow. Just wow. Good luck with that one pal.
Good lord…
Comment by Alice — May 29, 2012, @ 5:10 pm
The author’s confusion about “smooth surfaces” is also pretty revealing. To architects, the discussion seems so anti-intellectual, but so be it. Glass, steel, concrete, etc. - they all have their own properties when it comes to detail. In glass we have the fact that the color, opacity, and reflective qualities are always changing throughout the day. This in itself is its own form of detail. Good architects perceive that and use it, while laymen and architectural dilettantes overlook it - they haven’t exercised their “architectural muscles” well enough to perceive these kinds of alternate or subtle ways of perceiving detail. Concrete, steel, wood, etc. - all these materials reveal details at increasing levels of scale, if used properly and if analyzed thoughtfully. The decision to care about those details or not care about them is an arbitrary decision made by the individual. But Modernists shouldn’t really take New Urbanists seriously just because they value one form of detail (they might call it “ornament”) over another and/or are incapable of perceiving other kinds of detail. In the end, the author’s problem is more a socio-political fetish and an aesthetic hangup than it is a sincere understanding of detail and scale. Unfortunately, they don’t seem to have the capacity to recognize that shortcoming much less understand why it’s present.
Comment by Alice — May 29, 2012, @ 5:38 pm
Or compare the interior of a Gothic cathedral with Corbu’s church in Firminy. Without the “smooth” surfaces that would be cluttered up in a Gothic cathedral with ornament (and even a renaissance cathedral where light is more of a factor), the incredible light effects that occur via the pinpoint openings wouldn’t be possible in Corub’s church. And that would be a crime against architecture. In the end, the authors really just don’t understand scale, light, materiality, time and space. They only understand their socio-political stance and the fraudulent justifications they come up with to buttress it. That’s why they’re New Urbanists.
Comment by Alice — May 29, 2012, @ 6:56 pm
There is an informal essay at http://www3.amherst.edu/~rloldershaw entitled “Nature Adores Self-Similarity”. It is paper #14 in the “Selected Papers” section.
In the essay I identify about 80 examples of fractal self-similarity that commonly occur throughout nature - from atomic scales to galactic scales.
Clearly fractal organization is ubiquitous in nature because it is the most efficient and unified way to construct a universe.
In terms of efficiency, durability, resilience, and beauty, I doubt that we could improve on nature’s elegance in our functional and practical designs.
Robert L. Oldershaw
Discrete Scale Relativity
Fractal Cosmology
Comment by Robert L. Oldershaw — May 29, 2012, @ 9:44 pm
Comment to Alice:
Dear Alice,
I find your arguments very similar to many recent revisionist apologias for Le Corbusier — tellingly, by architects and not by mathematicians or physicists like Dr. Salingaros. Unfortunately, I fear you are seeing only what you want to see, while Le Corbusier’s mathematically primitive (or “fundamentalist”) ideas are very clearly on the record. (To be fair, the man was certainly not trained as a mathematician, as Dr. Salingaros was.)
See for example Le Corbusier’s very clear primitivist statement in “Towards a New Architecture,” p. 121:
“Gothic architecture is not, fundamentally, based on spheres, cones and cylinders. Only the nave is an expression of a simple form, but of a complex geometry of the second order (intersecting arches). It is for that reason that a cathedral is not very beautiful and that we search in it for compensations of a subjective kind outside plastic art. A cathedral interests us as the ingenious solution of a difficult problem, but a problem of which the postulates have been badly stated because they do not proceed from the great primary forms.”
Needless to say, this is the antithesis of modern fractal theory.
Personally I think we architects must break the spell of our thinking, and scholars from other disciplines, like Dr. Salingaros, can help us to do that — IF we will suspend our preconceptions for a moment (e.g.”new urbanism is a single style,” “tradition is all one thing,” etc etc…). What are we clinging to, really, but old and possibly outmoded design ideologies?
Regards,
Michael Mehaffy
Co-author
Comment by Michael Mehaffy — May 31, 2012, @ 8:40 pm
Michael, fractals are not the kind of complex forms that can serve architects in the way that mathematicians hope. They are self similar structures, not complex adaptive systems. No gothic cathedral ever accomplished the complexity and sublime wonder that occurs in the Firminy church under certain light conditions. I have my own problems with the naivety of Modernist men and their confidence in their own theories. That said, I have a lot less of a problem with their hubris than I do the hubris and paternalistic intentions of those who built the cathedrals. We’ve learned a lot since Le Corbusier, but the simplistic portrayal of his logic and his work in your text above completely fails the test from an architectural perspective. If you want to talk about mathematical systems in architecture, there are plenty of dimensional systems to think about, and fractal geometry is only one of them. Topological dimensioning and the work of Neil Denari is actually far more relevant to contemporary circumstances than even fractal systems, given M-Theory, etc. You can go after Le Corbusier for certain things, but what you cannot do is dumb down the discussion of his work by talking about “smooth straight” surfaces. And you can’t misrepresent his understanding of scale and detail and attention to human proportion and its relationship to architecture. Nobody who goes to La Tourette can pretend with any sincerity to make those mistakes. Nobody who goes to Ronchamp or Firminy can pretend that his work with light and form isn’t far more complex and far more sophisticated and effective than even the most incredible gothic cathedral. That’s just not a debate you’re going to be able to do much with in architecture. Architects don’t need to “break the spell of our thinking.” We’re all well aware of fractals, and topology, and Euclid, and all of the many issues revolving around the dimensional systems we might choose to best compliment whatever situation we might be dealing with architecturally - as is done in mathematics. But you and your partner are making the same arrogant mistake that I will agree to criticize Le Corbusier in making. You need to stop thinking you’re the only one who’s got an appropriate model for “a way forward.” Many many architects from Marcus Novak to Neil Denari (and most everyone at Sci-Arc or the AA) are well aware of the topics you’re discussing, and their work is about 10 steps further along than you give them credit for. As any mathematician who’s going to be honest about these issues will tell you, whether one chooses fractals, or Euclid, or topology is largely a matter of convenience and perception about the design problem at hand. Trying to cloak New Urbanist paternalism in science is misleading, but you show your hand in your insistence that one branch of dimensional mathematics somehow negates the in many ways unmatched achievements of Corbu in terms of integrating all the aspects of architecture (not just scale), including especially light. People who can’t fully see and appreciate those achievements for what they are really don’t have a valid context within which to situate their proposals about architecture going forward.
Comment by Alice — June 1, 2012, @ 1:09 pm
If we have learned anything from Modernism’s failures ( there were many successes) : mistrust Heros and Manifestos. We live in a “both and” world; not an “either or” one. It’s a complex and contradictory world where we can learn from everything and everyone. In architecture and urbanism, one can never “turn the proverbial page”.
Comment by Daniel — June 2, 2012, @ 11:05 am
The other important point is that gothic architecture is not fractal. It just has a lot of sculptural details at about the size of the human hand, so to the authors it seems complex in a similar way to a coastline or a snowflake, etc. But that’s just an aesthetic conceit, a dumbing down of these issues. You can’t take a small portion of a cathedral either in plan, section, elevation, or in detail and blow it up to have the same form at a larger scale or at the scale of the whole building. The authors are guilty of an aesthetic contrivance that fundamentally misleads and misunderstands what fractals are - which in itself is quite shocking. I think one would find that many rectangular, smooth surfaced buildings built with rectangular, smooth surfaced bricks are technically far more fractal in their geometry - if they were honest about it. But that’s not their intent: honesty. Their intent is to mislead, to get people to mistake a contrived level of detail at a certain scale for some sort of “mysterious” sounding mathematical contrivance, like a fractal. It’s a very low level mistake - the kind of thing an architecture student would probably be called on in a jury review of their work at a good school. In the end, the author’s only goal is to get people to accept New Urbanist principles in the guise of contemporary thought. But it’s a lie.
Comment by Alice — June 2, 2012, @ 1:35 pm
PS, the only places where fractal logic actually permeates society from the level of art, craft, hairstyling, to architecture and even urban design is Africa, and parts of India. Western culture and the cities and projects the author discuss are Euclidean geometries, not fractal geometries. Any fractal structures they find in “classical” Western architecture are either aesthetic contrivances on their part or isolated incidents that can’t be said to be common to any particular “classical” style or logic of antiquity. Another fundamental error. They can read Ron Eglash, etc.
Comment by Alice — June 2, 2012, @ 2:02 pm
@Alice;
“Trying to cloak New Urbanist paternalism in science is misleading, but you show your hand in your insistence that one branch of dimensional mathematics somehow negates the in many ways unmatched achievements of Corbu in terms of integrating all the aspects of architecture (not just scale), including especially light.”
Why do then contemporary architects fail in even implementing the most basic pattern of light from two sides in every room: http://www.patternlanguage.com/apl/aplsample/apl159/apl159.htm
By the way, what has paternalism to do with small streets, as the New Urbanists promote: http://www.smallstreets.org/
Is the paternalistic part that the children will be allowed to play in the streets, not to be stored away in kindergartens like this one (the drawing of a huge new kindergarten to be built in Brønnøysund, Norway, to gather all the kids in a new super-kindergarten): http://www.helgeland-arbeiderblad.no/nyheter/article6018842.ece
Personally I would prefer not to put away my daughter in a kindergarten like this, obviously inspired by Corbu, as I would fear for her mental health. Do I feel like this because I’m a paternalistic tyrant?
By the way, Alexander is not a New Urbanist, as he has advanced far beyond them in groundbreaking science. But hopefully they’ll catch up with him someday!
Comment by Øyvind Holmstad — June 3, 2012, @ 2:57 am
Mehaffy and Salingaros. Thank you for your thoughtful article.
Chapter 9 in A Theory of Architecture is really helpful!
Comment by Ngoc — June 4, 2012, @ 12:20 am
Oyvind Holmstad, cherry picking a few friendly-sounding items isn’t honest, but you knew that. There are plenty of contemporary architects who reject New Urbanism but promote walkable, green, inclusive cities. In fact, the recent dustup at Harvard that saw many New Urbanists leave the school was largely a fight between the old socially conservative New Urbanist crowd and more contemporary architects who wanted to push green strategies for our cities as the focus for urban design.
New Urbanist developments here in America are usually exclusive environments, like gated communities. Political protests aren’t allowed, for example. One can’t walk dogs over a certain size. Counter-culture behavior is barred. New Urbanism is by definition not a healthy environment for modern people, because it isn’t inclusive - it isn’t real urbanism. It’s urbanism for those that can afford it and who agree to behave according to conservative social customs. New Urbanism is really just a cloak for social conservatives, corporations and the super-rich to insulate and isolate communities so that our culture becomes more and more debased and bigoted. That’s why pretending it’s about architecture isn’t really even an honest debate. It’s really about socio-political issues.
One kindergarten from Norway isn’t a particularly good argument. There are plenty of terrible kindergartens, schools, etc. that are built according to New Urbanist principles, and plenty of great ones built according to more contemporary inclusive principles.
Personally, that kindergarten you link to doesn’t look so bad to me. And it looks more like the work of BIG than Corbu. But hey, feel free to send your kid to a New Urbanist development school… if you want them to grow up to be a Tea Party conservative. Personally, I consider that child abuse, but it’s your kid.
Comment by Alice — June 4, 2012, @ 8:11 pm
As entertaining as the spectacular polemics might be, they all miss a crucial point. Corbu was a product of his times as much New Urbanism is a product of ours. Call it zeitgeist, call it metis, call it what you want. Times change, people change, everything changes. This isn’t an argument over the virtues of platonic solids versus fractals as design templates as much as it is a reflection of a cultural morass that’s barely evolved past the level of a grade school playground. It’s a cartoon. You might as well be debating the superiority of batman versus the green power ranger. I don’t mean to disparage anyone’s good intentions, here. The sad thing, of course for some of us at least, is not that we eventually grow out of such things but we lose the sense of the fantastic and fun.
Comment by Randy — June 6, 2012, @ 8:51 pm
Alice,
I’m a card-carrying New Urbanist. I’m also a friend and colleague of Nikos and Michael. I do not understand why you have made an interesting essay by Nikos and Michael into an ideological war between New Urbanism and Modernism. They do not mention New Urbanism in their essay, you will not find fractals in the New Urban Charter, and you can find many who are both Modernists and New Urbanists.
There is much more Christopher Alexander influence in the essay than New Urbanism, and another of their friends here in the comments says, “Alexander is not a New Urbanist, as he has advanced far beyond them in groundbreaking science. But hopefully they’ll catch up with him someday!” That doesn’t sound very New Urban to me.
John
Comment by John Massengale — June 7, 2012, @ 3:52 pm
PS: For clarity, I wanted to separate this from the fatwa going on, but I was interested in your comment “the recent dustup at Harvard that saw many New Urbanists leave the school” - whom do you have in mind?
Comment by John Massengale — June 7, 2012, @ 3:56 pm
Randy, The debate over how our cities will be designed is hardly a grade school playground issue. It’s one of the most important things we face going forward. As in politics, there are always those who disparage the very debate, because ultimately they seek to destroy the issue and let corrupted market forced dictate our way forward (here I’m referring to the Tea Party types who don’t believe government has any relevant function whatsoever, for good or ill). No, the debate is important. And people who lack the courage to dignify the debate with anything but low brow anti-intellectualism have embraced the kind of nihilism we see from contractors and failed architecture students. Jump in and have the courage to be part of the conversation. But don’t make the mistake of thinking that your anti-intellectual cowardice is somehow masked by your condescension. Architects are all too familiar with those defensive and self-conscious methods of negating important issues simply because some people haven’t done the responsible hard work of learning about them.
Comment by Alice — June 7, 2012, @ 7:27 pm
PS, New Urbanism isn’t really a sign of our times. It’s a sign of the early 80’s. It’s just that the conservatives who hide behind New Urbanism haven’t really come up with any new ideas since. So they keep trying to rebrand their old ideas under the mantra of “fractals” or whatever they can think of. It’s a lot like the Republican party in that respect. Most architects and urban designers keep evolving. Conservatives just repackage their ideas like toothpaste commercials.
Comment by Alice — June 7, 2012, @ 7:34 pm
“Watersheds can be considered a type of real-world network that is characterized by self-repeating or fractal-like patterns. Fractals are geometric patterns that possess the same proportions on different scales. Rivers and glaciers cut through the planet’s surface, leaving behind landscapes that may appear random or haphazard, but are actually quite precise. Whereas such patterns have been frequently ignored in designing or altering man-made landscapes, there is now interest in emulating them to create more sustainable and eco-compatible designs.” – D.L. Marrin, Ph.D
See: http://www.energybulletin.net/stories/2011-08-11/hydromimicry-water-model-technology-and-management
Comment by Øyvind Holmstad — June 9, 2012, @ 5:07 am
A follow-up to Alice
Dear Alice,
You obviously have very strong ideological feelings about this, and may I just respectfully suggest to you that “there are more things in heaven and earth than are dreamt of in our philosophies.” If you are trying to make that point to me, the point is taken, I assure you. So perhaps we can both step beyond the shibboleths and the tropes, and have an actual discussion?
The trouble may be that so much of what passes for architectural discourse nowadays is the former dressed up as the latter. (In that sense, may I suggest it is we who are the radicals, upsetting the conservative status quo.) The straw-man arguments you offer about New Urbanism are a case in point. If you could suspend those, you might find that you and I agree about some criticisms of New Urbanism, and perhaps disagree strongly about others. (For example, the critique of CIAM doctrine as the profoundly unecological genesis of sprawl, or the critique of most avant-garde architecture as theoretically disguised product veneer over an essentially reactionary modernist paradigm.) So I wonder if any such dispassionate discourse is really possible. If so I would welcome it; I think we (and more importantly, the world we serve) badly need it just now.
Just one follow-up point on the specifics: you say “Michael, fractals are not the kind of complex forms that can serve architects in the way that mathematicians hope. They are self similar structures, not complex adaptive systems.” I fear this betrays an ignorance of the workings of complex adaptive systems, which do produce self-similar structures on a regular basis (indeed, the universe is full of them, which is why we can use fractal algorithms to simulate natural scenes so convincingly).
The bigger point for me is that the built environment has gradually devolved into a kind of planetary wreckage, from both an ecological and a human point of view, and we in the design world bear a considerable responsibility for this state of affairs. In that context, all our professional infighting seems very much beside the point. I think we had better cut through the elaborate theoretical apologias and get to some reliable truths about what is going on, and what is to be done. This is what science, in the best sense of the word, is all about. And I think it’s what science as a model of open (and open-source) inquiry offers to us in the design world, at a time we badly need it.
Kind Regards,
Michael Mehaffy
Comment by Michael Mehaffy — June 9, 2012, @ 11:56 am
Second reply to Alice:
“We’ve learned a lot since Le Corbusier”; yes, I know that WE (those of us working towards developing and implementing a humanly adapted buit environment) have, but evidently many architects have not. Pity. And I suspect it’s because they don’t want to. Hero worship is a hard habit to break.
The old and distasteful diversion: introduce irrelevant political themes to keep architecture students from breaking out of their mental straitjacket. Use plenty of polemics and personal attacks to fire up fanaticism, all the better to avoid rational analysis. It very often works.
Glass is a supercooled liquid without any fractal structure. Steel and concrete are essentially plastic, and depend upon being cast or worked upon for their form. But the vast majority of architectural uses nowadays (and for the past several decades) avoids ordered substructure because it is forbidden.
“Any fractal structures they find in ‘classical’ Western architecture are either aesthetic contrivances on their part or isolated incidents … The other important point is that gothic architecture is not fractal.” Sorry, but the literature contains rigorous mathematical analyses demonstrating that both Gothic and Classical architectural form languages are intrinsically fractal.
Best regards,
Nikos
Comment by Nikos Salingaros — June 11, 2012, @ 11:02 am
You aren’t the radicals. If you’re a New Urbanist or partnered with a New Urbanist, you have all the most powerful conservatives behind you. So no, I don’t think New Urbanists are radicals, quite the opposite. These are not strawman arguments. Your article’s misunderstanding and misreading of architecture and mathematics along New Urbanist principles was your proposition, not mine. I don’t think you want dispassionate discourse, your article’s misunderstanding of Corbusier is impassioned. You just want someone who agrees with you and for anyone else with passion to be quiet. Complex adaptive systems can in some limited cases involve fractals, but fractals aren’t inherently complex adaptive systems. You’ve confused yourself. Architects need to be freer than that, just like mathematicians are, and as I discussed in my text. The built environment is what it is because the powerful people (developers, politicians, etc) who are now behind New Urbanism have the kinds of values that prevent real progress. Again, professional debate isn’t beside the point. Stop trying to negate the discussion just because you want powerful people to dictate it in the absence of debate amongst people like us. Investigating science is fine. Misinterpreting it to underpin the essential “truths” in conservative sociopolitics (New Urbanism) is immoral, and intellectually dishonest.
Comment by Alice — June 11, 2012, @ 1:54 pm
Øyvind Holmstad, Yes, many natural forms have fractal characteristics, but they aren’t pure fractals. There’s a level of aesthetic contrivance that people apply to natural forms that remind them of fractals. But they really aren’t fractals in a precise sense any more than a rectangular building with rectangular bricks is. At some level of scale, it’s just no longer literal enough to be truly a fractal. Most of this is just aesthetic contrivance.
Comment by Alice — June 11, 2012, @ 7:10 pm
Alice, why always to come up with something “new”, like a fashion? The sheltering roof has done a very good job for a few thousand years now, why to abandon it: http://permaculture.org.au/2012/05/28/the-deep-truth-of-a-sheltering-roof/
Comment by Øyvind Holmstad — June 12, 2012, @ 3:32 pm
By the way Alice, I don’t really see your link between New Urbanism and right wing populism. Here in Norway we have a right wing party called “Fremskrittspartiet”, they are big supporters of the Tea Party movement in the USA and attend to their congregations, and the Tea Party like to promote the leader of “Fremskrittspartiet” Siv Jensen as a staunch supporter from Norway, giving her their microphone when she’s in the US.
Now as EU is going bankrupt Oslo is the fastest growing city of Europe, and to the population crisis “Fremskrittspartiet” offers two solutions:
1) To abandon the “wilderness boundary” around Oslo, to extend suburbia with huge new isolated villas into the wilderness, as the voters of “Fremskrittspartiet” seems to LOVE huge isolated villas in suburbia.
2) To build several huge skyscrapers in downtown Oslo, huge isolated towers into which to stock as many people as possible.
To me this sound like simplistic solutions to complex problems. But isn’t this kind of populism just the very earmark of the neoconservatives? New Urbanism is far too complex for “Fremskrittspartiet” and for the Tea Party movement.
If you had been more into New Urbanist discussion you would have noticed that the Tea Party activists are fierce opponents of New Urbanism, as they are like possessed with their private properties, and especially with their huge mansions in suburbia. In Norway as well as in the US.
Comment by Øyvind Holmstad — June 13, 2012, @ 2:39 am
LOL, Oyvind Holmstad. OK, you go live under the roof technology invented 2,000 years ago. Oh wait, your lifestyle depends on having a much cleaner hygienic environment, so you rely on contemporary systems. Contemporary architects aren’t stopping anyone from living in their own filth or from living in buildings that are outdated. So why are you so intent on stopping us from progress? The Earth isn’t flat, but if you want to live in buildings that were designed when people thought it was, go ahead. I’m not stopping you. There are plenty of buildings being constructed in informal settlements that are typical of what was being built 2,000 years ago, so feel free to live in them. There are plenty of buildings being built in cookie cutter housing developments that are simple and soul crushingly dull. So feel free to live there. Nobody’s stopping you.
Comment by Alice — June 14, 2012, @ 4:23 pm
Yes, your rightwingers want to create isolated developments with their own rules in suburbia. That’s what New Urbanism is in the United States. New Urbanism isn’t typically done in actual urban environments here. They normally create these exclusive faux urban developments in suburban areas, because that’s where the land is available. And yes, it is NeoConservative. If you look at the people who are behind New Urbanism politically in the US, it’s often NeoConservatives, because they believe in the paternalism and neo-traditionalism that underpins it. Tea Party members aren’t against New Urbanism. They believe strongly in the neo-traditionalist paternalistic underpinnings that distinguish New Urbanism from other green movements on the liberal side. Most liberals agree that walkable cities and neighborhoods are what we should be after, as do many conservatives. That’s not really a divisive issue. The thing that conservatives in the US grab onto in New Urbanism is the neo-traditional values and the exclusiveness of the developments. They see these projects as ways to screen out poorer minorities and other types of people they don’t want to be around. In the US, New Urbanism isn’t about socialist living. Quite the opposite. Everything is about markets. New Urbanism focuses on retail shopping and other consumer activities being close to residential spaces, but these retail slots aren’t for small local businesses, they’re for huge multi-national corporations. That’s the other reason conservatives here love New Urbanism. It kills small local business and feeds more money to the super-rich by trapping people into shopping at their companies.
Comment by Alice — June 14, 2012, @ 4:32 pm
Alice, no doubt you are a modernist liberalist! Personally I feel much more aligned with classical liberalism, as outlined by the new urbanist Charles Siegel in his new book on Classical Liberalism: http://www.preservenet.com/classicalliberalism/index.html
Comment by Øyvind Holmstad — June 15, 2012, @ 2:50 am