Tag Archives: geometric programs

Design, configuration and natural form

When did human creations stop being natural? We look at a tower block, a subdivision or a shopping mall parking lot and see the worst of industrial civilization translated into form. We tolerate them as necessary to achieve the material wealth of our civilization. Those human settlements that are still natural we grant special protections through UNESCO and historical preservation laws. We do not have a law that promotes the creation of new historic settlements because we are not quite sure how they are made.

I believe that our mistake is not in the things we make, that there is nothing unnatural about a shopping mall parking lot from a design point of view. What makes the shopping mall parking lots we build so unnatural are errors in configuration of the design elements. To understand this, one must understand the difference between design and configuration.

The form of a tree is an ideal example to illustrate the difference between the two concepts. Any particular species of tree will have a design that is essentially the same from one tree to the next. The design elements in the tree are all the named parts: trunk, branch, leaf, root, bark, and so on. These parts are organized into hierarchical relationships with the whole tree and with each other. We will always find the roots related with the trunk in the same way. This relationship is a design solution that achieves a specific result. However, the position of any of the parts is not fixed. In the DNA of the tree are rules that instruct cells to adapt themselves to the larger context the tree finds itself in. The different design solutions that result from this cellular action will therefore adopt a position that reflects the particulars of time and place, ensuring that the tree’s form is perfectly adapted to its environment. This is why it makes no sense to create a description of the forms of a leaf in order to make another leaf – that form is relevant only to this particular leaf, and another leaf, although it would have the same overall design of parts, will take a completely different configuration.

Adapted to chaos

A chaotic configuration of a standard design

If you’re having trouble seeing this, imagine the following scenario: we take the DNA of a tree and clone it 100 times. Then we lay out a grid 10 trees by 10 trees and watch them grow. What would happen would be that every tree would come out a different way, since the earth around them would be structured differently, the wind patterns would be different, the shade and the moisture would be different. The trees would each have the chaotic, random shape that we know trees to have, yet would all be perfectly symmetrical with one another without being identical. Each clone would adopt a unique configuration of the same design.

When we look at a traditional village, we find that the same house design is repeated time and time again, but configured in such a way that it is differently adapted than the other houses. The reiteration of an often very simple design is all that it takes to create a natural landscape, so long as each house is configured to adapt to its place, and the design elements of the house are themselves configured to adapt to these adaptations.

One design, many configurations

Even today this kind of natural adaptation takes place in modern settlements where planning regulation allows it, or fails at forbidding it.


This is the skyline of Monaco, which by necessity of the small size of the city had to be built piecemeal but yet is still made with an entirely modern building stock. The piecemeal process allowed each building to be configured to its site and thus, despite the fact that the buildings’ design is very basic modern architecture, the whole landscape looks natural. It would be even more natural were the architectural elements also adapted.


This the Rocinha favela of Rio de Janeiro. Here the building design is as bare as could be made, the houses being built by poor residents with little capital to invest. But the resulting configurations adapt perfectly to the shape of the hill and the other buildings, and the overall look of the place is that of a human jungle. (If you have the chance to see this summer’s The Incredible Hulk, the movie makes this point by fading from an overhead shot of Rocinha to that of a tropical jungle, subtlety be damned.) The buildings in Rocinha are just as natural as the trees.

How does that translate back into our shopping mall parking lot? It means that although the relationship between the parts, for example the lanes, the spaces and the paint that demarcates them, must be defined, the length of the spaces or the thickness of the demarcations do not have to be identical from one element to another. The chaos of nature requires that they be slightly different from one to the next, and that means that the people who make them must be able to make decisions while they are building. Simply copying an AutoCAD drawing is unnatural. The design must be translated into a language that instructs the builders to make configuration choices while constructing the defined forms. This kind of language is how builders have made traditional towns and how DNA makes organisms.

Separating design from configuration also allows us to make a second attempt at city planning. The plans of modernists all had fixed configurations, and their failure to adapt to their context meant the failure of urban planning. The conflict between design and configuration planning dates back even further, to the 19th century plans for Barcelona and Paris. In Barcelona, Cerda planned a grid of square blocks through which he ran grand diagonal avenues. Those were only two design elements in a very strict configuration that was made possible only by the enormous economic pressure to expand Barcelona. In Paris, Haussmann did not have the luxury of expanding the city with blocks, he had to upgrade a city of blocks that already existed with a new design element, the grand avenue. He deliberately left the configuration of his avenues open until they were completed, and placed them where he met the least resistance. Their effect on Paris is even today essential to life, and they could not have been realized unless their configuration was left adaptive.

What would a natural urban design look like? It must first be a definition of parts that must be related to each other in order to create urbanity. Describe the relationship between the avenue and the streets, the streets and the alleys, describe the relationship between the avenue and the pavement, the pedestrian crosswalks and the shade trees. Describe the relationships with the buildings without delimiting their size and shape. The city builders will then decide in what configuration these elements need to be to fit their context, and the resulting built form of the city plan will be perfectly natural as well as fully planned.

Classicism describes itself as the imitation of nature. Complexity, on the other hand, does not imitate. It is nature, applied to different problems. To create the urban design of our time requires not adopting a certain style or program, but ensuring that any style or program can be adapted to a particular context. It only requires us to use different tools than what we have become accustomed to.

Further reading:

Complex geometry and structured chaos, part I and part II.

Complex geometry and structured chaos part II

Complexity, to employ the definition proposed by Jane Jacobs in the final chapter of Death and Life of Great American Cities, is a juxtaposition of problems. This implies that a complex solution is a juxtaposition of solutions: fractal geometry.

How does the way we build arrive at complex solutions to complex problems without driving the builders to madness? How can we solve problems which exist at every scale in space, but also exist at every scale in time? Let’s take a look at St. Paul’s Cathedral in the City of London.

Let us focus on two different parts of it, the dome and the belltower. At first sight, there is nothing that a dome and belltower have in common. They are two different forms that solve two very different scales of problems. And if they had been built very far apart in two different neighborhoods of the city, one would never even associate them together. Yet in this case they are not only “dome” and “bell tower”, but they are also part of a greater form we call “St. Paul’s Cathedral”. That is to say, their form not only solves the problem of providing a dome and a bell tower, but it also contributes to solving the problem of providing a cathedral. Several scales of solutions are juxtaposed in the same space in order to form a complex solution. How was this result achieved?

Perhaps the architect Sir Robert Wren was a genius, but intuitively we doubt that, since the geometry in St. Paul’s cathedral is very similar to the baroque geometry employed throughout Europe at the time. And when we think back to how the Gothic cathedrals were built, very slowly, sometimes over more than a century, they were necessarily built by more than one architect. If they were all geniuses, then they must have been lucky to find so many geniuses idling about in medieval Europe. That sounds impossible given that medieval cathedrals appear to be even more complex than St. Paul’s cathedral, even though more people worked on their construction over a greater timespan. The sublime Antwerp cathedral, for example, was built from 1351 to 1521, and never completely finished.

There has to be a key to this riddle. How did we lose the skill to make this kind of complexity?

Since Leone Battista Alberti heralded modernity (not to be confused with modernism) in architecture, and until the mid-20th century, architects spent their first days in training learning to draw the classical orders. These classical orders supposedly held the finest refinement of western civilization’s building culture, having been in use since Greek antiquity and maybe earlier. It was an architect’s duty to reproduce this culture by learning the orders. Any deviation would certainly cause the doom of civilization. What the orders actually consisted of were fractal nesting rules, settled on more or less accidentally through the ages. Since the abstract concept of fractal nesting would not be discovered until Benoit Mandelbrot’s work in the 1970’s, the orders were simply understood to be unquestionable tradition. Since they were very simple local-form rules, any architect could use them to make his building, and they could be taught to any laborer working on any specific sub-section of a building without his having to know his role in the form of the whole. They could even be used to make simulations of the building, drawings and scale models that would later be used to convince patrons to fund construction. The rules were always the same. Only the problems to be solved changed.

Let’s take a look back at Wren’s cathedral. What does the dome consist of? Nested structures, including columns. What does the bell tower consist of? Nested structures, including the same kind of columns. The two different problems to be solved, dome and bell tower, also happen to share the same nested problems, and when they share a solution to this problem, they become connected into a whole.

Once we are aware of this rule we no longer need a necromancer to reanimate Wren in order to build an addition to the cathedral. We can simply decompile the geometric rules and apply them to solve the new problems we face. Whatever we produce that way will belong to the cathedral as much as the original parts. But we can also extend this to the scale of an entire city. If we apply these geometric rules to build a house or an office tower, it will appear to belong as much to St. Paul’s as the bell tower and the dome do. This enables us to achieve the complexity limit of urbanism. And when we look at all the great cities of the past, Paris, Rome, Venice, Amsterdam, Mediterranean hill towns, what we find is that they look whole because the builders who made them were all using the same rules in order to solve their individual problems. They didn’t realize they were doing it, they were just doing it because that’s how things were done.

If the classical orders were so great, why are they no longer being taught? Up to the 19th century, building technology changed very little, and so simply repeating the tradition was enough to create complexity. When metals and glass became massively affordable in the industrial revolution, architects faced a puzzle. Although the traditions succeeded at creating complex solutions, they were no longer solutions to problems that were relevant to anyone. Some architects experimented with new rules for nested structures using the new materials, more or less compatible with the old rules, and that gave us Art Nouveau and the Eiffel tower, for example. And some more radical architects, such as Louis Sullivan, said that modernity required the invention of a whole new architecture, and this became known as modernism. The modernists were right to declare the classical orders irrelevant, but in their rejection of the very foundations of architecture, the application of simple nesting rules, they also made it impossible for themselves to create complex buildings, and the result is the architectural wreck that unfolded starting in the 1930’s. The worse culprits, no doubt, were those modernists like Le Corbusier and even Albert Speer (bet you wouldn’t think he was a modernist) who favored abstraction and repetition in architecture. Abstraction is only the denial of complexity, the physical nature of our universe. It is the architectural equivalent of playing ostrich.

Post-modernism tried to bring back traditional forms without really giving up modernism, and that was a disaster perhaps worse than modernism was. Since post-modernists did not create nesting rules for their architecture, and on top of that were bringing up forms that were solutions even less relevant now than when they were abandoned, the result was a worldwide goofy architecture that everyone mocks as pastiche.

Some architects have been stumbling upon the right path these last few decades. The most remarkable effort has been the remodeling of the Reichstag in Berlin by Norman Foster.

The old building represented the federalist traditions of Germany, but also had to be adapted to the new philosophy of popular democracy. Foster built a glass dome from which the people can look at their politicians at work while enjoying a wonderful panoramic view of Berlin. Foster nested a new solution to a new a problem within the traditional geometry of the Reichstag, and thus created complexity that is relevant to the problems of today.

Architecture is, ultimately, just the repetitive computation of simple geometric rules to solve complex problems. Necessarily that creates complex solutions, and truly fractal buildings. With the right ruleset, anyone can do architecture, and by extension, great cities. The rules guide your hand.

Architecture should be abolished

Just what exactly does this have to do with constructing buildings and cities? When you can just as easily make jewelry as boats, you are not an architect. You are someone who draws shapes.

The architect was once the person responsible for directing the construction of a building, start-to-finish. For some of the grandest buildings, like the Gothic cathedrals of Europe, they didn’t even draw any plans. Now the building part is done by engineers, and for a rare proportion of buildings a jewel-artist is hired to create some kind of absurd shell in which to put the structure, which inevitably makes the structure less efficient. So there’s no such thing as architecture anymore. Just end the pretense. Shut down the schools. From the subdivision to the big box store to the shoebox office building, the majority of people in North America do not come into contact with any architecture during their daily lives, and they are the lucky ones.

These are the people who will gain the most from the development of emergent construction. By following simple geometric programs, the most banal builders will be able to create buildings of great beauty and complexity. These are the people who will have earned the right to call themselves architects.