Category Archives: Theory

Defining a new traditional urbanism

Sometime last year this website attracted the attention of several members of the International Network for Traditional Building, Architecture and Urbanism, an organization sponsored by the Prince of Wales Foundation in order to support and renew traditions of construction. While this organization does great work to preserve the techniques of traditional building cultures, they have yet to define what the traditional urbanism of their name really implies. The importance of such a definition I believe to be primordial. If modern planning measures continue to be adopted from one country to the next, any traditional technique of construction will become irrelevant, as they have in western industrialized (and post-industrialized) countries.

This all became obvious when a miniature controversy erupted and swept through the various internet discussion groups and blogs of the community over a proposed redevelopment of the Chelsea Barracks in London’s Chelsea borough. An old modernist military installation was to be torn down and replaced by its new owner, the Emir of Qatar, with a new modernist megahousing development designed by Lord Rogers. There was nothing particularly interesting about this Rogers design, but Lord Rogers having written the plan of London, a plan that specifically calls for better design, it made sense that a Rogers design would be swiftly approved by the planning authorities. Hiring Rogers was the most risk-free option available for a multi-million pound development project.

Getting wind of this, and noticing that the Rogers design was an unremarkable piece of rehashed modern housing, the Prince of Wales hired his preferred architect Quinlan Terry to sketch up a counter-proposal that was more in harmony with the architecture of the landmark Royal Chelsea Hospital across the street from the barracks, which he then proposed to the Emir of Qatar through his personal relationship with him. The Emir, alien to the local culture and uncertain of what London considers to be “good design”, then decided to dump Rogers and re-think the development.

The Prince Charles and Quinlan Terry counter-proposal

The Prince of Wales and Quinlan Terry counter-proposal

Lord Rogers' Chelsea Barracks redevelopment proposal

Lord Rogers' Chelsea Barracks redevelopment proposal

I am not going to analyze the controversy from all of its fascinating angles, such as the design quality of the architecture, Lord Rogers (of the House of Lords) teaming up with British Republicans to denounce the monarchy’s interference with civilian life, or the absence of affordable housing in Chelsea. I am interested in only one question: is this traditional urbanism?

At first sight, the Terry design is reminiscent of the 18th/19th century style of palatial construction in Europe. (In fact one of the “blocks” features echoes of Buckingham Palace.) In terms of authenticity, the proposal is flawless. The Rogers proposal is also a palace, although one with much fewer attractive qualities. But does Chelsea really need a palace?

Providing a response to that inquiry is precisely what a system of urbanism is supposed to achieve. The system in place for London unfortunately requires that one have enormous financial means in order to participate in any kind of development, and inevitably that implies that only large speculative development will be so much as imaginable. The Chelsea Barracks proposal is entirely a product of modern urbanism, and by intervening into that system, the Prince of Wales and other traditionalists are sanctioning the very thing they claim to be opposed to.

As luck would have it, I wrote about the different processes of urban development using London neighborhoods such as Chelsea last year. Combining this with our models of the processes of urban emergence, we can develop the idea even further and try to conceive of a proposal for a traditional urbanism that develops the Chelsea Barracks site.

When I last covered Chelsea, I used its housing typology as an example of a linear, non-complex model of housing development. While linear housing is characteristic of the neighborhood, it is not the entire tissue of it. If we analyze the morphology of the neighborhood we find many clusters of housing rows, but these clusters do not necessarily repeat from one block to the next, and they are intermingled with other, uniquely programmed buildings of varying scale, the most prominent of which being the Royal Hospital. This means that, despite the neighborhood’s texture being only semi-random and not completely emergent, it performs at a remarkable level of complexity.

Chelsea

This kind of fabric is very common of British-American subdivision development during the 19th century. Here it is in a pure grid form in one of Montreal’s inner core “Plateau” neighborhoods.

Montreal

We can observe that the middle of blocks is populated very differently from the major streets, despite the fact that they are not very different from a design standpoint. We don’t need to propose anything more complicated than self-optimization to explain this pattern. During development, housing builders would work from the center of blocks outwards, where there was the least perceptible traffic, and shops, churches and other activities located where there was the most traffic. The outcome is a complex tissue with perceptible characteristics, not only random noise.

In comparison, here is the texture of a new neighborhood in Las Vegas (Henderson), Nevada.

henderson

It is the same housing model repeated a thousand times, some lots facing backwards from the main roads. This new neighborhood might as well define linear development processes. The only feature of this neighborhood is the house, and so it can only function at any level of complexity by ejecting its residents out into town for any activity.

Of course some might say this is not a fair comparison. Those old neighborhoods are old, and therefore have had a long time to achieve maturity. But a neighborhood maturing implies that the neighborhood is planned to have a life cycle taking place in time, of which the early stage of growth is critical to its final morphology. What did a young, new neighborhood look like in 19th century British-American urbanism? It consisted mostly of very large lots of gardens and other large events (such as, for example, a Royal Hospital). These new neighborhoods were advertised as a pastoral refuge from the city. Look at this engraving of Milwaukee’s outskirts in 1858.

Milwaukee_1858

Its overall density is much lesser than that of Las Vegas new neighborhoods, and it has a distinctively pastoral quality. Yet what happened to those traditional neighborhoods was often that, very rapidly (the span of 2-3 decades) they became very dense urban neighborhoods, at which point the rate of new growth plunged and the fabric remained stable.

See for example this comparison of the urban fabric (1897-1915) of the Morningside Heights neighborhood of Manhattan, from the book Retrofitting Suburbia: Urban Design Solutions for Redesigning Suburbs.

MorningsideHeights18971915

In less than two decades the neighborhood was populated from a pastoral grid dominated by the campus of Columbia University to the dense, New York-style neighborhood it remains today. In these examples, growing a mature neighborhood was intrinsic to the development process adopted, and once this process wound down there was very little left to change to it. The neighborhood was mature because it had reached its equilibrium with the socio-economic context. Correcting deficiencies is what is meant by a neighborhood maturing, and developing a mature city implies that one is avoiding mistakes during its development. If we are employing a development model that is set in advance, no mistake can be either corrected or avoided during production.

Notice then that in traditional neighborhoods, the construction of mass-produced housing came last, after the neighborhood had established itself as a socio-economic system at the fringe of an existing city. Because of this, the mass-produced housing is a complement to that tissue, and contributes to the established complexity of the neighborhood, even super-charging it with population density. This not only ensured that there was no environmental alienation for the new residents, but also that there was a limit to how much repetition there could be from housing builders.

In modern urbanism we require all new developments to be programmed for a certain type of use, whether we are building a housing subdivision, an office or industrial zone, or a “mixed-used” development. If this is not know and debated in public, no development project can be approved. Only when a proposal has gone through this ordeal can anything be built, and making changes involves going through the process again, so the developers just subsidize the mistakes, or leave certain parts of the plan unrealized and a gaping hole.

In traditional urbanism this is never necessary. In fact it is possible for entire blocks to be left as pasture or gardens, creating an ultra-low density urban tissue. Only as further development becomes truly needed are these blocks transformed into housing and other programs. A critical difference is that no planning permit or approval is necessary to further develop a neighborhood. Instead the residents have an envelope of building rights set in building codes, and everything within that space is considered to be automatically approved. Because of this the development of a neighborhood can be undertaken in a large number of successive decisions, where the next building to be added is not only determined by the citywide market but also by the current state of the neighborhood. This in turn allows a local community and economy to grow, which is absent from modern developments.

This is all very interesting for new neighborhoods, but how would that apply to a small urban redevelopment site in the middle of a centuries-old neighborhood? Clearly we aren’t going to be building up from pastures. This is where a “new” traditional urbanism becomes relevant, as we need to invent a new process that restores the features of traditional urbanism, but can also function in the context of mature cities and modern structural requirements.

Although the redevelopment of a large urban block is usually undertaken as a large real-estate project, it can also be considered as a nested process of urbanism (urbanism within urbanism). Much like the city-wide process of urbanism is characterized by regulations intended to achieve equilibrium, the redevelopment of a block of the city should also be designed as to achieve its equilibrium with the city as a whole but (and here is the defining characteristic of a traditional urbanism) also within itself. This is what does not happen in linear development processes such as housing subdivisions, or 19th century housing terraces. They provide equilibrium with the larger scale, but amongst themselves they provide no complement. For this reason, although you’re likely to see a lot of some housing model repeated in one place, you’ll rarely ever see it used again elsewhere. Mass-production does not work for buildings the way it does in automobiles.

Time and interaction are the critical factors. The reason large-scale development like the Rogers and Terry proposals get approved and built is that everything must be conceived and approved in one step. The architectural design is rushed in order to make proposals as soon as possible. The form can’t evolve over the course of development. This process is justified by the need to control the architectural character of the city, but it is not necessarily so. It only follows from controlling architectural character because we rely on static information systems and processes to conduct building. In fact, many of the traditional building techniques that preservationists are attempting to preserve do not translate into modern information systems (building plans). If instead of drawing the full plans, the proposals simply supplied the component patterns and a parameter space for them, then there could be an infinite variety of different instances of these patterns populating the new space, all fitting a particular need and applying a specific method of returning to equilibrium. If we wanted to release control even more, we could define some buildings from the neighborhood as models and whatever patterns they featured as automatically approved. And seeing as this is the 21st century, we could define these patterns inside software that could randomly generate any possible permutation, such as the City Engine.

With the architecture out of the way, there would only need to be a fixed design for the frame of spaces around which the urbanization will take place. Grids are flat and unspecific, and so a good project will have a place structure that creates inequalities of movement. (Even New York’s grid has subtle inequalities in the short-blocked avenues and long-blocked streets, creating vastly different spaces in character.) Crescents, squares and alleys on a completely open surface should be the extent of planning a new neighborhood, and it will be important that this design have value all of its own. It is quite possible, for whatever economic reasons, that only part of the surface will be built, or even that nothing will be built. A good urban design must work in all states, including with nothing on it. Remove the buildings from the Terry proposal and there is still a rather interesting landscape. The Rogers proposal, without its buildings, has nothing. Terry is therefore much closer to the goal.

Negative space in modern plots

Negative space in modern plots

In the final step, how does the developer make money? Sustainable development, after all, has to be profitable in order to be sustainable. In a traditional city, plots were subdivided over time as the need arose. In a modern city lots are defined as a standard shape, and then later sold off for some standard price. This approach has the unfortunate side effect of creating a lot of negative space. The developer of the Chelsea Barracks could instead sell or auction off space as an elastic product. The first buyer would choose the first spot on the open surface, in relation to the hierarchy of the urban grid. The second buyer would place himself in relation to the urban grid and the first buyer. These buyers at first would come from long-time residents of the neigborhood aware of some particular way of extending the neighborhood, but unable to find a lot a space at the right size before this project became open to the public. This process would continue until all the space had been consumed, and the end result would be that all buildings would be related to one another through the sales process. If the space was priced high enough, the later projects would only be initiated after the initial ones had been completed, and the impact of time would generate the demand for building programs complementing the initial projects.

In such a way the urbanism within urbanism would create its own socio-economic subsystem, would feature a randomly adapted but uniform architectural signature, and would complement and extend the external urban tissue.

While I’ve detailed a process for developing a small block within a city, this process is just as applicable for doing development of new cities, or new suburbs of cities. There are fewer constraints and difficulties involved in these other cases, which is why I wanted to use the example of the Chelsea Barracks site. Urbanisation is a universal phenomenon, and although the patterns change, the underlying principles are everywhere the same.

Principles published

The full article conceptualizing the principles of emergent urbanism has been published by the International Journal of Architectural Research volume 3 issue 2. You can download the complete article or read the whole issue.

The Cultivation of a Spontaneous City

This is the last of a series of excerpts from my article in the upcoming issue of the International Journal of Architectural Research, about the principles of emergent urbanism. Click here for part I, The Journey to Emergence. Click here for part II, The Fundamentals of Urban Complexity.

How emergent urbanism works

In a traditional spontaneous city, 100% of the surface is initially a network structure, open land. From this surface the best paths are selected to fit the networks that are emerging, and the leftover space is progressively built upon. Starting with a completely open, fully-connected land structure, the city’s design can consist of a purely negative process by placing constraints on construction over important paths. In this way the street structure and hierarchy becomes an evolved structure that matches the history of its networks, and the placement of buildings and uses is also an evolved structure that matches the flows of movement. Over time these paths are paved and upgraded, and important junctions of paths become the central open space of the city. The central square of a spontaneous town can be explained as the remainder of a fractal process of subtraction, with the most underused part of the spatial network being removed at each additional step of feedback until no further network subtractions are possible. With the circulation of people optimized, the remaining space is augmented with street furniture specifically designed for crowds, such as benches, transit stops, billboards, kiosks and so on.

An emergent city similarly begins with a network structure, although one that is much more sophisticated than open land. In modern design the typical asphalt street produces a network that is suited particularly to automobile networks, but also has the unfortunate side-effect of cutting pedestrian networks that normally enjoy the entire surface in a spontaneous city. As a remedy these streets are equipped with sidewalks that are often narrow and unpleasant (if not dangerous) to walk, an effort at translating strict traffic control methods to the pedestrian. It is not surprising that pedestrians are so rare in modern cities, but some efforts have shown that pedestrian networks can emerge from modern design. One example is the three-story deck of the La Défense business city in Paris (shown in figure 7), which contains parking but also regional rail and subway links, as well as being an open pedestrian surface. At the ends of this network structure a generative process of spontaneous development creates the actual networks of the city. As evidenced by the crowds present on that surface and the abundance of neighborhood shops the pedestrian networks function quite well. What is more surprising is that the automobile networks are underused and some parking structures empty, despite the neighborhood having been conceived for the automobile.

Figure 7

Figure 7. The “pedestrian slab” style of design was blamed for the failure of modernist urban planning projects, but at La Défense the slab is a working structure. The developer adopted spontaneous building development instead of applying the complete architectural plan, enabling the formation of a dense local economy.

Because of the high costs and other complexities involved in producing networks for modern transportation systems it is not possible to practice a purely negative and subtractive process of street formation. However the network structure must still be an evolved structure that is produced with feedback from lot development instead of building an entire grid before it has been decided what size of lot is needed. Most importantly all forms of movement must be in balance in the street design so that one type of network structure does not cut another and prevent the network formation process. (Salingaros, 1998)

The cultivation of a spontaneous city

Once a network structure is in place the process of network formation can begin.

Wiki systems have shown that simple freedom to create does not necessarily produce networks unless there also exists a simple interface to this network. The World Wide Web provided a system of linked websites that could spontaneously produce an encyclopedia for many years before the Wikipedia system catalyzed the distributed knowledge of millions of people into an exponentially growing and internally coherent system. The creation of crowd-catalyzing systems has since been named “crowdsourcing.” Translating crowdsourcing principles to planning processes, Alexander described in The Oregon Experiment how an institution could directly support the spontaneous development of its city by providing designers and managers to assist individuals and realize the program that the individual users have in mind. (Alexander, 1975)

With the initiative for developing new building programs left deliberately undefined and in the hands of the individuals and organizations that develop the socio-economic networks of the city, there remains the issue of producing a geometrically coherent landscape that is harmonious and distinctive. This is accomplished with shared generative processes, (Alexander, 2004) and particularly the nesting of generative processes into one another (also known as a shape grammar or form language), as shown in figure 8.  No matter what configurations of space are required by any individual building program, if this configuration is realized physically by the same building process as for any other random configuration then the two realized buildings will share symmetric properties and the result will be a harmonious geometric order. This has been employed in many instances by the regulation of construction materials, which creates a geometric order at the scale of texture, but it also applies for any other scale of geometry, as evidenced by the geometric order created by the advertisements in Times Square.

Figure 8

Figure 8. Three volumes are randomly defined in space without relation to each other. When a shared feedback function is applied to transform these volumes the volumes become related by these transformations. The function in this case is: 1 – Cut out the top corners to half the volume’s height, 2 – Raise the center of the roof.

By defining construction processes instead of fixed building designs it is possible to plan for future growth without eliminating spontaneous growth and feedback. A developer that is initiating a program of emergent urbanism can therefore prepare for construction in advance of any projects having been determined. Building high-technology structures is a complex art that requires significant expertise and a skilled workforce. The developer that creates adaptive building processes that can be used to generate and realize building plans easily and rapidly will provide the same spontaneity as squatter settlements achieve.

As evidenced by the popularity of historic towns of Europe and particularly the Mediterranean as tourist destinations there is enormous demand for and profit to be made from cities that adopt the geometry of emergent cities. For this to work however the development and banking industries must be persuaded of the effectiveness of process design as opposed to master planning, and the municipal authorities must be willing to approve urban design with no fixed configuration. (Alexander, 2004) Political issues also create a significant obstacle. The long approval processes that one must go through to develop a new city or neighborhood have significantly increased the length of the feedback loops and favored large-scale development as well as made small communities less competitive. Even when long review or public consultation processes can be avoided, a development has to comply with weighty subdivision and building codes that consume time to absorb and understand, and in so doing contribute to lengthening the feedback loops and making the urban tissue less adaptive and less sustainable.

References

Alexander, Christopher (1975). The Oregon Experiment, Oxford University Press, USA
Alexander, Christopher (2004). The Process of Creating Life, The Nature of Order Vol. 2, Center for Environmental Structure
Salingaros, Nikos (1998). ‘Theory of the Urban Web’, Journal of Urban Design, vol. 3, also in Chapter 1 of PRINCIPLES OF URBAN STRUCTURE, Techne Press, Amsterdam, Holland, 2005.

The genesis of complex geometry

I don’t believe that there is a dichotomy between a supposedly modern and traditional architecture. Instead there exist different geometric processes, and while traditionally builders have employed nesting processes in their work, for perhaps no other reason than it came naturally to them, modern builders have restricted themselves to linear geometric processes due to drawing their inspiration from Cartesian science and engineering.

In attempting to transform architecture into a vessel for artistic expression, modern architects have been trapped by their limited tool set, and the product of their work has often been confusing, silly, or utterly corrupt. There are only so many tricks that one can perform with linear geometry, although computers have extended the reach of those tricks. But the confusion of modern architects becomes even more obvious when they ascribe artistic merits to traditional builders who never aspired to be artists at all. One such instance is the introduction of a recent biography of the 18th century french military engineer Vauban by official starchitect Jean Nouvel, who described Vauban’s fortresses as an early form of land-art and morphing. Jean Nouvel asks, could a man be an artist without being aware of it? Vauban was not an artist at all. Military necessity led him to employ geometric processes that significantly increased the complexity of fortifications, and it is merely incidental that today we find his projects to have artistic merits.

The process through which Vauban’s work became worthy of architectural praise provides the key to the distinction between linear and nesting geometry. Vauban was not himself the inventor of the star fort. Those had been around for more than a century when he began his career for the army of king Louis XIV. The basic star fort was a simple concept: the old masonry walls of the medieval age had shown themselves to be obsolete with the advent of cannons, and they had been replaced with thick banks of earth dug out of trenches whose major flaw was to provide space out of reach of defensive fire at its angles. The angles were thus extended into diamond-shaped turrets in the first pass at a feedback correction, introducing nesting geometry and initiating the first step of the genesis of a fractal.

180px-Neuhäusel1680

A basic, early star fort

While the star fort was successful at resisting attacks, it was not impregnable. A method was devised to capture them by digging trenches in zig-zagging patterns through which troops could assault the walls without being exposed to cannon fire. In fact this is how Vauban built his career, and some of his “plans” for besieging star forts are significant civil engineering projects of their own.

Siege de Turin 1706

The siege of Turin. From an encircling trench, Vauban built successively denser trenches to capture the citadel and take the city, a process that was extremely expensive and time-consuming.

While star forts never truly became obsolete (as medieval fortifications had) until well into the 19th century, military engineers did improve on their effectiveness by correcting their vulnerabilities, which happened to be at the angles they were characterized by. And so, by another layer of feedback, the geometric depth of the star fort concept increased.

Citadelle San Martin

San Martin Citadel, a “second generation” star fort.

Vauban’s great invention was nothing much more than repeating this process of increasing depth one more time, creating what many now consider to be his masterpiece, the Citadel of Lille, a showcase of complex geometry made from the refinement produced by centuries of feedback of the star fort concept.

Citadelle de Lille (2)Nouvelle enceinte de Lille

Citadel of Lille and the system of fortification of the City of Lille, as designed by Vauban

If you only understand Cartesian processes, then the only idea that may come to you to improve on the basic star fort would be to add dozens of diamond-shaped turrets, a change that would most certainly make the concept worse instead of better. The military engineers of the time however were well aware that the diamond turrets were optimal in their shape. What was needed was a shape that extended the diamond, and this was achieved by increasing the depth of the whole object.

Another aspect of the complexity of a geometric process seen in the Lille example is its configuration adaptiveness. The shape of the city and the surrounding landscape is completely random, and the encircling fortifications bend to match this randomness, leading to Nouvel’s claim that it is an early example of morphing. But once again there is no deliberate attempt at morphing going on. Since each component of a star fort is defined as a recursive relational transformation of the basic wall, Vauban only had to design the wall and the other parts aligned themselves as a result of the wall’s configuration. If the outcome has artistic value, it is once again only incidental.

It is important to note that the Vauban extensions to star fortifications did not mean that the simple 3-part star fort became obsolete. In fact many simple star forts were built in the 18th and 19th century in America as the threat was low and the cities to be defended underdeveloped. The difference between a simple fort and Vauban’s complex fort is one of depth and effectiveness, and there is a real cost-benefit choice to make. The star fort only became obsolete when the bunker replaced it, and the early bunkers reset the process of complex geometry genesis by being simple concrete shells in their early incarnations.

When we undertake to create symmetry in an urban environment, we want buildings to be as alike as possible while allowing for adaptation to context. If we understand geometric depth we can build in such a way that poor and expensive buildings have the same basic design in their first levels of geometry, but expensive buildings have many more scales of geometry nested within that basic design. It is not necessary for an entire city to be made of the same materials as materials are one of the last visible scales of geometry, and so we can have a city of mud bricks and marble buildings that nevertheless share 95% of their geometry and beautifully complement each other, while both poor and rich citizens have a home adapted to their situation.

We can look at these examples from Korean traditional architecture for an illustration.

48799484.CIMG0512Tomb_of_King_Tongmyong,_Pyongyang,_North_Korea-2

On the left is a simple house and on the right is the tomb of a great king. Both buildings have the same design, but the building on the right has much greater depth in this design.

Another interesting comparison is between the Golden Gate bridge in San Francisco and the Verrazano Narrows bridge in New York.800px-Golden_Gate_Bridge_from_underneath800px-VerrazanoFromNCLDawn

The bridges are the same in design, but the Golden Gate bridge has more depth within this design, and is for this reason the more famous of the two bridges. That doesn’t mean the Verrazano Narrows bridge isn’t beautiful on its own.

And to make things as simple as they can get, we can compare a Sierpinski triangle with four levels of iteration with one that has six levels.

Geometric depth

The fractal on the right has all the same elements as the one on the left, but also has more.

A lot of the residential buildings we create today would benefit from being more like the Verrazano Narrows bridge. They try to be more than a simple house for a simple family and end up covered in tacky, useless ornament that have obviously been forced into the design. Simplicity, if it is adapted to context, can create as beautiful a landscape as complexity. Postmodernistic nonsense geometry does not. We would be better served going back to the simplicity of 1950’s international style modernism than what is being built by architects today. The best architects would reinvent it with greater depth.

Previous topics

References

Vauban, l’intelligence du territoire

Hommage a Vauban 1969

A modern artist’s homage to Vauban. This artist did not understand complex geometry.

Organization and intelligence

1. Sun Tzu said: The control of a large force
is the same principle as the control of a few men:
it is merely a question of dividing up their numbers.

2. Fighting with a large army under your command
is nowise different from fighting with a small one:
it is merely a question of instituting signs and signals.
– From The Art of War by Sun Tzu

The problem of social cooperation is how to order many individuals into large-scale patterns, and thus acquire the benefits of these larger patterns. The military arts were the first to face this problem, war being a field where inferiority carries severe consequences, and lessons are learned quickly. The solution was known in the time of Sun Tzu: the superior army was the one that could act as a single force, applying a single decision multiplied by however many men were at the command of this army. More men were always better, but past a certain scale it became unmanageable for a commander to yell out orders to everyone and maintain command. In order to resolve this the military men invented hierarchy, a command structure through which the commander’s orders would be distributed so that a group of any size could act as a single force.

For most of history success in war came from achieving and maintaining organization, lines of command from a center to the individuals that compose an army such that the commander could deploy the army in the most effective pattern he could think of. Discipline and complete obedience to orders was required, even if the situation as it appeared to the lowly grunt was in total contradiction to the orders he had been signaled. As far as he knew, the commander had a larger picture of the war and the orders ought to work out correctly. But the flaw in organization is that as an organization becomes larger, as the layers of hierarchy increase, the commander becomes more remote and more isolated from his army. The lines of communication become inefficient, the orders become irrelevant, and many men die stupidly.

Nevertheless, for centuries the sheer overwhelming force of numbers more than made up for the losses due to bad orders. The principle of organization triumphed. Reformers started looking for plans to organize industries, entire nations (the command economy of the Soviet Union), and of course, cities. The C.I.A.M. Athens Conference resulted in the publication in 1942, by Le Corbusier, of the Athens Charter, the document upon which the plans to organize modern cities, and be rid of the spontaneous historic city, were founded.

Between the time of the Athens Conference and the publication of the Athens Charter, the military concept of large-scale organization was completely discredited.

In June 1940 the German army invaded France. The two armies were evenly matched in men and weapons, France even having a advantage in tanks. Within one month the French army organization collapsed and millions of men surrendered without having put up much of a fight, resulting in many decades of American jokes about French surrender. In reality the two armies were far from evenly matched; the German generals had discovered a mean to overcome the weakness in the principle of organization, that it relied on a central, single commander. Their model of cooperation has been called Blitzkrieg, the lightning war, and its intent was to reduce the delay in receiving and sending the “signs and signals” of command by removing them. German commanders out in the field were given broad directives and trusted to figure out on their own how to fulfill them, with glory and medals as reward for success. The French had instead refined organization and bureaucracy into a precise art. Within days of breaching into France, autonomous German tank divisions destroyed the lines of communication of the French army and paralyzed the front-line units. It became impossible for it to act as a single force, never mind stopping an invasion.

The German system of directive command was in fact the universal principle of emergence applied to military action. Instead of building a hierarchy of orders to communicate the will of a central commander, the armies were organized in parallel, directed to respond to their observed context, a context which was itself produced by other units of the same army. Instead of deploying the intelligence of a single commander holed up in an office in Berlin, the German system linked the intelligence of all of its officers into a more effective super-intelligence that could see all of the battlefield simultaneously. The collapse of the French army was therefore inevitable. It was a case of one against many.

As already mentioned, war teaches quickly, and the allies eventually adopted a similar operations model to fight the war to victory. German operations theorists went on to design the structure of NATO’s European defense, a war that we fortunately never witnessed. Urban planners did not have to learn this lesson, and they opted to organize cities to ruin.

hierarchy-network

The network structure is often, incorrectly, called a “bottom-up” organization. My opinion is that this label makes no sense. There is no up or down in a network. There is neither bottom nor top. Those are descriptions that apply to hierarchies only. In a network actions happen horizontally, in parallel. Large-scale patterns are made up of links between those local actions, as seen in the figure above. Human intelligence, for example, cannot be explained as a collection of cells. It is the patterns formed by the links between these cells that is intelligent, and it is these patterns that allow us humans to be several orders of magnitude more complex than individual cells.

The paralysis inflicted on the French army organization was in parts self-inflicted. Longer chains of command involved delays in transmitting information (reports from the field), analyzing the information, planning a reaction and ordering the new deployment. The bigger the army became, the more paralysis it suffered. This organization was in much the same situation as the dinosaur who did not feel a hit on his tail because the nerves were too far from his brain. The bigger it became, the more exposed it was to a paralysis-focused attack.

It should not come as a surprise that what caused the death of cities is also self-inflicted paralysis. But the case of cities is much more tragic. The German operations model was novel and innovative, a radical improvement in military art. Cities, however, had always been emergent. They were the product of a spontaneous order, a phenomenon that was barely understood at the height of rationalist planning. What science did understand was organization. Since it was accepted as the pinnacle of science, no rational thinker could reject the new urban planning. The planners did not notice the hints: what they were organizing had not been a creation of anyone.

In a complex emergent system, the number of unique patterns scales up with the size of the system. (What some emergence commentators call “more is different,” another expression that makes no sense.) While an organization attempts to create a large-scale pattern to outmatch smaller patterns, a complex system is made up of both small and large patterns, in proportion to a power law, either nested together or juxtaposed randomly (a fractal). If an emergent system is intelligent, it will structure itself into patterns that no one had expected.

For centuries people had been accustomed to such patterns as the street of similar shopkeepers. Many streets in European cities bear the name of a particular trade, such as baker’s street or threadneedle street. But when cities passed a critical scale during the industrial revolution, a whole new pattern emerged: the central business district. An entire city within the city became the center of commerce, not simply specific streets next to residences. Although it appeared unexpectedly during the 19th century (the Haussmannian renovation of the Opera district of Paris was meant to create a neighborhood for the upper classes, but it became a business center immediately and has remained so ever since), a central business district came to be what a major city was all about. When planners set out to organize a modern city, they planned it around the CBD as the central feature. They did this by drawing a square on the map and applying a different set of rules to this square. Within a few years, their CBDs began dying. The small scale patterns nested within them had been zoned out.

In retrospect it was inevitable for an attempt at organization to severely interfere with urban processes, the principle of organization being a step down in complexity from the principle of emergence. Organization had a sinister advantage: it gave the planners the illusion that they could predict what the city was going to become. An emergent system cannot be predicted with precision. The very basis of its intelligence is that it has not yet been decided what it is going to do. Embracing an emergent system means accepting that patterns will appear that are beyond our comprehension. (In Wolfram’s terminology, the system is computationally equivalent to our own intelligence.)

By trusting their front line officers to run the war for themselves, the German general staff took a leap of faith that paid off decisively and confronted every opposing military with their crippling inferiority. I suspect the first modern city to give up on the principle of organization will trigger a similar revolution.

The Fundamentals of Urban Complexity

This is part II in an ongoing series of excerpts of an article set to be published this summer in The International Journal of Architectural Research, tentatively titled The Principles of Emergent Urbanism. Click here for part I, The Journey to Emergence.

The qualities of an emergent city

The adoption of mass-production processes, or development, in substitution for spontaneous urban growth in the mid-20th century created for the first time a phenomenon of alienation between the inhabitants and their environment. While the physical features of spontaneous cities could be traced to complex histories of families, businesses, and organizations, the physical features of planned cities owe their origin only to the act of planning and speculation. This has severe consequences towards the sustainability of place as there will not grow any particular attachment by the residents, their presence there being only a temporary economic necessity and not the outcome of their life’s growth. Mass-production of the environment left people as nothing more than consumers of cities where they used to be their creators. A building culture was replaced with a development industry, leaving the landscape culture-less and with no particular sense of identity. This took place despite the evidence that a building which has a unique history and has been fitted to someone’s life, as opposed to speculatively produced, generates market value for that property. (Alexander, 1975) This is why, although the demolition of so-called “slums” to replace them with modern housing projects created a great deal of opposition against urban renewal programs, the demolition of the housing projects later on did not lead to a popular preservationist opposition. They were not the physical expression of any culture.

In additional to cultural patterns, spontaneous settlements also have a peculiar morphology that has not successfully been imitated by modern growth processes. Spontaneous settlement processes give individuals full freedom to determine the boundaries of their properties. Spontaneous settlement is one where total randomness in building configuration is allowed, with no pre-determined property lines acting as artificial boundaries. Buildings and building lots as such acquire general configurations comparable to cell structure in living tissues, unique sizes and boundaries that are purely adapted to the context in which they were defined. In the absence of abstract property boundaries, property rights are bounded by real physical limits such as a neighbor’s wall. (Hakim, 2007)

Very attractive spontaneous cities have a specific pattern of the urban tissue. It consists of similar vernacular buildings that appear very simple when considered individually, but produce a visually fascinating landscape when considered as a whole. This is a form of fractal geometry. In mathematics a fractal is a geometric object of infinite scale that is defined recursively, as an equation or computation that feeds back on itself. For example the Sierpinski triangle is defined by three triangles taking the place of one triangle as in figure 4.

Sierpinski_triangle_evolution

Figure 4. A triangle triggers a feedback function that produces three triangles, which themselves trigger the feedback function to produce nine triangles, and so on. This process can unfold as long as computational resources can be invested to increase the complexity of the object.

The Mandelbrot Set is a much more interesting fractal that is defined as a simple recursive mathematical equation, yet requires a computation to visualize in its full complexity. When computing how many cycles of feedback it takes for the equation to escape to infinity for specific coordinates, figure 5 is the outcome.

Mandelbrotset

Figure 5. The image on the right is a deeper magnification of the image on the left, produced with a narrower range of coordinates as the input of the Mandelbrot set’s feedback function.

In addition to its remarkable similarity to natural phenomena, this form of geometric order informs us of a very important law in geometry: a feedback loop that is fed through the same function will produce an ordered but unpredictable geometric pattern out of any random input.

This tells us why cities of vernacular buildings have such appealing geometric properties at the large scale, despite being often shabby and improvised at the scale of individual buildings. Shanties made of scrap metal and tarp look rough at the scale of the material, but because multiple shanties share the construction process and originate from similar feedback conditions they form an ordered geometric pattern with its specific “texture”. The same process takes place at other scales of feedback, for example the production of a door. Whether the input for one door is larger, taller, wider than another door, if the same production process is employed the two doors will contribute to the overall fractal order of the urban space. This law has been employed not only in traditional and spontaneous cities, but also for modern urban planning initiatives. In the New York City neighborhood of Times Square the structure of billboard advertisements is defined by a building code that determines their configuration in relation to the configuration of the building. The outcome is a unique tissue of advertisement billboards that has become more characteristic of the neighborhood than the buildings themselves, which are not produced by a shared feedback function.

Fundamentals of urban complexity

Christopher Alexander showed in A City is not a Tree (Alexander, 1965) that social and economic networks formed complex semi-lattice patterns, but that people who observed them limited their descriptions to a simple mathematical tree of segregated parts and sub-parts, eliminating connections in the process. (Figure 6 compares the structure of a tree and semi-lattice.) In attempting to plan for urban structure, a single human mind, without a supporting computational process, falls back on tree structures to maintain conceptual control of the plan, thus computing below spontaneous urban complexity, a phenomenon that is consistent with Wolfram’s theory of computational irreducibility of complex systems. (Computational irreducibility states that the only accurate description of a complex system is the system itself and that no abstraction or reduction to a simpler process is possible.) Nikos A. Salingaros later detailed the laws of urban networks in Theory of the Urban Web. (Salingaros, 1998) Network connections form between nodes that are complementary, and therefore the complexity of networks depends on an increasing diversity of nodes. Salingaros describes the urban web as a system that is perpetually moving and growing, and in order to do this the urban tissue has to grow and move with it. Consider for example the smallest social network, the family. Debate over accessory units or “granny flats” has intensified as normal aging has forced the elderly out of their neighborhoods and into retirement complexes, while at the other end of the network young adults entering higher education or the labor market vanish from a subdivision, leaving a large homogeneous group of empty-nesters occupying what was once an area full of children, and often forcing school closures (a clear expression of unsustainability).

treelattice

Figure 6. A comparison of a tree pattern on the left and a semi-lattice pattern on the right. The tree structure is made of groups and sub-groups that can be manipulated separately from others. The semi-lattice pattern is purely random without distinct sub-parts.

These social networks grow more complex with increasing building density, but a forced increased in density does not force social networks to grow more complex. For instance the spontaneous settlements of slums in the developing world show remarkable resilience that authorities have had difficulty acknowledging. Because of squalid living conditions authorities have conducted campaigns to trade property in the slum for modern apartments with adequate sanitary conditions. To the authorities’ befuddlement some of the residents later returned to live in the slum in order to once again enjoy the rich social networks that had not factored in the design of the modern apartments and neighborhoods, demonstrating that the modern neighborhoods were less socially sustainable than the slums.

In commercial networks, space syntax research (Hillier, 1996), using a method for ranking nodes of semi-lattice networks, has shown that shops spontaneously organize around the multiple scales of centrality of the urban grid at its whole, creating not only commercial centers but a hierarchy of commercial centers that starts with sporadic local shops along neighborhood centers and goes all the way to a central business district located in the global center of the spatial network. The distribution of shops is therefore a probabilistic function of centrality in the urban grid. Because the information necessary to know one’s place in the hierarchy of large urban grids exceeds what is available at the design stage, and because any act of extension or transformation of the grid changes the optimal paths between any two random points of the city, it is only possible to create a distribution of use through a feedback process that begins with the grid’s real traffic and unfolds in time.

The built equilibrium

Although they may appear to be random, new buildings and developments do not arise randomly. They are programmed when the individuals who inhabit a particular place determine that the current building set no longer provides an acceptable solution to environmental conditions, some resulting from external events but some being the outcome of the process of urban growth itself. It is these contextual conditions that fluctuate randomly and throw the equilibrium of the building set out of balance. In order to restore this equilibrium there will be movement of the urban tissue by the addition or subtraction of a building or other structure. In this way an urban tissue is a system that fluctuates chaotically, but it does so in response to random events in order to restore its equilibrium.

This explains why spontaneous cities achieve a natural, “organic” morphology that art historians have had so much difficulty to describe. Every step in the movement of a spontaneous city is a local adaptation in space and time that is proportional to the length of the feedback loops and the scale of the disequilibrium. For spontaneous cities in societies that experience little change the feedback loops are short and the scale of disequilibrium small, and so the urban tissue will grow by adding sometimes as little as one room at a time to a building. Societies experiencing rapid change will produce very large additions to the urban tissue. For example, the skyscraper index correlates the construction of very tall buildings with economic boom-times, and their completion with economic busts. The physical presence of a skyscraper is thus the representation of a major disequilibrium that had to be resolved. (Thornton, 2005) The morphology of this change is fractal in a similar way that the movement of a stock market is, a pattern that Mandelbrot has studied. In general we can describe the property of a city to adapt to change as a form of time-complexity, where the problems to be solved by the system at one point in time are different from those to be solved at a later point in time. The shorter the time-span between urban tissue transformations, meaning the shorter the feedback loops of urban growth, the closer to equilibrium the urban tissue will be at any particular point in time.

Modern urban plans do not include a dimension of time, and so cannot enable the creation of new networks either internally or externally. They determine an end-state whose objective is to restore a built equilibrium through a large, often highly speculative single effort. They accomplish this by creating a large-scale node on existing networks. In order for such a plan to be attempted the state of disequilibrium in the built environment must have grown large enough to justify the immense expense of the new plan. This is why development will concentrate very large numbers of the same building program in one place, whether it is a cluster of 1000 identical single-family homes or a regional shopping mall, just like the skyscraper concentrates multiple identical floors in one place. Demand for these buildings has become so urgent that they can find a buyer despite the absence of local networks, the standardized building plan, or the monotonous setting. This is not as problematic for large cities for which a single subdivision is only a small share of the total urban fabric, but for smaller towns the same project can double the size of the urban fabric and overshoot the built equilibrium into an opposite and severe disequilibrium.

The mixed-used real estate development has attempted to recreate the sustainable features of the spontaneous city by imitating the morphology of sustainable local economic networks. It has not reintroduced the time dimension in economic network growth. Often this has resulted in a commercial sector that serves not the local neighborhood but the larger region first, consistent with the commercial sector being a product of large-scale economic network disequilibrium. In other developments the commercial sectors have struggled and been kept alive through subsidies from residential development, which is evidence of its unsustainability as part of the system.

References

Alexander, Christopher (1965). ‘A City is not a Tree’, Architectural Forum, vol. 122 no. 2
Alexander, Christopher (1975). The Oregon Experiment, Oxford University Press, USA
Hakim, Besim (2007). ‘Revitalizing Historic Towns and Heritage Districts,’ International Journal of Architectural Research, vol. 1 issue 3
Hillier, Bill (1996). Space is the Machine, Cambridge University Press, UK
Salingaros, Nikos (1998). ‘Theory of the Urban Web’, Journal of Urban Design, vol. 3
Thornton, Mark (2005). ‘Skyscrapers and Business Cycles,’ Quarterly Journal of Austrian Economics, vol. 8 no. 1
Wolfram, Stephen (2002). A New Kind of Science, Wolfram Media, USA

The Journey to Emergence

This is part I of a series of excerpts of an article to be published in the International Journal of Architectural Research entitled The Principles of Emergent Urbanism. Additional parts will be posted on this blog with the editor’s permission until the complete article appears exclusively in the journal’s upcoming issue.

Of the different domains of design urban design is an oddity. While the design of a machine can be traced to a definite, deliberate act of invention, and even the design of buildings (architecture) is rooted in known production processes, the design of cities was never seriously attempted until well after cities had become a normal, ordinary aspect of civilized living, and while the design of machines and buildings was a conscious effort to solve a particular problem or set of problems, cities appeared in the landscape spontaneously and without conscious effort. This places the efficacy of urban design in doubt. The designers of machines and buildings know fully how the processes that realize their design operate, and this knowledge allows them to predictably conceive the form they are designing. Urban designers do not enjoy such a certainty.

How is it possible for what is obviously a human artifact to arise as if by an act of nature? The theory of a spontaneous order provides an explanation. According to Friedrich A. von Hayek (Hayek, 1973) a spontaneous order arises when multiple actors spontaneously adopt a set of actions that provides them with a competitive advantage, and this behavior creates a pattern that is self-sustaining, attracting more actors and growing the pattern. This takes place without any of the actors being conscious of the creation of this pattern at an individual level. The spontaneous order is a by-product of individuals acting in pursuit of some other end.

In this way cities appear as agglomerations of individually initiated buildings along natural paths of movement, which originally do not require any act of production as dirt paths suffice. As the construction of individual buildings continues the most intensely used natural paths of movement acquire an importance that makes them unbuildable and these paths eventually form the familiar “organic” pattern of streets seen in medieval cities. This process still takes place today in areas where government is weak or dysfunctional, notably in Africa where urban planning often consists of catching up to spontaneous settlement, and in the infamous squatter slums that have proliferated in the 20th century.

transect-of-tultepec

A transect of the city of Tultepec in Mexico provides a snapshot of the different phases of spontaneous urban growth. (Google Earth image)

As urbanization becomes denser, the increasing proximity of concurrent, competing individual interests causes conflicts between the inhabitants of the emerging town. Individuals build out their properties in such a way that it interferes with others, for example by blocking paths or views. These acts threaten the sustainability of the spontaneous order, and to resolve this situation the parties involved appeal to the same judges that rule on matters of justice. These judges, again according to Hayek, are required to restore and preserve the spontaneous order with their rulings. These rulings provide the first building regulations and, when government authority becomes powerful enough to do so, are compiled into comprehensive building codes to be applied wherever the force of that government extends. (Hakim, 2001)

The compiled building codes are later brought by colonists to create new settlements, reproducing the morphology across multiple towns but each time in a pattern that is adapted to the local context. Early town planning efforts are attempts at regularizing the building codes in order to plan for long-term organization of cities, but maintain the spontaneous production process. Most notably the rapid urbanization of New York City was accomplished by very simple rules on the size of blocks laid out in the 1811 Commissioners Plan for New York. Unlike the experience of urbanization in previous centuries, where urban growth was slow and often stagnant, the urbanization of New York took place in a time of rapid social and economic changes, and the city government had to invent building codes involving issues that never could arise in a pre-capitalist society: first the tenement, then the skyscraper, and ultimately, the automobile.

Modernism: the replacement for the spontaneous order

Architects and urban planners of the early 20th century, confident in the techniques of engineering and industrial production, believed that the spontaneous city had become irrational and had to be replaced with a new design fully integrating new industrial technology. The Swiss architect Le Corbusier is famous for designing a complete city around the automobile and building models of his design. In so doing he adopted a process of urbanization that was completely planned hierarchically, applying the processes familiar to architects at the scale of an entire city. He also ridiculed the morphology of spontaneous cities as being the product of donkey-paths.

villa-radieuse

This scale model of Le Corbusier’s Plan Voisin marks the turning point where city plans as constraints on individual initiative are replaced with architectural design at the scale of millions of inhabitants. (Le Corbusier, 1964)

Although the architectural program of high-rise living of Le Corbusier was discovered to be a colossal failure, the modernist process of development replaced spontaneous urbanization in the industrialized world. The housing subdivision substituted adequately for the high-rise tower block, providing affordable housing in large numbers to a war-impoverished society. This production process is still in force today, separating cities into three distinct zones: residential subdivisions, industrial and office parks, and commercial strips.

Modern city planning has been successful at its stated objective, producing a city designed specifically around automobile use, yet it was immediately and has been perpetually the target of criticisms. Most significantly the vocabulary of these criticisms had to be invented in order to spell out the critics’ thoughts because the type of deficiency they were observing had never been seen. Words like placeless or cookie-cutter were invoked but fell on the deaf ears of urban planners who were trained in Cartesian processes and industrial production techniques.

The most devastating criticism of modernist urban planning came in the form of a sociological study and personal defense of the spontaneous city, the book Death and Life of Great American Cities by Jane Jacobs. (Jacobs, 1961) In it she described in great details how the functions of a spontaneous city related and supported each other. Her concluding chapter, the kind of problem a city is, is still the most relevant. In it she attacks the scientific foundations of urban planning at a paradigmatic level, and claims that the methodology of the life sciences, at the time undergoing the revolution created by the discovery of DNA, is the correct approach to studying cities.

Death and Life of Great American Cities has been adopted by contemporary urban planners as a textbook for urbanity. Its descriptions of the characteristics of a city are now the models upon which new developments are planned. The old urban development of housing subdivisions and office parks is being substituted for the new urban development that has streets, blocks, and mixed uses, just as Jacobs had described to be characteristic of life in the city. A major difference between Jane Jacobs’ preferred city and the new urban plans remains. The layout of mixed uses is organized and planned in the same process as Le Corbusier planned his city designs. The scientific suggestions of Jacobs have been ignored.

The discovery of emergence and complexity science

In the time since Jacobs published her attack on planning science molecular biology has made great technological achievements and provided countless insights into the morphology of life. In parallel the computer revolution has transformed the technology of every human activity, including that of design. But the computer revolution brought along some paradigm-altering discoveries along with its powerful technology. In geometry, the sudden abundance of computing power made it possible for Benoit Mandelbrot to investigate recursive functions and his discovery, fractal geometry, generated a universe of patterns that occurred in many aspects of the physical universe as well as living organisms. (Mandelbrot, 1986)

Some thinkers saw that the life sciences were part of a much more general scientific domain. They formed the Santa Fe Institute and under the label complexity studied not only organisms but also groups of organisms, weather systems, abstract computational systems and social systems. This research formed a body of theory called complexity science that has resulted in the creation of similar research institutes in many other places, including some centers dedicated specifically to urban complexity.

Their scientific revolution culminated in two major treatises within the last decade, both from physicists practicing in a field of complexity. The first was A New Kind of Science by computer scientist and mathematician Stephen Wolfram (Wolfram, 2002), where he presents an alternative scientific method necessary to explore the type of processes that traditional science has failed to explain, presenting a theory of the universe as a computational rule system instead of a mathematical system. The second was The Nature of Order (Alexander, 2004) by architect Christopher Alexander, where he presents a theory of morphogenesis for both natural physical phenomena and human productions.

A definition of emergence

To define what is meant by emergence we will use the abstract computational system upon which Wolfram bases his theories, the cellular automaton. Each cell in a row is an actor, making a decision on its next action based on its state and the states of its direct neighbors (its context). All cells share the same rule set to determine how to do this, that is to say all cells will act the same way with the same context. In this way each row is the product of the actions of the cells in a previous row, forming a feedback loop. The patterns of these rows are not in themselves interesting, but when collected in a sequence and displayed as a two-dimensional matrix, they develop complex structures in this dimension.

rule30

The 30th rule of all possible rules of one-dimensional cellular automata produces a chaotic fractal when displayed as a two-dimensional matrix, but most other rules do not create complex two-dimensional structures. The first line of the matrix is a single cell that multiplies into three cells in the second line in accordance with the transformation rules pictured below the matrix. This process is reiterated for the change from the second to the third line, and so on. All the information necessary to create structures of this complexity is contained within the rules and the matrix-generating process. (Wolfram, 2002)

The same general principle underlies all other emergent processes. In a biological organism a single cell multiplies into exponentially greater number of cells that share the same DNA rules. These cells create structures in a higher dimension, tissues and organs, which form the entire organism. In the insect world complex nests such as termite colonies emerge from the instinctual behavior of individual termites. And in urbanization, buildings form into shopping streets, industrial quarters and residential neighborhoods, themselves overlapping into a single whole system, the city.

References

Alexander, Christopher (2004). ‘The Process of Creating Life’, The Nature of Order Vol. 2, Center for Environmental Structure
Corbusier, Le (1964). La Ville Radieuse. Éléments d’une doctrine d’urbanisme pour l’équipement de la civilisation machiniste, Édition Vincent Fréal et Cie, Paris, France
Hakim, Besim (2001). ‘Julian of Ascalon’s Treatise of Construction and Design Rules from Sixth-Century Palestine,’ Journal of the Society of Architectural Historian, vol. 60 no. 1
Hayek, Friedrich A. (1973). ‘Rules and Order’, Law, Legislation and Liberty Vol. 1, Routledge and Kegan Paul, London and Henley, UK
Jacobs, J. (1961). The Death and Life of Great American Cities, Random House and Vintage Books, New York, USA
Mandelbrot, Benoit (1986). The Fractal Geometry of Nature, W.H. Freeman, New York, USA
Wolfram, Stephen (2002). A New Kind of Science, Wolfram Media, USA