Bill Hillier of Space Syntax is, along with Christopher Alexander and Michael Batty, part of the British old school of urban complexity researchers. (Hillier has joked that he would have used the term "Pattern Language" instead of Space Syntax had Alexander not used it first.) He has studied the functional impact of spatial relationships on human behavior over a career spanning several decades, and came upon some very insightful results. The synthesis of his career was published last year in the book Space is the Machine, which you can read here.

Hillier presents a theory of urban emergence founded upon two ideas. First, that circulation in a city is determined by the configuration of lines into a global hierarchy of depth, which he calls integration. Second, that activities in the city adapt to take maximum advantage of this movement, a phenomenon he calls a "movement economy."

How did he draw this conclusion? By observing that integration of lines could predict where all the major shopping streets in London are.

Which then is primary? Let us argue this through the spatial distribution of retail, the commonest non-residential land use. We may already have been suspected of having confused the effects of spatial configuration on movement with the effect of shops. Are not the shops the main attractors of movement? And do they not lie on the main integrators? This is of course true. But it does not undermine what is being said about the structure of the grid as the prime determinant of movement. On the contrary it makes the argument far more powerful. Both the shops and the people are found on main integrators, but the question is: why are the shops there? The presence of shops can attract people but they cannot change the integration value of a line, since this is purely a spatial measure of the position of the line in the grid. It can only be that the shops were selectively located on integrating lines, and this must be because they are the lines which naturally carry the most movement. So, far from explaining away the relation between grid structure and movement by pointing to the shops, we have explained the location
of the shops by pointing to the relation between grid and movement. (SITM 125)

Once it has been demonstrated that it is the global network structure that determines where most of the movement will go, not any particular destination, then what remains to do is to exploit this movement. This is the movement economy. It is, in one sense or another, behind every act of urbanism, operating at every scale.

Every trip in an urban system has three elements: an origin, a destination, and the series of spaces that are passed through on the way from one to the other. We can think of passage through these spaces as the by-product of going from a to b. We already know that this byproduct, when taken at the aggregate level, is determined by the structure of the grid, even if the location of all the a’s and b’s is not.

Location in the grid therefore has a crucial effect. It either increases or diminishes the degree to which movement by-product is available as potential contact. As we saw in the coloured-up maps, this applies not only to individual lines, but to the groups of lines that make up local areas. Thus there will be more integrating and less integrating areas, depending on how the internal structure of the area is married into the larger-scale structure of the grid, and this will mean also areas with more by-product and areas with less.

Now if cities are, as they were always said to be, ‘mechanisms for generating contact’, then this means that some locations have more potential than others because they have more by-product and this will depend on the structure of the grid and how they relate to it. Such locations will therefore tend to have higher densities of development to take advantage of this, and higher densities will in turn have a multiplier effect. This will in turn attract new buildings and uses, to take advantage of the multiplier effect. It is this positive feedback loop built on a foundation of the relation between the grid structure and movement this gives rise to the urban buzz, which we prefer to be romantic or mystical about, but which arises from the co-incidence in certain locations of large numbers of different activities involving people going about their business in different ways. (SITM 126)

From this knowledge, we can arrive at a paradigmatic definition of urbanity. A space can be considered urban if it makes maximum economy of the movement that passes through it. A city, at any scale, will be qualified as a good city if the experience of movement is not felt as a burden but as an opportunity and pleasure.

A visitor from Canada once remarked to me that he had walked from the Eiffel tower to the Pantheon, a trip of more than 4 kilometers, without feeling the distance. This is something he could never have done back home, where inevitably one would run into long stretches of mind-numbing repetition or parking lots. Paris, on the other hand, offered him a path through the city that was rewarding his presence. Certainly the excellent late 19th-century residential architecture plays a role in creating a basic comfort level, but architecture alone does not distract for such a long distance.

Paris is known as a city of highly sophisticated urbanity, and this is attributable to the efficient movement economy that was seeded there during the Haussmannian period. The most integrated lines, the typical boulevards and avenues, have been constructed in such a way that they make maximum use of residual movement. And what may be most surprising, a revelation that the occasional tourist will miss out on, is that the least integrated lines, the common residential streets, are generally quite boring, bordering on unpleasant. They are rarely seen by anyone except their residents due to their spatial segregation. It is safe to say, then, that the "real" Paris, what makes the city worth visiting, are its highly integrated spaces.

How do these spaces realize movement economies? Firstly they provide multiple scales of movement as well as the interfaces between those scales of movement. The grand avenues centered on the Arc de Triomphe are in fact three different scales of movement: promenade, street and highway, connecting into each other. While someone crossing the city in an automobile would be exposed to all the activity taking place on the promenades, he could decide to pull over into the street section, curb-separated from the highway section, and park his car in an available spot, then walk to his chosen destination. While walking there, he encounters shops he could stop in if it occurred to him to make a purchase. Restaurants and fast-food outlets provide him with a convenient option for dining. On the street side, news kiosks offer him information and headlines. All of this benefits him and occupies his mind at no cost as he was already taking this path for other reasons.

While he is walking to his destination, people are sitting in sidewalk terraces drinking beer and coffee, watching him walk by. They are also taking advantage of movement. William H. Whyte, author of the classic The Social Life of Small Urban Spaces, observed that the primary activity that takes place in plazas is people-watching, people moving through that is. On the Avenue des Champs-Élysées, the most trafficked in the city, restaurants have outdoor dining rooms right between the highway and the pedestrian flow. They are highly prized, despite the noise and wind, because people enjoy watching the movement.

Since Alphand, the city of Paris has split promenades into three strips. The center strip is the open space through which pedestrians walk. The street-side strip is for street furniture such as kiosks, public washrooms, benches, bus stops, and so on. The building-side strip is for "concessionaires", retailers and restaurants renting a part of the street to open their space to the exterior. The formula for a good promenade is that simple.

Needless to say, it takes quite a lot of movement to support so many mutually-dependent activities. But high-end avenues are not the only spaces that can take advantage of movement economies. Urban movement is fractal (it occurs at all scales). Hillier found that placing a limit on the range of movement, one obtained a local integration map that was different than the global integration map, and the movement in this locally integrated space was qualitatively different than global movement. These locally integrated paths develop local movement economies of their own. Typically, while highly integrated paths will become high-end shopping streets, locally integrated paths will be neighborhood service streets. Instead of trendy restaurants, fashion boutiques and cinemas, you find supermarkets, bakeries, post offices and cafes. And when we look at things with enough abstraction, we can see that even a shopping mall is a form of locally-integrated movement economy, where anchors terminate important axis and boutiques support each other by intercepting movement. Kiosks and cafes now take up even more space in the center of shopping mall promenades than they do in Parisian boulevards. It should be no surprise that people who live in suburban cities reflexively head to the mall for activity. Shopping malls, in the suburbs, have the most densely developed movement economies!

Besides creating commercial potential, movement economies also provide security. This is something that Jane Jacobs insisted on in Death and Life of Great American Cities through her concept of eyes on the street, but Hillier found an inverse statistical correlation between burglaries and spatial integration. What this brings us to is that there is a lower bound to urbanity, that we have defined as the realization of movement economies, where spaces lose integration and become segregated. If there is not enough movement, there is no purpose to public space. This is the point where public space becomes pathological, and where "defensible space" becomes necessary. Disastrous social housing projects have become the textbook case for failed public space, and their segregation explains their pathologies.

Parisian urbanism offers another excellent solution out of this problem. While the avenues are congested and noisy, full of life and activity, the lots are organized as courtyards from which several buildings are accessible. These courtyards are locked behind digitally-secured coach doors. It is rarely the case that one is invited to a dinner party without being given several "digicodes" to get through the secured, segregated spaces. Once in the courtyard, the noisy street becomes peaceful silence. These courtyards are functionally identical to the despised suburban cul-de-sac. But the cul-de-sac is not the problem, the streets they connect to are the problem. Paris balances two extremes, highly public, highly integrated space and completely private, gated space, side-by-side, supporting each other. Manhattan's street-and-skyscraper urbanism is essentially the same, except that instead of going deep away from the street, one has to go up after entering segregated space.

New Urbanists in America and compact city advocates in Europe insist on having fully open grids, sometimes with alleys, instead of cul-de-sacs. There is nothing wrong with a cul-de-sac in itself; it is only a large residential building turned on its side. The important work is creating density in highly integrated lines. Arturo Soria y Mata invented the linear city in the 19th century as a utopia, but in reality, all cities are linear cities, functioning at fractal scales. The realization that the spatial integrity of the line is more important than anything that goes on behind the buildings occurred to me while taking a bus through the west Paris city of Nanterre, widely acknowledged to be a wasteland. The line the bus was taking was well composed, and I did not realize where I was until I caught a glimpse of wasteland Nanterre in a gap between two buildings. So far as anyone on that street was concerned, this didn't affect them negatively. That is how resilient urban fabric can be.

Afterword

From Space is the Machine, global and local integration maps of Central London.

Self-organization of cities around natural movement is an important demonstration of complexity. Without anyone having willed or designed it that way, the aggregate actions of the millions of residents of London, all randomly travelling from one point to another of the network, resulted in the production of a fractal structure of the urban grid.

References

Bill Hillier. Space is the Machine
New Science. New Urbanism. New Architecture - Proceedings from a London conference, Katarxis.