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Complexity and Urban Coherence

NIKOS A. SALINGAROS Division of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA. Email: Journal of Urban Design, vol. 5 (2000), pages 291-316. Carfax Publishing, Taylor & Francis Ltd.

ABSTRACT. Structural principles developed in biology, computer science, and economics are applied here to urban design. The coherence of urban form can be understood from the theory of complex interacting systems. Complex large-scale wholes are assembled from tightly interacting subunits on many different levels of scale, in a hierarchy going down to the natural structure of materials. A variety of elements and functions on the small scale is necessary for large-scale coherence. Dead urban and suburban regions may be resurrected in part by reconnecting their geometry. If these suggestions are put into practice, new projects could even approach the coherence that characterizes the best-loved urban regions built in the past. The proposed design rules differ radically from ones in use today. In a major revision of contemporary urban practice, it is shown that grid alignment does not connect a city, giving only the misleading impression of doing so. Although these ideas are consistent with the New Urbanism, they come from science and are independent of traditional urbanist arguments.

IntroductionThis paper uses scientific principles to understand urban coherence. From small manmade objects -- such as sculptures, pottery, and textiles -- to buildings, the best examples share a particular geometrical quality. Though not usually viewed from this perspective, we will argue that the form of cities and the urban fabric is also governed by the same general rules. Geometrical principles that produce a beautiful sculpture or textile generate a positive emotional response: can we identify similar rules for an urban setting the size of a neighborhood or an entire city? If so, then the resonance with human beings that characterizes great urban environments could be explainable in terms of geometry. The

ideas developed here have been encouraged by recent work of Christopher Alexander (Alexander, 2000). An essential quality shared by all living cities is a high degree of organized complexity (Jacobs, 1961). The geometrical assembly of elements to achieve coherence results in a definite and identifiable urban morphology. It turns out that this morphology closely resembles that of traditional cities and towns: unplanned villages of many different cultures around the world; cities as they were before the middle of the nineteenth century; and to some degree, free squatter settlements. The morphology of a geometrically coherent system resembles planned twentieth-century cities the least of all. Contemporary rules for urban form, which reduce both complexity and connectivity in today's cities, are not capable of generating urban coherence. We analyze why this is so, and offer new rules that do. Different components of the urban fabric: streets, shops, offices, houses, pedestrian zones, green spaces, plazas, parking lots, etc. connect to generate a successful city, creating an efficient, livable, and psychologically nourishing human environment. The success of the result depends on geometrical coherence. The transportation network defines city form; a city lives and works according to its network of connective paths (Alexander, Neis et al., 1987; Hillier, 1999; Salingaros, 1998). In addition, it will have pedestrian life if its urban spaces accommodate and support pedestrian paths (Alexander, Neis et al., 1987; Gehl, 1987; Hillier, 1997; Salingaros, 1999). A third, purely geometrical factor -- urban coherence -- determines the success of a city, and has its own set of rules. These need to be studied independently of the path structure and the formation of urban spaces. To achieve geometrical coherence in any system, a tightly-knit and complex whole is generated via general rules. Geometrical coherence is an identifiable quality that ties the city together through form, and is an essential prerequisite for the vitality of the urban fabric. The underlying idea is very simple: a city is a network of paths, which are topologically deformable (Salingaros, 1998). Coherent city form must also be plastic; i.e., able to follow the bending, extension, and compression of paths without tearing. In order to do this, the urban fabric must be strongly connected on the smallest scale, and loosely connected on the largest scale. Connectivity on all scales thus leads to urban coherence. In living cities, every urban element is formed by the combination of subelements defined on a hierarchy of different scales. Complementary elements of roughly the same size couple strongly to become an element of the next-higher order in size (Salingaros, 1995). Different types of connections tie elements of different sizes together, so that every element is linked to every other element. The strongest connections are local (closerange) ones. Connections between smaller and larger elements, or between internal subelements of distinct modules, are weaker. Repeated similar units do not connect: coupling works either by contrasting qualities, or via an intermediate catalyst. Elements are therefore necessary, not only for their own primary function, but also for their secondary role in linking other elements that cannot couple directly by themselves.

This paper presents theoretical rules for assembling components into coherent wholes, developed outside urbanism. The components that influence urban morphology are then reviewed. We derive and explain geometrical coherence, while at the same time applying the proposed rules to analyze the urban fabric on successive scales. First, we identify the basic interactions between components on the small scale. Fractal interfaces and the autocatalytic threshold are discussed. We then review modular decomposition, and Alexander's Pattern Language. After this, we examine ordering mechanisms on the large scale. The key role of entropy in alignment forces is explained. Finally, these ideas are applied to cities. We emphasize the need for mixed use, and argue that long-term stability depends upon allowing for emergent connections.

Rules for geometrical coherenceIn a general complex system, as for example an organism or a large computer program, certain rules of assembly are followed so that the parts cooperate and the whole functions well. There is little formal difference between such systems and the urban fabric (Lozano, 1990). A few structural rules have evolved in the study of complex systems. Initially stated by Herbert Simon for economics (Simon, 1962; Simon and Ando, 1961), some were re-invented in the context of computer programming (Booch, 1991; Courtois, 1985; Pree, 1995). Others appeared independently in engineering and biology (Mesarovic, Macko et al., 1970; Miller, 1978; Passioura, 1979). Of the many different possible statements of system rules, the following list is critically relevant to urban design.

Rule 1. COUPLINGS: Strongly-coupled elements on the same scale form a module. There should be no unconnected elements inside a module. Rule 2. DIVERSITY: Similar elements do not couple. A critical diversity of different elements is needed because some will catalyze couplings between others. Rule 3. BOUNDARIES: Different modules couple via their boundary elements. Connections form between modules, and not between their internal elements. Rule 4. FORCES: Interactions are naturally strongest on the smallest scale, and weakest on the largest scale. Reversing them generates pathologies. Rule 5. ORGANIZATION: Long-range forces create the large scale from welldefined structure on the smaller scales. Alignment does not establish, but can destroy short-range couplings. Rule 6. HIERARCHY: A system's components assemble progressively from small to large. This process generates linked units defined on many distinct scales. Rule 7. INTERDEPENDENCE: Elements and modules on different scales do not depend on each other in a symmetric manner: a higher scale requires all lower scales, but not vice versa. Rule 8. DECOMPOSITION: A coherent system cannot be completely decomposed into constituent parts. There exist many inequivalent decompositions based on different types of units.

These eight rules are offered as generic principles of urban form. We will be analyzing in some detail where the rules come from, giving original arguments with visual, scientific, and urban examples. The whole point is to convince the reader of their inevitability in assembling a living city. A system's development in time defines an underlying sequence. The smaller scales need to be defined before the larger scales: their elements must couple in a stable manner before the higher-order modules can even begin to form and interact. Elements on the smallest scale, along with their couplings, thus provide the foundations for the entire structure. Requiring a hierarchy of nested scales means that not even one scale can be missing, otherwise the whole system is unstable. The coherence of a complex interacting system may be understood as it connects progressively. During a short time period, strong couplings will establish internal equilibrium in each module, with little change in the relationship among different modules. (One analogy is the initial formation of many small isolated crystals in a solution). Over a longer time period, the weaker couplings between modules will take them towards a larger-order equilibrium, while their internal equilibria are of course maintained. The process iterates, so that on even longer time periods, modules of modules tend towards equilibrium, and so on. The end result is a global equilibrium state for the entire system (corresponding to a single complex crystal).

Components of the urban fab