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## SVG <path> elementComplexity in Urbanism

Complex systems theory consolidates developments from several fields spanning evolutionary theory, computer science, information theory, and network analysis. There is some debate about whether and how ‘Complexity Science’ should be defined (Haken 2012), with attempts at formalisation broaching conceptions such as size, entropy, algorithmic information content, logical depth, statistical complexity, fractal complexity, and hierarchical complexity (Mitchell 2009, p.96–100). More simply, collections of agents demonstrating emergent dynamics transcending the wherewithal of the individual elements characterises a complex system; thus, systems “in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution” (Mitchell 2009, pp.13, 94). The now prevalent application of complex systems theories to cities (Batty & Longley 1994; Batty 2005; Portugali 2012) heralds a shift in conception from static to dynamic and from top-down to bottom-up, in effect recognising cities as out-of-equilibrium systems that can exhibit hard to predict emergent phenomena.

Earlier rumination on these themes can be traced back to three prominent urban theorists. The first, Patrick Geddes, initially trained as a biologist and used ecological metaphors to describe the complex processes he observed in cities. He advocated conservative surgery consisting of contextually appropriate and smaller-scaled planning interventions that are sensitive to bottom-up evolutionary dynamics (Geddes 1915; Batty & Marshall 2012). Though unappreciative of Geddes’ background and thinking, Jane Jacobs subsequently developed this theme and insisted that small-scale particularities and ‘unaverages’ — obscured by aggregate statistical methods — are critical to understanding how cities work. She argues that any analysis of cities must proceed from “particulars to the general, rather than the reverse” and that it is necessary to “seek for ‘unaverage’ clues involving very small quantities, which reveal the way larger and more ‘average’ quantities are operating” (Jacobs 1961, p.440). In associating particularities with the emergent and dynamic systems-level processes they generate, she makes the first explicit link from The Kind of Problem a City Is to cities as complex systems. Jacobs’ contemporary, Christopher Alexander, puts forward a complementary argument. He argues that modernist approaches to problem-solving in architecture and urban planning are reductionist and result in inferior outcomes compared to traditional methods, wherein incremental and iterative feedback processes — akin to contemporary conceptions of complex systems — generate successful solutions in the form of time-tested traditions. (Alexander 1964) (Traditionalist aesthetic interpretations, as advocated by some of Alexander’s more ardent disciples, need not necessarily be conflated with this notion).

Implicit within Jacobs’ and Alexander’s hypotheses is the understanding that cities are systems of networks energised by diverse assortments of functions, thus presaging an emerging complex systems interpretation of cities going beyond strictly spatial and visual conceptions of urban space to acknowledge the flows engendered by those spaces explicitly. Cities are thus “constellations of interactions, communications, relations, flows, and networks… location is, in effect, a synthesis of interactions” (Batty 2013, pp.13, 15). This view denotes a dynamic interpretation of cities complete with feedback processes, self-organisation, and emergent behaviour, a perspective that is difficult to reconcile with the intentionality required of urban master-planning, which favours the abrupt imposition of large and rigid spatial arrangements that can incapacitate the more gradual and contextual self-organising character of cities as evolutionary artefacts (Marshall 2009; Marshall 2012; Portugali 2012). The low-density sprawl of North American suburbia represents this conundrum in its most extreme, the characteristics of which represent a complete inversion of the dynamics exhibited by more incrementally developed cities: buildings detach from their surroundings by focusing inwards and minimising spatial and functional integration with adjacent streets (as typified by garage-lined residential cul-de-sacs, office parks, and big-box stores); road networks selectively connect distant places at the expense of local connectivity, resulting in fragmented spaces where social and functional integration is discouraged or, in extreme cases, specifically prohibited by gated communities; and, streets and interstitial space cease to function as spatially connective tissue and have no social or functional capacity for use as public space (Graham & Marvin 2001; Katz 1994; Langdon 1994; Duany et al. 2000; Ellin 1999; Gehl & Gemzøe 2000; Salingaros 2000).

Jacobs and Alexander posit that urban planners can take specific morphological characteristics into account, allowing evolutionary forms of urban dynamics to unfold unimpeded across space and time. These approaches are arguably replicable in new development by following principles encapsulated by Jacobs’ ‘generators of diversity’ and echoed in various incarnations of contemporary urban design philosophies. Assumption of simplistic links between the spatial form of cities and their social and economic characteristics is not to be assumed. These design principles permit rather than coerce the dynamics which may consequently unfold. Therefore, whereas sufficiently fine-scaled, mixed-use, and densely interconnected urban environments can support large sets of combinatorial possibilities across space, the exact expression of these configurations arise from bottom-up processes as they unfold, or, if initially imposed in the form of master plans, should be permitted to adapt over time in response to evolving pressures. Dense, walkable, and mixed-use urban substrates are, for the same reasons, not necessarily at odds with the advent of recent changes such as online shopping and services. On the contrary — and unlike suburbia’s hegemonic shopping malls — granular substrates have a substantial capacity for resilience because they permit incremental adaptations as the nature and role of spatial networks change over time. Thus, by way of example, we observe high-streets evolving towards social and specialist services: coffee shops, boutique stores, eateries, local grocers, convenience stores, post offices, and so forth, and away from traditional services now better consumed through online interfaces, such as banks and department stores.

It is in the above-described sense that urbanism is akin to computational substrates resembling cellular automata (Wolfram 2002; Salingaros 2012). Suburbia represents one extreme, an amnesiac non-computational state in which the ‘fast dynamics’ — flows of urban energy generated by social and economic activity — remain detached from the ‘slow dynamics’ of the urban fabric. These are brittle substrates: they take tremendous energy to create or change and cannot, therefore, adapt in response to small fluctuations accumulating through time. Conversely, granular urban substrates and the ensuing complexity and unpredictability that unfolds therein represents a computational state through the lens of complex adaptive systems, wherein “the fast dynamics of the flows are successfully coupled to the slow dynamics of long-term adaptation and evolution” (Holland 1995, p.166). This slow-fast coupling of information allows the feedback over time between the urban substrate — the mix and intensities of land-uses — and the flows of ‘energy’ that unfold through these spaces, thus permitting co-evolution to an edge of chaos wherein streets, neighbourhoods, and districts compete to seek-out and harness the flows and their endless permutations evolving through time.

If applied judiciously, complexity theories offer a means to bridge the sometimes disjointed qualitative and quantitative approaches towards cities (Portugali 2012). Notably, a complex systems lens provides a substantive theoretical basis underpinning qualitative interpretations of urbanism while providing a link to the quantitative methods further developed in this work. Street network centrality methods derived from network science and mixed-use measures derived from information theories are here explicitly interpreted as proxies for potentially complex cascades of interactions to unfold across a given urban substrate.

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