Keywords

1 Introduction

One of the more interesting socio-urban dichotomies present in contemporary urbanities is the concurrent manifestation of globalisation practices that have seen cities turned into veritable test-beds of multicultural integration on the one hand, and a rise in socio-urban fragmentation and community fortification on the other. In previous research we have argued that, following Bateson’s theories on unstructured liminality, such a dichotomy confronting globalisation with confinement is a sign of a schismogenic urban development, leading to a feedback loop caused by the urban environment whereby, as Madsen & van Naerssen [9] have noted, “multiculturalism is no longer the postmodern thrill of encountering differences and creating new forms of hybrid cultures, but rather as something that separates”. A separation that finds its exemplar paradigm in the gated enclave—a type that can be simply defined in space as a single walled collection of long-term habitation possessing an exclusive open sky private commons.

Our research shows that this dichotomy however, appears to be not so much related to the individual characterisation of enclaves, but to how they function in synergy. Sadly, whilst contemporary community fortification has enjoyed growing prominence in urban research (as the work of David Harvey, Stephen Graham, Saskia Sassen, or Setha Low attest), the same has rarely translated into scientific theory founded on empirical evidence and reproducible models (the work of Laura Vaughan being a notable exception). Whilst the reasons for this handicap are numerous we can distil them into three main limitations that can be roughly categorised as technological, aetiological, and epistemological, or, in cruder terms, referring to the research instrument, the phenomenon’s origin, and its analysis. These have manifested themselves through often incomplete data, hindering the observation of the phenomena; a focus on modest cross-sectional studies leading to limited temporal inferences of the morphotype; and finally, a predominance within the fields of architecture and urban planning of, at worst, what C. P. Snow termed the ‘literary intellectuals’ in his Rede Lecture, averse to technological innovation or, at best, what Ihde termed the ‘Idealists’ [6], who consider technology as subsidiary to science, leading in our view to a focus on localised case studies with limited insight on their combined behaviour on the city as intrinsic components of a complex system. In what follows, we will briefly summarise these three limitations in Sects. 1.1–1.3, demonstrate the general methodology applied to address them within the Lisbon Metropolitan Area (AML) in Sect. 2, introduce one of the algorithms applied in Sect. 2.4, followed by some initial results for discussion.

1.1 Observing Enclaves in Place

It is hardly surprising that following a literature review on gated enclave research, it is the technological limitation through data-gathering and observation instruments that is most prevalent, as only recently has the necessary data and technology become publicly available. From the onset of research into the gated phenomenon, which for the sake of brevity we can place as Blakely and Snyder’s 1997 Fortress America [2], data acquisition has focused almost exclusively on secondary sources, raising questions of bias, imprecision or incompleteness. Blakely and Snyder’s research for instance, along with studies that capitalise on their findings, is based on data from household polls carried out by Community Associations Institute members representing the gated enclave home-owners themselves and therefore can hardly be considered impartial. To our knowledge, the scale of their study is comparable only to Atkinson’s [1] report on England’s gated enclaves and Landman’s [8] national survey of gated enclaves in South Africa, both written in the first decade of this millennium and relying on postal surveys of local planning authorities. Whilst targeting public authorities may offer greater impartiality in the survey responses, it is not void of issues, as Landman herself acknowledged. For one, certain local authorities have a vested interest in concealing the true scale of gated enclaves within their territories, but mostly they are simply not aware, due to either inadequate public surveys or a lack of consensus on what constitutes a gated enclave. These limitations were promptly encountered by Raposo [13] during her 2002 study of gated enclaves within the AML, leading her to dismiss public authorities as a viable source of data and turning instead to a survey of real estate publicity. Replacing the interlocutor however, does not solve the underlying issue, namely the reliance on secondary sources for data on an object which is neither easily defined nor discernible. The reason is simple: a survey of real estate publicity reveals only the realtor’s desired portrayal of their product to his target audience, leading to certain developments being characterised as gated enclaves when in fact they’re not and other developments clearly concealing the fact. Disconcertingly, this particular methodology failed to identify a high number of enclaves, putting the total number initially at 97 developments, significantly below our own survey results that put the number at 328 for the same period.

1.2 Observing Enclaves in Time

The aetiological limitation, involving the search for the origins and ontology of the phenomenon, is patent in the bulk of studies on gated enclaves. In the majority of cases this has led to a misconception that gated developments are a new phenomenon originating in the US during the 1970s. This incredibly short-sighted assumption which was particularly prevalent in early social criticism of gated enclaves has, thankfully, been put to rest by an increasing number of researchers in the past two decades suggesting other comparable examples in history, from the gated commons of the Western European bourgeoisie starting in the seventeenth century, through the ideal communities of the Romantic era, to the various ‘total’ or ‘disciplinary’ institutions defined by Goffman and Foucault. These early types however, were all exceptions to the residential norm of the time. They were not the rule, nor did they ever threaten to become the rule. Their influence over the city was relatively minor, in terms of both the population they housed and the urban space they occupied. All these types had their versions in Lisbon, but none can compare with the scale and extent to which contemporary gated enclaves have begun to dominate the landscape since the late 1990s. As our survey will show, to find another single architectural type that had a comparable impact on the enclosure of open space within the city and subsequent formation of private communities, we have to travel back centuries, to before the modern age of company compounds and social housing, before the enlightenment and industrial age that led to the romantic gardens, to what is commonly referred to as a much darker age in Europe and yet was responsible for originating many of the spatial and social institutions that last to this day: to the late medieval age of monastic enclosure.

1.3 Observing Enclaves in Synergy

Where we’re lucky to obtain a study relying primarily on spatial primary sources, incorporating the entire geographical extent of the affected territory and applying longitudinal analysis to assess its development, we are nevertheless often faced with a final constraint which we tentatively term epistemological as it goes to the heart of the entire research process, from data gathering, through treatment, analysis, and ultimately, interpretation. Essentially, this is chiefly a result of one’s definition of the city and consequently, of how it should be studied. The majority of studies on gated enclaves have so far presented their results as aggregate statistics varying in scale from the metropolitan level to the municipality. Such methodologies have the unfortunate consequence of interpreting gated enclaves as singular independent entities, or, at most, a conglomerate of entities with unknown relations. Consequently, such results only inform a part of reality, ignoring the intricate connections that play a vital part in urban and complex systems where the whole is greater than the sum of its parts. We would argue this has been the case with a majority of studies on architectural typology and is often repeated when researching the city as a singular object, as in Busquet’s et al. [3] momentous morphological study of urban grids, employing a methodology summarised as a “series of abstract reflections that are open to varied interpretations”. One of the fallacies of such morphological studies is that virtually their entire preoccupation and object of analysis is not the phenomenon they often seek to study (a hypothetical fragmentation of the city caused by an architectural type), but what they consider to be the causation of the phenomenon. They seek answers not in the affected territory, but through observations into what they assume shapes it. This constitutes an inversion of the hypothetico-deductive scientific method, eschewing measurement-based deductive logic in favour of pure inductive reasoning coupled with posterior measurements on a sample of hypothesised generators of the problematique. Such use of latent variable models via direct observation of disparate observable quantities is common in several fields where the object of study cannot be directly observed, either due to ineffective instrumentation or incalculable measurements. These limitations in instrumentation and computational power however, no longer apply to urban phenomena. Furthermore, the use of classical urban morphology consisting primarily of typo-morphological inventories of a limited number of urban elements, devised primarily through figure-ground representations based on Nolli maps with limited applicability, producing findings with non-objective interpretation and restricted reproducibility, is simply not compatible with our understanding both of the city as the most complex artificial entity known to man and with the various mature scientific sub-fields that have arisen in the past century specifically to study such complex phenomena.

2 Methodology

Our research on the development of gated enclaves within the AML, home to approximately 2.8 million people, has sought to address these three limitations by augmenting the quality and breadth of previous urban observations, substantially increase the temporal delimitation of the survey, whilst preserving the intricate connections and relations that play a vital part in complex systems. This was accomplished through the development of a methodology targeting bias and incompleteness of previous surveys whilst adhering to the definition of the urban as a complex artificial organism, equipping the researcher, one hopes, with the tools that allow for fine-grained long-term urban analysis, from data acquisition, through treatment, analytics, and interpretation. It does this by addressing all three limitations that have plagued a majority of studies on the problematique through an exhaustive aerial survey of the region, a secondary survey targeting the initial development of a comparable type, and the generation of digital twin models allowing for the analysis of the totality of surveyed elements and their effects on the socio-urban landscape.

2.1 Searching in Place

Our response to the first limitation—quality, integrity, and completion of observations—was implemented through an aerial survey of gated enclaves in the AML undertaken between 2016 and 2017. Rather than relying on existent or incomplete public records or publicity material, our intention was to survey de facto gated enclaves through a spatial definition stipulated as: clearly cordoned long-term habitations or collection of habitations, possessing a common open sky area, accessible by the majority of the inhabitants whilst barred to the outside public. The survey, based on ortho-rectified aerial imagery provided by Google, was carried out on a GIS platform through manual examination of the built landscape occupying a virtual square grid consisting of 11 688 0.25 km2 cells, providing a viewing scale of approximately 1:2 000 which we deemed sufficient to detect any potential gated enclaves for further inspection and final validation through street-level imagery or direct field observation. Whilst the use of remotely sensed data is more popular in other fields of study, the increase in freely available high resolution imagery has made it a viable means of observation in architecture and urban studies. This resulted in the identification, georeferencing, and characterisation of 770 inhabited gated enclaves occupying a total area of 2 260 ha.

2.2 Searching in Time

The multiple conjectures on the origin of contemporary gated enclaves have led to numerous branches within the tree of self-segregated habitation being pinpointed as proto-enclaves or the origin of this type, particularly during the late nineteenth century. We find most of the evidence severely flawed, principally because we can find alternative earlier examples that are at once more complete, mature, and achieved a far greater distribution, in number and in population, within the walls of cities, their fringes and across different continents, nations, and cultures (such as the 10th century Chinese fang or the 17th century Latin American reductions). As such we proposed to study the hypothesis that, whilst the notion of self-segregation and potentially its basic morphological representation are at least as old as cities themselves, it would be the development of coenobitic monasticism and its dissemination within Europe’s nations and overseas colonies that constitutes the typological aetiology of contemporary globalised gated enclaves as repeatable, persistent and adaptable architectural objects as defined by Moneo and Habraken [11]. This was tested within the geographic delimitations of the AML across an extended temporal delimitation covering the late medieval, through the early and late modern periods, to the current era. The identification of past and present monastic structures within the AML required the consultation of sources ranging from sixteenth century manuscripts to the latest data from the national Architectural Heritage Information System and a welcome recent survey of religious houses within the Lisbon municipality [12]. The precise location, footprint, territorial walls, and entries of the religious houses were subsequently determined through a combination of aerial imagery, street-view photography, and period sources. This resulted in the identification, georeferencing, and characterisation of 153 monastic houses at different points in history, with 140 active at its height during the decade of 1750, occupying a total area of 432 ha.

2.3 A Model for Informed Urban Analysis

The survey results are sufficient to carry out certain morphological classifications of the enclaves or simple aggregate statistical analysis based on administrative boundaries. In order to perform a fine-grained cross-sectional study at the scale of the smallest element, undertake comparative analysis with different past configurations of the city, and unmask morphological and behavioural patterns within the immaterial in-between spaces connecting urban elements, these results were introduced within a digital model of the city augmented with ancillary data acquired primarily from the 1801 and 2011 census. This data was then converted into a population dot map produced by its spatial disaggregation into a continuous surface of geo-referenced demographic information through statistical sampling based on Mennis’ [10] Intelligent Dasymetric Mapping, where each geographic point is equal to one person in space, thereby responding to possible modifiable area unit problems and ecological fallacies that may arise (see Fig. 1).

Fig. 1.
figure 1

Multi-spatial demographic metrics. The original census subtract (a) is intersected with various land-use and building footprints (b) which result in a disaggregated population point map containing socio-economic attributes through a process of empirical sampling (c). The resulting point map is then processed to inform multiple spaces, such as individual buildings (i), blocks or gated enclaves (ii), geospatial buffers or clusters (iii), isochrones (iv), sub-networks (v), and street segments (vi).

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In total, eight geographic digital models of the AML were produced: focusing on the monastic houses and covering the XVII, XVIII pre- and post-earthquake, and XIX centuries: and focusing on contemporary gated enclaves and covering the periods of 1991, 2001, 2011, and 2016. Between the dissolution of the monasteries in 1838 to the mid-1980s, no comparable occupation of land by alternative self-segregated typologies took place. As such, these two models can be seen to represent the final epoch of a form of self-segregated living that arose in Lisbon since the Second Crusade of the XII century, and its contemporary spatial equivalent. The analysis of the models—entailing the formulation of a series of methods and algorithms—works within a typical closed control research system, receiving its input from the data collection stage, calibrating the algorithms and finally constructing the specific methods and subsequent geospatial execution. These methods can summarily be partitioned and sorted by ascending scale of analysis into:

  • Descriptive which uses field and satellite imagery observations to qualify and quantify the principal observable and qualitative features of gated enclaves, thereby affording an initial set of indicators and classification of these structures.

  • Demographic which relies on population statistics and ancillary socio-economic measures obtained primarily from census and scraped public data, disaggregated and combined with quantitative metrics, to inform the spatial and structural patterns revealed within the city.

  • Morphological which, in conformity with the postulate that the shape of things have an effect on, and are affected by the environment in which they are located, we look at the finer details of the geometry of each individual enclave urban footprint, predominantly through shape metrics stemming from the field of landscape ecology.

  • Zonal which seeks to chart the extent and geometry of the specific zones within the metropolitan area that are affected by gated enclaves or demonstrate shared configurational attributes and is primarily implemented through the computation of density clusters and isochronic polygons.

  • Configurational which seeks to examine the structural configuration of the city as a single organism, implemented primarily through space syntax and derived network measures of the vehicular and pedestrian urban structure.

Each method provides its own set of measures and indicators targeting their disciplinary paradigm which are in turn aggregated to explore their effects at multiple scales within areal or linear geometries. In what follows, we present an example of measures and algorithms devised for the configurational method, which is our preferred means of addressing the third limitation.

2.4 Configurational Analysis

If gated enclaves constitute an architectural type, than their morphological characterisation would have us identify such a type in dramatically different moments in history, spread throughout considerably disparate geographies. And yet, whilst this characterisation may aid us in identifying the elements of a typological set, it does not necessarily define nor validate the typology. One of the fundamental properties of a building type is the measure of its reproduction to the extent that it has an effect on a much larger relative scale of increasing complexity. As such, its validation and ultimate definition should derive from measurable observations of its impact with reality, that is to say, the behavioural, social, economic, or environmental concerns that are defined by and define the type and which constitute our principal source of observations once we move away from the purely formal definition of the element. Consequently, our response to the final limitation is ultimately built upon an early development of complex systems studies through morphic language and graph theory, establishing a number of methodologies which Karl Kropf terms the ‘configurational approach’, and whose most mature conception is arguably Hillier & Hanson’s [5] space syntax.

In addition to computing these syntactic measures, we proceeded to devise a set of custom indicators, using street segment geometry from standard space syntax angular segmentation. We were interested in augmenting the information derived from Hillier’s methodology by introducing disaggregated population, commerce, and service sector counts onto the network. Our logic is that, as syntactic measures are often used to portray estimates of pedestrian movement, we can gain accuracy and specificity if we weight these measures with a social metric residing within the area of influence of each street segment. As such, an integrated street segment in a highly populated area would receive a higher value than a similarly integrated segment in a less populated area. This also has the advantage that the population coefficient can be qualitative, as it is based on census surveys, and therefore associated with other demographic attributes. Furthermore, such a process can be replicated for different time periods since such population counts have been taking place since at least medieval times.

Segment Population (SP), Segment Service (SS) and Segment Commerce (SC), are measures derived from a method we propose to introduce demographic and socio-economic geospatial information into angular street segment analysis. These measures represent, respectively, the resident population, number of service sector establishments, and number of commerce establishments closest to each street segment, calculated by Euclidean distance through a Voronoi tessellation of the urban mesh defined by street network segments and intersected either with a disaggregated dot distribution map of the population (allowing for further implementation of demographic measures), or the geospatial point locations of the relevant objects being measured (in this case service or commerce establishments). They can be used either independently or combined with angular segment analysis, producing population- or trade-weighted syntax measures. When implemented on the street network, we have found our SS and SC measures to be highly correlated with the space syntax measure of choice as well as pedestrian count from a modest dataset. Our SP measure however, was found to be inversely correlated to pedestrian movement, presumably an effect of the commuter town to central city pendular effect on street occupation and land value. Together, they afford our network model with some much needed local socio-economic differentiation.

Fig. 2.
figure 2

Integrating population in network analysis. From left to right: disaggregated 1801 Lisbon population dot map; resulting population by street segment voronoi cells; integration of voronoi values on network.

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Naturally, one can simply combine demographic data, in its original geographic tract unit with the aggregated street segments intersecting the unit. However, in our case, we aspired to attribute a coefficient to each individual segment, acting therefore on the original data from the space syntax analysis, in the case of combined measures, and on the original street segment geometry alone, in the case of pure population measures. To achieve this, we take advantage of a population dot map produced by the spatial disaggregation of census data into a continuous surface of georeferenced demographic information as previously described in Sect. 2.3. This time, the disaggregated population is assigned to the relevant street segment by partitioning the street network into a set of cells in such a way that the borders of each cell are at equal distance to the next closest segment through the use of Thiessen polygons, more commonly known as Voronoi diagrams. This is achieved through a series of spatial operations summarised below.

Given a space syntax network relation N, an operator pt which returns the vertices of a vector, an operator sp\(_{x}\) which splits a street segment vector geometry g into a series of vectors k at x meter intervals, and an operator vor which returns a two-dimensional Voronoi diagram from the supplied vertices, we first derive the relation R of Voronoi regions \(R_{k}\) for a street network diagram through the following expression:

$$\begin{aligned} R = \varPi _{{\text {vor}} g} \sigma _{({\text {pt}}({\text {sp}}_6 g))} (N) \end{aligned}$$
(1)

Following that, deriving the sample of a population within the sphere of influence of a network segment part k is a simple operation of counting the number of previously disaggregated population points in D within each Voronoi region R, such that the relation A containing the a attribute count of elements closest to a street segment part k can be had calculating:

$$\begin{aligned} A = \varPi _{\rho _a {\text {count}} d_g \in R_k}\sigma _a\left( \begin{array}{c} R \bowtie D\\ g \cap g \end{array}\right) \end{aligned}$$
(2)

We nevertheless need to account for the fact that our street segments are generally split into multiple lines (to afford length consistency and diminish edge effects), and that a Voronoi cell may be intersected by more than one street segment. This means that the population of a Voronoi cell belonging to a specific street segment, may be acting upon either a large or small percentage of that segment. Depending on the size of the region, the length of the segment will also differ. Finally, if other street segments are intersecting the cell, they may be more affected by the population depending how much of the cell they intersect. We therefore cannot simply attach the standardised population from a cell to the intersecting segment. Rather, we need to allocate the population to the intersecting segments according to their relative importance within the cell. We approach this issue by taking the sum of the length of the intersection of individual parts of the segment intersecting the Voronoi cell as S, and by taking the sum of the parts of the intersection of all the segments intersecting the Voronoi cell as C, such that:

$$\begin{aligned} S&= \varPi _{^\gamma n, ^\gamma r, \rho _s \sum {\Vert g \Vert }} \mathord {^{\left( \begin{array}{c} N \bowtie R\\ g \cap g \end{array}\right) }}\end{aligned}$$
(3)
$$\begin{aligned} C&= \varPi _{^\gamma r, \rho _c \sum {\Vert g \Vert }} \mathord {^{\left( \begin{array}{c} N \bowtie R\\ g \cap g \end{array}\right) }} \end{aligned}$$
(4)

Thus far we have created a Voronoi diagram where each cell represents the total number of attribute elements closest to a street segment, be they people, commerce, services, or any unique georeferenced element. To be able to apply these attributes to the network we normalise the sum of the attribute values contained in the set of Voronoi cells representing each unique network segment into a uniform range. Finally, the relation \(N_{w}\) representing the population weighted street network is derived as the sum, for all segments parts f of a unique street segment \(n \in N\), of the ratio derived from the division of s by c, calculated in Eqs. (3–4), multiplied by a scaled attribute \(a \in A\), to construct the network diagram of attributes, or multiplied by a scaled attribute \(a \in A\) and a respective syntactic measure \(n_{a} \in N\), to construct the space syntax attribute-weighted network diagram, such that:

$$\begin{aligned} N_w = \varPi _{\rho _a \left( \sum \limits _{f \in n}{\frac{s}{c} \cdot a}\right) , \dots , \rho _s \left( \sum \limits _{f \in n} {\frac{s}{c} \cdot a \cdot n_a}\right) } \mathord {^{\left( N \bowtie A \bowtie S \bowtie C\right) }} \end{aligned}$$
(5)

This final relation essentially distributes a series of attributes (consisting of population, commerce, service, integration, choice, and weighted combinations of these attributes) through the street network, allowing us to visualise the variation of effect the network has on these properties, establish correlations between street segment measures and gated enclaves, or identify socio-urban patterns (see Fig. 2). These are further explored through the use of what we term zonal methods which assume that distance and interaction are inversely proportional and therefore hold distance as the primary metric of classification. This premise was used to implement three techniques to determine the spatial extent and morphology of zones deeply affected by gated enclaves, through buffer, isochrone, and density based cluster analysis.

We generated isochrones at a variety of temporal distances for each entry point of each gated enclave within the metropolitan area, allowing us to visualise in one stroke how accessible these enclaves are, how far their accessibility extends, to which urban areas this access is granted, and what urban pockets are excluded. In addition, we generated similar isochrones for the walled perimeter of the enclaves. This in turn allowed us to visualise the reach and area of influence that these walled obstacles and blind façades generate on urban mobility. The isochrone maps we’ve produced for the AML covering different eras from the fifteenth to the twenty-first century, all focus on answering the same key question, which is to uncover how the spatial-temporal spheres of influence of gated enclaves manifest themselves in the city. Combined with disaggregated or segment data, they become isochronic aggregators of spatio-temporal properties focusing on the space of public movement. For both isochrone and density clusters this can be achieved by calculating the total public street segment attributes within the area of influence as summarised in Eq. 6, where P represents the target area’s street segment population estimate, W represents the target area’s street segment geometric intersection ratio, and M the original target street segment attributes.

$$\begin{aligned} A = \varPi _{\left( \frac{P_{s} \cdot W_{w}}{{\text {max}}\left( P_{p}\right) }+1\right) \cdot M_{x}}\left( P \bowtie W \bowtie M \right) \end{aligned}$$
(6)

3 Results

At the small printed scale, the isochrone maps provide a good macro perspective of the region’s enclaves, showing how these are distributed along the system’s network, and where and how a single architectural type is responsible for substantial occupation at strategic points within the grid. Figure 3 depicts the area of influence created by gated enclave footprints, represented through isochrones calculated for 5-, 10-, and 15-min intervals for the walled footprint of all 768 gated enclaves found to be active in 2016 within the AML for three different scenarios. These areas of influence can be directly compared to our 1821 model of the same geographic extent, revealing a staggering increase in scale, extent, and coverage of the influence areas. The sum total area of the 15-min pedestrian isochrones increases seven-fold, in line with the upsurge in number of enclaves. And while this area of influence is now more fragmented due to the higher number of enclaves in the contemporary model, the inverse is true once we account for contemporary modes of transportation, where we observe between five isochrone regions covering 37% of the area’s landmass for a 15-min vehicle isochrone during peak times to a singular region covering 67% of the metropolitan area’s landmass during low traffic. Moreover, it is not just the areas of influence that occupy a significant portion. In certain municipalities for instance, the land occupied by the walled area of gated enclaves exceeds that occupied by all other residential types combined. Whether we focus on the isochrones or the enclave footprints, the growth in urban occupation during both the medieval and contemporary periods is vertiginous.

Fig. 3.
figure 3

AML delimitation in 2016 depicting gated enclaves, in black, and isochrones of enclave walls for the, from left to right, pedestrian network, high traffic, and low traffic vehicle network.

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If we add the street network graduated according to the space syntax measure of global angular segment choice, which has been shown to be a faithful measure of pedestrian movement, we achieve a model that is designed to portray the physical and cognitive impact of the enclave walls on the public street network, rather than the accessibility of the enclave entry points, and consequently, is particularly suited as a street-perspective counterpart to spatial analysis. What our observations on the dynamics of the bulk of monastic houses in the region have shown, is that the traditional view that these structures functioned as population attractors playing a vital part in the foundation of new settlements, is not portrayed in either their materiality which is designed to deter entry, the low relative population of their particular locations within the region, the morphology of their footprints which minimise contact with the network, and through their interaction with the local settlements, which portrays a constant that we have found repeatedly in our observations within the AML, century upon century, and produce one of the great contradictions of this typology, one that harkens back to the early prototypical forms of gated enclaves springing in the Nitrian desert at the doorsteps to Alexandria nearly two millennia ago. It is the need to be at once close to population centres whilst yearning to remove themselves from them. This contradiction has been a constant of gated enclaves and its inhabitants, from the earliest forms of asceticism, eremitism, and cenobitic monasticism—they are all a reaction to the city, and therefore, inexplicably linked to it.

Such observations however, continue to be somewhat subjective, hindered as they are by the limitations of the human eye and cartographic visualisation. These become harder to sustain the more complex the network becomes and the more built structures we have to examine. It is necessary therefore to leave the domain of cartographic representations of space and enter the fields of statistical analysis, data visualisation, and probabilistic pattern recognition, where we can handle a much greater quantity of data, visualise multiple scales and measures simultaneously, while generating interactive reproducible computational workflows.

Fig. 4.
figure 4

Angular integration in the 2016 AML network and its enclaves. Left: r = n. Middle: r = 2400. Right: Kernel density of NAIN for closest street segment to all gated enclaves (GE), vs all residential buildings (AML).

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A simple example can be had through a kernel density plot comparing the behaviour in probability density of normalised angular integration (NAIN) for the closest street segment to gated enclave walls, to that of all other predominantly residential buildings in the AML. This results in a similar, yet negatively shifted (by approximately 12%), multimodal distribution, whereupon the mean syntactic measure for NAIN for the entire universe of surveyed gated enclaves is lower than that for the remaining residential built types occupying the AML region (see Fig. 4). It seems therefore that gated enclaves are associated with lower levels of street network integration. However one views gated enclaves, as urban attractors or detractors, generators or impediments of local socio-urban development, in the AML they are consistently associated with a decreased level of urban integration in the street network, creating a disruption in the wider street grid system in addition to the obstructions already created by their walls. This reduction, by operating within the medium and global foreground grid, takes on a life of its own, disseminating its impact across the network to affect a much wider area than other forms of residential constructions are typically capable of, but also to subvert the effects of what are traditionally recognised to be socio-urban attractors.

Integration however, is only part of the story surrounding gated enclaves. At the local scale, where we study the behaviour of through-movement within the local grid systems surrounding gated enclaves through segment angular choice, the mutually exclusive constant of enclaves being at once part of the city and apart from it becomes apparent, with reproducible results that are at once more complex to interpret, and pose some uncomfortable questions. It is here that we observe a high frequency of zero-choice street segments within the areas of influence of both medieval and contemporary enclaves. These tend to represent the dead-end streets artificially created by the gates. But even if one were to remove the gates, open up the enclaves so to speak, these would remain dead-end streets, reducing choice and flow within the network. Little is achieved by opening up enclaves in this way. We also observe differences among these measures depending on whether the foci are the gates, the walls, or the surrounding extramural local network grids. Gates are the most integrated and have the least choice, walls have higher levels of choice, whilst the perimeter has the highest SP values. This describes a reproducible environment amongst gated enclaves of a strong residential area on its periphery, exhibiting high street population SP values, surrounded by a network with stifled through-movement potential, and exhibiting high relative choice but low commercial SC and SS values, leading to enclave gates that are globally integrated within the city whilst locally marginalised. To put it in another way, gated enclaves not only segregate through walls. We have found that they also segregate through the topology of the surrounding road network and the morphology of their urban footprints, and they do so consistently and repeatedly, across several scales, epochs, and diverse locations within the Lisbon Metropolitan Area.

4 Conclusion

If the measure of successful methodology is the questions it unearths rather than those it answers, than we have, unfortunately, met our goal. For the initial dichotomy that informed our problematique has led us to identify a second dichotomy. Why is it that enclave gates, being the area of highest relative integration, are also the area with the lowest relative choice? It helps to understand what exactly normalised angular choice measures in space syntax. It is often used as a predictor of movement, and for good reason, but it is nevertheless based on the graph theory measure of betweenness centrality, which measures the degree to which a node is likely to lie in between others, and therefore more connected to others. The most connected node was initially termed ‘the relayer’ by Marvin Shaw, representing the point with most potential for control of the system’s information flow, precisely because it was the point through which most information passed. The entry points of gated enclaves may be consistently well integrated within the network, but they nevertheless remain isolated from it—they receive little to no information from outside their exclusive private network, and as such, they complete the apparently mutually exclusive constant of being at once part of the city and apart from it. Conversely, the low integration and high choice present within the sub-grids emanating from the streets lining the exterior of the enclave walls, exacerbated by high SP and low SC and SS values, suggest that whilst gated enclaves are located adjacent to, or artificially create, connection routes between the various sub-centres in their vicinity, the potential for connection is not realised. The ‘relayer’ has essentially been cut. As such, where G represents the gates, P represents the perimeter of the urban footprint, i and c their respective integration and choice values, a standard gated enclave type E can be summarised as \(E = G_i > P_i \wedge G_c < P_c\).

Combined with the withdrawn circular morphology of enclaves and the exposed structure of the adjacent residential background grid, what we obtain, in laymen’s terms, is the prime routes for a series of local highways connecting all neighbouring sub-centres. But this comes at a cost. These local highways are in turn affected by the hermetic qualities of the adjacent enclave walls or blind arcades, which act as both a physical deterrent, on the enclave side, and a cognitive deterrent, on the city side, to local and micro socio-economic activity, depopulating the streets from pedestrians and further increasing the vehicle-centric focus of the road. What we end up with is not only a hermetic occupation of varying extents of land on the part of gated enclaves, but equally the suppression of adjacent pedestrian traffic and socio-economic micro-structures on the very routes that are most appropriate to sustain them within the local background grid subsystems.

The streets that most suffer from socio-urban desertification throughout the Lisbon Metropolitan Area are the streets that were best placed to accommodate it. It is the paradox that emanates from betweenness centrality. For an element to be located within a privileged position of a network system in such a way that communication favours running through it, to be in such a position of control, the element must also be exposed to the system and therefore exposed to attacks by forces within the system. The most effective way of disrupting a connected system is by targeting its most central and exposed node. This is precisely what is taking place with gated enclaves in the AML. The danger here is that removing highly connected nodes can have serious consequences—in the extreme it can split the global system into multiple independent components. And yet there are hundreds of gated enclaves, and thousands of circulation routes surrounding them all of which are adding to the disruption and segregation of the system. In this sense, one need not wait for some kind of post-enclave counteraction emanating from a feedback loop due to symmetric schismogenesis. The system can be brought down, and is being brought down, by the gated enclaves themselves.

This brings us to a delicate final question. Are gated enclaves a foreign, generic, and universal product of the foreground grid injected into the culturally specific background grid of the city? An initially top-down process descending from global capital and used as mechanisms of neoliberal localisation, in turn reinforced bottom up through a global scalar structuration often termed glocalization? Or are they instead, ultimately a universal product, but generated predominantly within the background grid in a bottom-up democratic process, revealing a basic and primordial characteristic of human dwelling and socialisation? The political and socio-economic background of a series of intensified periods of gated enclave development during the past millennia both in Lisbon and other cities we have studied, combined with a predominance of street segments with zero-choice values within the immediacy of enclaves, and further taking into account Coates findings of zero-choice as a possible indicator of autopoeitic urban genesis in his 1970s Damascene models [4], leads us to suggest that gated enclaves, and their interaction with the city, may represent a basic characteristic of urban development. That perhaps the cities-first social model of trade and interaction that Jacobs [7] favoured should be seen as cities-last, with trade and integration a consequence of posterior top-down correction of an unstable, defensive reality.