Mark David Major, Velina Mirincheva, Heba O.Tannous

Introduction

In The Social Logic of Space, Hillier and Hanson(1984) identify a restricted random process based on simple rules of adjacency and permeability in giving rise to a characteristic ‘deformed wheel’spatial structure in small European settlements,which tends to structure spatial layout like a wheel and spokes in a non-geometrical fashion from center to edge. Subsequently, Hillier (1989)identifies three laws of the urban object; namely physical, functional, and cultural, which are all related to generic function - the most basic requirements of occupation and movement - to one degree or another in settlements (Hillier,1996; Major, 2018). Over time, deformed grid settlements tend to develop a distinctive ‘hidden geometry’ of open- and near-right angles related to macro- and micro-scale movement patterns of transaction and access in the foreground and background network of cities, respectively (Hillier, 1999 and 2002). In The Syntax of City Space,Major (2018) identifies a limited set of spatio-formal processes - street extension, block manipulation, grid expansion and deformation, and discrete separation - shaping the urban morphology of American cities (Major, 2013). Geometry in the American urban pattern allows for easier identification of these processes but they appear universal to all cities at varying scales in resolving Hillier’s(1996) paradox of centrality and linearity, i.e., the most internally integrating shape is a circle (akin to an urban block) and most externally integrating shape is a line (akin to a street) (Major, 2018).

A key part of the story is missing, which is the urban morphology of settlements in the Middle East North Africa (MENA) region. This is unsurprising despite periodic research about such settlements using space syntax over the previous three decades. Urbanism in this region is difficult to classify due to：

•Intercontinental nature, i.e., Africa, Asia, and Europe;

•Physical variations ranging from highly-structured deformed to strongly-ordered geometric grids;

•Numerous, seemingly opposing socio-cultural influences, i.e., Fertile Crescent/River Nile Delta,Greco-Roman/Turkish Ottoman, Christianity/Islam, Arabian/Persian, and so forth; and,

•Time factor.

This region includes ancient cities continuously-inhabited for about 5,000 years such as Jerusalem, Damascus, Beirut, and others, which appear to have much in common with the oldest cities of Europe such as Athens, Lisbon, Rome, and intercontinental Istanbul. It also includes relatively youthful cities inhabited for less than 500 years such as modern Amman (significantly older but abandoned for 500 years during the Ottoman Period), old Doha in Qatar, Manama in Bahrain,and others. Finally, it includes modern skyscraper cities such as Dubai/Abu Dhabi in the United Arab Emirates and West Bay/Lusail City in Doha(Figure 1).

It is typical to view the urban pattern of such settlements before the advent of modern transportation planning as simply evolving for a much longer time based on restricted random aggregation,which gives rise to the quintessential deformed grid of ‘organic cities’ in a naturally-occurring process relative to overall human population size(Hillier and Hanson,1984; Kostoff, 1991; Batty and Longley, 1994). There were fewer people in the world. By necessity, city growth was more incremental before the advent of industrialisation,rapid urbanisation, and globalisation, i.e., 18th century to the present day (Salama and Wiedmann, 2012). There was a less urgent need for top-down planning interventions to mediate for city size in resolving Hillier’s paradox of centrality and linearity in urban form. This might be true to a certain degree. However, it fails to adequately explain the persistence of distinctive urban morphologies in Middle Eastern settlements even after industrialisation and modernisation without resorting to gross oversight or benign neglect as part of the explanation. This suggests there is something else at work than merely restricted random aggregation over a prolonged period. There is a cultural intent.

Our understanding of Middle Eastern urban form typically leads to characterization of local neighborhoods as labyrinthine. We argue this is misleading. The paper proposes there is a basic plan model at work in the local areas of many Middle Eastern settlements based on a spatio-formal process of hierarchal separation by linear integration; adapting Penn’s terminology about the linear nature of shopping streets, i.e., marginal separation by linear integration. The simple basis of this spatio-formal process in Middle Eastern urban patterns is block manipulation. It is unlike the American urban pattern where the upsizing/subdivision of blocks is an important tool in privileging the historical area/Central Business District(CBD) during subsequent stages of urban growth for large-scale geometric grids. In Middle Eastern urban patterns, this process is a consequence of a spatial strategy seeking to generate a distinctive spatial hierarchy between center/edge streets and interstitial streets providing immediate access to building lots (especially residential ones) without a radical loss of connectivity. This tends to result in greater overall spatial depth in the urban network but we argue this is a more sophisticated model of structured depth as opposed to an ordered one in the American model, i.e., discrete separation by linear segregation in American suburban sprawl (Major, 2018). We say more sophisticated because it is not dependent on radical disconnection from the surrounding urban context. This is what tends to occurs in the design and planning of suburban developments in the United States, i.e., hierarchal ‘tree-like’ spatial layouts based on repetitive deformity and turning movement/road capacity requirements of modern roadway classifications (highway, arterial, collector, local, cul-de-sac) (Alexander, 1965; West,2017; Major, 2018).

The origin of this plan model is Hillier and Hanson’s (1984) restricted random process and the emergent deformed wheel spatial structure of small settlements. However, at some point, there is a transformation from mere aggregation based on simple rules of adjacency and permeability to design replication based on cultural intent. It represents a distinctive transformation from first to third laws - from form to culture - in the urban object. When this might occur is an independent variable specific to the history of urban growth in each settlement. The paper deploys an ‘artificial geometry’ in notional plan models using space syntax to better illustrate the principles of this design strategy. It represents an idealization of spatial structure based on strongly ordered plan concepts even though such structures rarely occur in such an obvious geometric manner; at least before the 20th century. Given the historical age and cultural significance of many settlements in the MENA region, we argue this is a more profound plan model of urbanism than previously realised, equal in importance and pre-dating the more well-known Alberti/Spanish Laws of the Indies and Vitruvius/Roman plan castrum models,which merely represent geometrically-ordered variations on this much older spatial strategy.

The Pervasive Deformed Wheel

Major (2018) identifies two basic plan models underlying the geometric urban pattern of most American settlements：the Vitruvian/Roman plan castrum and Alberti/Spanish Laws of the Indies models. The first is a simple 4×4 block pattern with a central cross-axis of streets (cardo and decumanus) dividing the plan into quarters with secondary cross-axes composed of street segments in each quarter. The second is a simple 3×3 block pattern (the minimal conditions for an orthogonal grid) with a dual cross-axis of streets defining the edges of a central plaza/square. He also identifies a synthesis of these models in Oglethorpe’s ward model for the famous plan of Savannah, Georgia(Reps, 1968; Major, 2001 and 2018). It is a simple 6×2 block pattern with a north-south axis (cardo)and a trio of east-west cross-axes (decumani)passing through and/or along the edges of a central square combined with the American tendency for elongated blocks to maximize the number of building lots (Figure 2). What is distinctive about these models is the structuring of topo-geometrical properties in the elemental cross-axis from center-to-edge-to-corner based on the odd or even number of blocks, provision of open space, and a square or rectangular block shape (Major, 2018).

In a sense, these already represent marginal deformed wheel spatial structures because the generation of ‘all lines’ is angular visibility from the corner of each urban block to the corner of every other in the plan. However, it is more accurate to state these are ordered idealisations of a deformed wheel spatial structure since the generation of axial lines is symmetrical, meaning we could rotate/mirror the first two in any dimension and rotate/mirror the latter along its central axis in either dimension (i.e., a bilateral symmetry)and the spatial structure would remain the same(Stewart and Golubitsky, 1992).

If we examine the spatial structure of almost any city in the world, the pervasive nature of the deformed wheel structure based on accessibility,line length, and/or connectivity at the macro- and/or micro-scale of the urban environment seems evident to one degree or another. For example,it pervades the 2018 space syntax model of Metropolitan Doha for integration (r=8) at the macro-scale and local integration (r=3) at the microscale of the urban environment (Figure 3). This model of Metropolitan Doha encompasses 23,800 streets over a metric area of about 130 km² (50 sq.mi), which stretches from Al Khor in the north to Sealine Beach in the south and from the Arabian/Persian Gulf in the east to the recently completed Salwa-Lusail Orbital Road to the west. The deformed wheel spatial structure of Metropolitan Doha at the macro-scale is evident in the high degree of accessibility along the core of Salwa Road (longest, most connected east-west street in the city), Al Waab Street paralleling Salwa Road to the immediate north, segments of the D-Ring Road/Doha Expressway running north-south in the city, Furousiya Road/East Industrial Road forming another orbital route in the city further to the west, and even segments of the new Salwa-Lusail Orbital Road at the western edge of the metropolitan region.

If we examine parts of Doha from the oldest to the most recent, beginning south of Doha Bay near the historical origins of the settlement to the north adjacent to the under-construction megaproject of Lusail city, we can detect and illustrate the evolving nature and scale of the deformed wheel spatial structure in local areas of the city over time (Figure 4). Beginning with two areas of old Doha, Msheireb Downtown and Souq Waqif(‘the standing market’) both subject to significant restoration/regeneration projects over the last 20 years, we can detect a simplified deformed wheel structure encompassing the perimeter streets and streets directly penetrating from three of the edges into the (more or less) geometric centre of the overall shape in the superblock. Adjacent to the southeast of Souq Waqif, Al Najada is also part of old Doha. Historically, Souq Waqif and Msheireb Downtown are approximately 20 years older than Al Najada. It consists of two sub-areas(West and East divided by the north-south Banks Street), which are each approximately 7.5% larger in metric area than the nearby older areas. The typology of the deformed wheel structure in both areas crisscrosses north-to-south and east-to-west to all perimeter streets via open-angle and nearright angle connections internal to each area.

Al Duhail in north Doha is northwest of the West Bay area and southwest of the Qatar University campus. The earliest areas of old Doha predate Al Duhail by approximately 60 years. One of its sub-areas (Al Duhail NE) is approximately twice as large and Al Duhail itself is approximately 12 times larger in metric area than Al Najada West or East. The simplified land pattern for Al Duhail consists of six superblocks. The deformed wheel typology connects all perimeter streets in a more readily-apparent geometrical manner related to the overall shape of the superblock. There is a well-defined north-south axis (two overlapping axial lines composing Umm Lakhba Environment Street) and a dual east-west axis of streets(Al Akhafji Street to the north and Saihan Road running roughly parallel further to the south). A deformed wheel typology also characterises the sub-area of Al-Duhail NE in a more geometrical manner but directly connects to only three of four perimeter streets in a similar manner to Souq Waqif and Msheireb downtown in old Doha. In all three (old and modern) areas, there are short,lowly-connected routes available to the excluded perimeter but they are not part of the clearly-defined deformed wheel structure typology of the neighbourhood (refer to Figure 3). In other words,there is always a way through to every perimeter street from every other. However, it is not always immediately obvious in the same manner to one edge as it is to the other three.

Finally, a more recent area in north Doha shows many of the same traits in a more geometrical manner. Al Daayen/Lusail West is adjacent to the Lusail city masterplan by Foster + Partners. The earliest areas of old Doha predate Al Daayen/Lusail West by approximately 80 years. One of its sub-areas (southwest neighborhood) is approximately 2.5 times larger and Al Daayen/Lusail West itself is approximately 13 times larger in metric area than Al Najada West or East. The simplified land pattern consists of four superblocks,which are clearly rectangular to the east and less so to the west due to open-angle connections along the Salwa-Lusail Orbital Road and an extension of Arab League Street to enable a nearright angle connection between these two arterial streets at the northeast corner of the superblock.These are the only open-angle connections at the macro-scale of the area. Such connections occur along short, lowly connected streets within the interstitial areas of the superblocks. However,their explicit purpose is realisation of a formal geometric order in plan to generate quiet, segregated residential streets with low connectivity of only 2, 3 or 4 connections instead of indicating the continuation of a through route in the emergent spatial structure. The simplified land pattern of Al Daayen/Lusail West also illustrates a clear cross-axis of streets (cardo and decumanus)directly connecting from perimeter to perimeter in all cardinal directions. In its southwest neighborhood, there is a distinctive ‘pin-wheel’ cross axis connecting from the eastern and western edges of the superblock to a street defining the opposite perimeter of a central block/space. The same occurs from a northern street internalised within the superblock, which directly connects the eastern and western edges of that superblock.This street effectively defines the north edge of this neighborhood instead of the Al Daayen/Lusail West decumanus itself. The plan mirrors this geometric logic to the south except the last ‘spoke’of this pin-wheel axis does not directly connect to the south perimeter street of the superblock. The southern street internalised within the superblock(mirroring the northern one) directly connects to the western edge of the superblock but not(except indirectly) to the Al Daayen/Lusail West cardo itself on the eastern edge. In the central block/space of the neighborhood, a school complex occupies a corner parcel but the majority(about75%) remains vacant open space.

These examples are generally representative of what occurs in the rest of the ortho-radial grid in Metropolitan Doha especially where residential land uses characterize an area. It is also a simple illustration of Hanson and Hillier’s arguments that deformed grids become increasingly geometric with urban growth：line length increases in the foreground network, block shape become more rectangular, and the incidence of nearright angle connections tend to increase (Hillier and Hanson, 1984; Hanson, 1989; Hillier, 1996,1999, and 2002). The metric area of the individual neighborhoods in Al Duhail is approximately 2 times larger, and Al Daayen/Lusail West is approximately 3 times larger in metric area than Al Najada East and West, which are themselves approximately 7.5% larger than Souq Waqif and Msheireb Downtown Doha. Al Duhail and Al Daayen/Lusail West are not only metrically larger but the formal geometric order of their design and planning is more apparent. The evolution of the deformed wheel typology in these areas of Doha also appears to demonstrate Batty’s (2008)contention there is a fractal dimension to the scale, size, and shape of urban form in cities and,along the same lines, Carvalho and Penn’s (2004)concept of self-similarity at various scales of the urban environment.

More than this, deep structures also appear to characterize several areas of the ortho-radial grid in Metropolitan Doha to facilitate intelligible movement from the macro- to the micro-scale of urban environment tailored to the superblock pattern and degree of depth in the spatial network. This includes linear intensification (or a ‘strip effect’) along the longest length of Salwa Road and intelligible ‘unidirectional’ distribution subsystems into adjacent neighborhoods along the sequence of streets composing Salwa Road from the C-Ring Road to Wadi Musheirib in old Doha(Major, 2018). Intelligible distribution subsystem means turning right or left from the principal street into a local area. Unidirectional means the segment of the Salwa Road/ Wadi Musheirib sequence you are on forms part of an intelligible distribution system directly：in front of you if traveling east-to-west out of town; or, behind you if traveling west-to-east into old Doha. There is also a well-defined local area effect in Souq Waqif itself. All of this occurs in the relationship between integration (r=8) and local integration(r=3) due to the pattern of structured depth in the urban spatial network of Doha.

Anatomy of a Plan Model

Collectively, this offers clues to developing a plan model for these settlements. The random restricted aggregation and deformed wheel spatial structure is a crucial part of the story. In the older areas of Doha, overlapping open-angle connections internal to the area and subtle design variations in block shape (such as chamfered corners or variations thereof) generate micro-scale convex open spaces, which tend to become localised nodes for non-residential activity (Figure 5). This is hardly a new phenomenon. In fact, it is a very old one.Hillier (1996) identifies the importance of such micro-scale spaces in the urban functioning of the deformed grid in the City of London. The scale of such spaces is often so small that they are alltoo-easy to overlook as trivial in town planning,which tends to lack the necessary resolution about the spatio-functioning of such urban spaces. As urban form becomes more geometric, overlapping open-angle connections tend to generate such spaces - becoming less convex and more linear -along the perimeter streets of urban areas. They tend to become part of the public right-of-way for arterial roads due to modern transportation planning practice. This is what occurs in Al Duhail in defining the edge between neighborhoods (far right in Figure 5). When this happens, specific planning provisions becomes necessary to cater for the potential of such localized non-residential activities.

This is evident in the provision of a central block/space in the southwest neighborhood of the Al Daayen/Lusail West superblock (refer to Figure 5 far right). It also occurs in the contemporary planning for many newer areas of Doha via this mechanism of a geometrically-realised pin-wheel cross-axis (Figure 6). Sometimes this occurs with the provision of a central green space such as Alnuami West in north Doha and Onaiza 65 East in West Bay. Sometimes it occurs around a large central block such as all neighborhoods of the Mimar Compound in south Doha. Other developments do not provide a central space/block at all,i.e., dual decumani of the pin-wheel cross-axis in the Wadi Al Sheeniya area of south Doha. It depends on the socio-economic aims of the individual development. However, it appears quite common for this pin-wheel cross-axis to directly connect to three of the four perimeter streets and only indirectly to the other one in newer areas of Doha, if the superblock is (more or less) rectangular in overall shape.

This pin-wheel cross-axis pattern is pervasive in the urban form of Doha. It is easy to understand.This is a formal geometric idealisation of Hillier and Hanson’s (1984) deformed wheel spatial structure, which tends to emerge in the deformed grid of older areas of Doha. These areas of old Doha tend to directly connect via overlapping axial lines with open-angle connections from a minimum of three perimeters (sometimes all perimeters such as Al Najada) to the geometric centre - more or less, depending on proximity and intensity of nearby land uses - defined by the overall shape of the superblock. In Souq Waqif,not only is there a very large plaza adjacent to the nexus of the pin-wheel cross-axis but also a mosque. As noted previously, micro-scale open spaces form part of the pin-wheel cross-axis structure in the areas of Al Najada due to overlapping axial lines with open-angle connections and accentuation of block facades.

In contrast, provisions for surface parking lots sacrifice any potential for such spaces due to large-scale, high-rise redevelopment in the Al Marfa area, which ironically includes the principal planning agency of Qatar, i.e., Ministry of Municipality and Environment. In any case, we have a working outline of a basic plan model for local areas of Middle Eastern settlements based on Doha：

• Pin-wheel cross-axis via overlapping, open-angle connections in a deformed grid and/or offset by action on urban blocks (block manipulation) in a geometric grid.

• Relatively direct center-to-edge connection of this cross-axis to three perimeters - though sometimes, all perimeters - if the shape of the superblock is roughly rectangular, i.e., a deformed wheel.

• Hierarchy of convex open spaces from the macro- to the micro-scale of the superblock in terms of the metric area of such spaces either via overlapping, open-angle connections/accentuation of building facades or simple planning provision of a central block/space with its edges serving as an organizing mechanism for the pin-wheel crossaxis.

This occurs in deformed or geometric grids primarily via local actions on blocks. However, this leaves the question of why pursue such a spatial strategy in the first place? The newer areas of Doha suggest we can use geometry to illustrate the reason.

Hierarchal Separation by Linear Integration

We can begin with the 4 x 4 block pattern of a central cross-axis of streets defining four quarters in the Vitruvian/Roman plan castrum model (Figure 7). Initially, all street widths and block shapes(e.g., square) are the same. We can generate an offset pin-wheel cross-axis and small central space in each quarter of the plan with marginal actions on blocks. Marginal actions mean minor,even subtle design actions. In this case, increasing block length in one dimension into a rectangle(still ‘near square’ in shape, within 6%), alternating the offset of the blocks to pin-wheel around a small central open space, and marginally narrowing all street widths except for the cardo/decumanus and perimeter streets. This formally generates more clear-cut superblocks in each quarter where all streets are internal to each superblock unless defining an edge. This effectively illustrates the purpose of this spatial strategy by intensifying segregation along streets providing immediate access to building lots internally within each superblock. It also introduces a stronger hierarchy in the spatial structure of the plan compared to the Roman plan castrum model. This hierarchy is(in order of integration from highest to lowest)：cardo/decumanus cross-axis, perimeter streets,and superblock interstitial streets. There is even a starker spatial differentiation between interstitial streets in access to lots from center-to-edge due to topo-geometric characteristics of overall plan shape. Like the Roman plan castrum model, there is still only one block size/shape for sixteen urban blocks in a 4×4 urban pattern encompassing the same metric area. There are now two street widths instead of one and a small convex open space at the centre of each superblock.

However, the cardo/decumanus cross-axis does not incorporate a macro-scale pin-wheel structure nor a convex open space. We can generate a pinwheel structure in this cross-axis with further marginal actions on blocks and re-instating a common narrow street width in all streets except for the perimeter ones. It is only necessary to manipulate block sizes in two quarters diagonally opposite to each other (NE/SW or NW/SE). It is an ‘either or’ proposition, it does not matter which but this results in four different block sizes.The plan encompasses the same metric area as the Roman plan castrum and all blocks are roughly the same area with marginally different length and width. All blocks are marginal ‘near-square’shapes (i.e., within 6%) to maintain good economy of building, i.e., it is less expensive to build with right angles (Major, 2018). There are still only two street widths (again, marginally so) for the perimeter streets and all others, respectively.This generates a central convex open space at the intersection of the formal pin-wheel cross-axis of streets at the centre of the plan. The provision of this central space allows axial lines of the crossaxis to diagonalise across the plan from edge-toedge at 8° to the cardinal directions. However,all convex open spaces are the same size. At this point, the rigid geometry of the plan only leaves two minimal choices to enlarge the central open space in the formal composition and generate a hierarchy in terms of metric area so the central space is larger than those in each superblock.Either：

• Increase the width of cross-axis streets along two internal edges a single superblock, which introduces three additional block sizes (again,‘near-square’ rectangles with roughly the same metric area but marginally different in length and width compared to the others); or

• Maintain street widths and adjust the corner building facades on a minimum of two urban blocks immediately adjacent to the intersection of the central pin-wheel cross-axis to generate marginal L-shaped blocks, which creates a central open space that is 50% larger in metric area than those in each superblock and only introduces a single different block shape/size.

The preferable choice depends on whether the design and planning priority is street capacity or construction economy, i.e., street width or block shape. We can describe the latter as the ‘Philadelphia strategy’ since William Penn incorporated L-shaped blocks around the central plaza space of that city in his 1682 plan. We can accomplish the same thing using chamfered corners like Ildefons Cerdà’s Barcelona Exiample but without the benefit of maintaining right angles in block shape for good economy of building (Major, 2018).

In any case, this effectively demonstrates in a geometrical fashion how such spatial structures may emerge solely by local actions on blocks at the level of the building lot. In the restricted random aggregation of individual dwelling units before top-down regulatory planning requirements, construction economy (i.e., block shape)will tend to take priority. The owner of an individual lot is unlikely to resolve street capacity issues without the cooperation of owners of adjacent/neighboring lots on that street. In fact, we can demonstrate how such a spatial structure emerges in the restricted random process of aggregation based on simple rule of adjacency and permeability by returning to Hillier and Hanson’s (1984)experiments with their students and running allline axial analysis on the emergent pattern. In this case, the largest of the four examples (Figure 8). What emerges in the spatial pattern is：

• Integrated spaces associated with the perimeter bound;

• More segregated spaces in the central interstitial area providing access to the most cells;

• Dual cross-axis utilising a common decumanus;

• A cross-axis forming a traditional cardo/decumanus intersection at a near-right angle;

• A cross-axis forming a pin-wheel cross-axis due to angular visibility and the width of spaces;and,

• Dual cross-axis directly connects to only three of the four perimeter spaces.

The pin-wheel cross-axis emerges due to two open-angle connections (radial, i.e., near 45°)and a near-right angle connection to the integrated perimeter in three directions. Collectively,this generates an overlapping ring of circulation, which at least suggests the potential for a convex open space of localised activity within the central interstitial area. Of course, no such space emerges due to the rigid geometry of square-shaped cells in the original experiment.This also suggest that the asymmetrical access to all perimeters (usually one in four) in newer neighborhoods of Doha represents a cultural replication of an emergent pattern of the restricted random aggregation process in older areas of the city.

Discussion

Common descriptions of Middle Eastern urban form tend to focus on a street hierarchy classification at neighborhood level - public, semi-public, semi-private, and private - derived from Christopher Alexander’s (1977) book, A Pattern Language (Jaidah and Bourennane, Eds., 2010;Salama and Wiedmann, 2012; Radoine, 2017).In this sense, private space does not refer to legal definitions of land ownership but ill-defined notions of privacy and territoriality about the people living in the buildings adjacent to such streets.These descriptions often include the provision of a central space/block for a neighborhood mosque,which is the same concept of religious or government buildings occupying such locations in the Western tradition of town planning. For the former, there is an inherent problem with the street hierarchy classification. This is the distinction (or lack thereof) between semi-public and semi-private. As noted by many, this represents a ‘glass half-empty/full’ logical tautology since semi-public and semi-private mean the same thing. To address this problem, architects and town planners tend to focus on design features intrinsic to such streets to better distinguish the differences between a semi-public and semi-private street;most usually building constitution and fenestration, i.e., doors and windows. What this means in design and planning terms is such distinctions tend towards subjectivity of the person observing and assessing the design quality of the street.The analysis of this paper suggests there might be a more objective means of understanding such neighborhood patterns without resorting to ill-defined, subjective notions of privacy and territoriality. This might seem especially true because of the more complex spatial structures in the emergent urban pattern of Middle Eastern settlements,which are due to the less geometrical nature of superblocks in real examples than presented in the notional plans of this paper. Such an understanding would tend to encompass the relationships of individual building lot access to a central crossaxes, the perimeter streets, and adjacency/metric nearness to loci with non-residential activities at the macro and micro-scale of the neighborhood,superblock, and larger urban context.

There is an even simpler manner for a pin-wheel cross-axis to emerge in an urban pattern. We can begin with an odd number of blocks such as the Alberti/Spanish Laws of the Indies plan model and elongate the square blocks into rectangular ones by interrupting streets while maintaining overall metric area (Figure 9). This simple layout generates the same spatial traits：integrated perimeter streets, integrated central space due to angular visibility across that space, and less-integrated pin-wheel cross-axis streets providing access to the most building lots. This is another variation on the principles of maximizing perimeter surface such as the outward facing block, internal core/external ring in the bastide (or ‘fortified town’)model at the settlement level - typical in Spanish presidios during colonisation of the New World and American military forts during Westward Expansion the USA - or with an intervening ring of circulation at the building level especially in office buildings (Major, 2018). The key difference is this simple layout introduces a stark spatial differentiation between center/edge and streets providing access to building lots in outward-facing blocks since most entrances tend to occur along their longest length. We could fairly describe this emergent pattern as the geometrical distillation of Hillier and Hanson’s (1984) deformed wheel spatial structure and the spatio-formal process of hierarchal separation by linear integration in their purest form.

This spatial structure characterises many neighborhoods of Doha simply because they do tend to be older than other cities of the world. These settlements aggregate dwelling units based on Hillier and Hanson’s (1984) restricted random process for a longer time relative to population size and urban growth rate, unique to specific cities and times. However, at some point in the life of Doha,this transforms from a (first law) emergent property of a restricted random aggregation process into (third law) design strategy of cultural intent to segregate access to building lots especially residential land uses. However, unlike the radical disconnections in the spatio-formal process of discrete separation by linear integration in American suburban sprawl, there is almost always a way through a neighborhood; often more than one. It will not necessarily be obvious nor equidistant to all perimeters of the neighborhood. However, it will tend to be present. In this sense, spatial layout in some earlier suburbs of the City Beautiful/Garden City Movements in Western societies such as Frederick Law Olmstead’s Riverside, Illinois and Barry Parker and Sir Raymond Unwin’s Hampstead Garden Suburb in London have much more in common with this much older, more sophisticated plan model in the Middle Eastern neighborhoods of Doha than the worst examples of late 20th century American suburban sprawl(Figure 10).

CONCLUSION

It has been notoriously difficult to find objective descriptions of Middle Eastern urban patterns in the architecture and town planning literature due to a variety of geographical, physical, functional,cultural, and temporal factors in such settlements.Despite this, it seemed readily-apparent Middle Eastern urban patterns follow the same spatio-formal processes emergent in other cities of the world (Hillier, 1996; Major, 2018). The paper examined the spatial structure of Metropolitan Doha, Qatar using space syntax. We argued that the ‘deformed wheel’ spatial structure, initially emerging as a (first law) consequence of restricted random aggregation based on simple rules of adjacency and permeability, at some point purposefully transformed into (third law) design replication of a spatial strategy based on cultural intent(Hillier, 1989). The paper analysed several local neighborhoods of Doha as well as some notional plan models utilizing an artificial geometry to better illustrate the spatial implications of this design and planning strategy described as hierarchal separation by linear integration. The paper concluded this spatio-formal process represents a much older plan model for settlement form and the distillation of Hillier and Hanson’s (1984) ‘deformed wheel’spatial structure to its purest form.

ACKNOWLEDGEMENTS

This research was supported by an internal grant of Qatar University (Grant ID：QUSDCENG-2018/2019-4).