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Received: 2021/10/23 | Accepted: 2022/01/3 | Published: 2022/02/22
Received: 2021/10/23 | Accepted: 2022/01/3 | Published: 2022/02/22
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Ali Akbari E, Mousakazemi S, Gholami S. Physical Form Coherence from Connectivity Point of View; Case Study of Shiraz, Iran. GeoRes 2022; 37 (1) :15-26
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1- Department of Geography & Urban Planning, Payam-e Noor University, Tehran, Iran
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Introduction
One of the major concerns in the field of urban spatial planning is the preparation of plans within the framework of objective urban planning regulations, particularly the provision of per capita service levels. This issue creates challenges regarding the priority or sequencing of social urbanization versus physical urban development. Urban development plans seek to restore dynamism and vitality to urban fabrics; however, neglect of existing structures and reliance on replicating previous plans have turned the definition of a sustainable urban form into a challenge for urban planners.
The social dynamism of a city depends on its spaces and places. Human interactions and social relationships take shape within the physical fabric of the city, while the physical form itself derives its identity from existing social life [Shakibaei Bidaruni et al., 2018]. The spatial structure of a city is closely related to the manner in which internal and external transportation corridors develop; the way these corridors are connected leads to the growth and development of different parts of the city [Abdollahi Torkamani et al., 2019]. In urban studies, form can be considered equivalent to physical structure. Kevin Lynch, in The Image of the City, have defined urban form as the “physical and visible manifestations of the city” [Mokhtarpour & Manteghi Fasaie, 2018]. In defining urban form, many scholars refer to the spatial pattern of large, immobile, and permanent physical elements (such as buildings, streets, rivers, and possibly trees) and define it as the spatial distribution pattern of human activities at a specific point in time [Mider, 2012]. Within urban form, a set of scales is interconnected through a hierarchical system of relationships [Jiang, 2013]. The city is composed of components and the relationships among them; the loss of these relationships, by preventing complementary land uses from fulfilling their roles in relation to one another, threatens the integrity of the city as a whole [Bahreini & Froughi-Far, 2015]. In recent years, comprehensive urban plans, by encouraging low-density growth through zoning regulations and the separation of major urban functions, have further fragmented urban structures [Ghoraba & Tabibian, 2017]. The spatial structure of a city refers to the distribution of residential areas and economic activities across space, shaped over long-term processes by locational preferences and public policies [Burgalassi & Tommaso, 2015].
Studies related to cohesive form indicate that more than 77% of scholars in this field have emphasized the composition of elements (streets, land uses, buildings) in analyzing form cohesion, while only 33% have defined cohesion based on the internal coherence of a single element [Mokhtarzadeh, 2018]. Raimbaut proposed an urban morphological model based on the interaction between access networks and built environments, showing that the existing spatial correlations between them reflect non-stationary and multi-scalar processes [Raimbaut, 2019]. Giannopoulou, in her research, demonstrates that measuring the degree of integration and connectivity in space syntax is an important tool for analyzing urban spatial configurations. According to this method, the relationship between connectivity and integration can indicate urban land value and accessibility, and these factors significantly influence the growth of areas by increasing accessibility under specific economic conditions [Giannopoulou et al., 2016]. Chen employed multiple fractal analysis indices to classify urban physical form patterns [Chen, 2016]. Shafieion and Zamani have examined urban form parameters (residential density, land-use mix, and connectivity) in relation to the walkability index in District 14 of Isfahan; the results show that variations in these indices and differences in urban form affect residents’ physical activity levels [Shafieion, 2021]. Nikpoor et al. assess the capacity of Babolsar’s neighborhoods based on the compact city model and found that compact neighborhoods perform better in physical, infrastructural, social, and economic terms, and due to their higher livability quality, show a greater tendency toward residential preference [Nikpoor et al., 2017]. Ghadami et al., aiming to propose a sustainable urban form for Sari, evaluate citizens’ travel tendencies using land-use mix, connectivity, and density indicators across compact, semi-compact, and sprawled forms [Ghadami et al., 2017]. Movahed et al. have examined different urban forms to explain the spatial expansion pattern of Saqqez from a sustainable urban form perspective and ultimately have proposed the compact growth pattern as the future development model for the city [Movahed et al., 2014]. Azizi and Araste have analyzed the process of urban sprawl and unsustainable development in Yazd by considering the effects of building density, population density, land prices, accessibility, and urban block size on urban form and spatial changes [Azizi & Araste, 2011]. Mohajeri, by examining complexity and cohesion in fractal urban form design, have compared physical sustainability in traditional Iranian cities with contemporary ones and introduced principles and criteria for urban physical sustainability [Mohajeri, 2006]. In the context of holistic urban planning, various aspects of urban cohesion have been examined in previous studies based on their respective research objectives; however, the existing gap and the rationale for this study lies in the limited presentation of a planning perspective capable of explaining a cohesive urban form and identifying the factors that generate it.
In growing cities where components continuously increase, urban form faces new challenges regarding the integration of these units into the larger urban system [Tavalaee, 2002]. If urban form is considered a combination of physical, natural, and functional factors along with the element of time, the prominent and stable elements of this set constitute the urban structure. Therefore, urban structure represents the main component of urban form, reflecting its overall characteristics and defining its structural framework [Daneshpoor & Roosta, 2012]. Structural cohesion emerges through the creation of interdependence within the city’s communication network. In fact, as each unit becomes embedded within a broader form, a close spatial relationship is established to preserve and strengthen the whole; thus, space as a cohesive element and the spatial network as a connecting element are of critical importance to urban function. Consequently, urban planning must recognize the characteristics of place and incorporate them into the planning process [Tavalaee, 2002]. Tsai, in a quantitative study of urban form at the micro-morphological scale, focused on the spatial distribution of population [Tsai, 2005]. Guerois and Paulus show that to understand the effects of independent and distinct units in a city, one may consider components of the built environment (morphology), urban functions, or administrative boundaries [Guerois & Paulus, 2002]. Poorjafar and Esmaelian have identified the main principles of urban cohesion as physical, functional, and identity dimensions [Poorjafar & Esmaelian, 2013]. Ana Julia et al., by considering physical and functional dimensions, have demonstrated that the cohesion of urban spaces is realized within the framework of network-based dimensions [Julia et al., 2010].
Different urban units are integrated through interfaces or boundary elements. These interfaces are responsible for establishing connections among various urban units [Mohajeri, 2006]. According to this principle, the boundary elements of one module connect to those of another, and some elements may interlock like pieces of a puzzle. Desirable boundaries in urban space can be achieved by considering appropriate visual principles derived from geometric rules [Roshani et al., 2017].
According to systems theory, any system can be divided into several subsystems, and each subsystem into multiple smaller components. Each of these constituent parts is considered a center or a distinct set of points in space [Nadimi et al., 2014]. Cohesion of physical form is a process that links physical form elements to one another through an orderly organization [Tavalaee, 2002]. By using the street network as the primary element, the entire physical space of the city can be scaled: the street network is decomposed into multiple blocks, with the size of each block representing its scaling characteristics. The recurring pattern of block sizes reveals the latent order embedded in the city’s physical form [Jiang & Liu, 2015]. This latent order indicates the interconnection among urban blocks, leading to the integration of physical form elements [Tavalaee, 2002].
Despite the relational nature of urban physical form, by identifying interactions between areas, a cohesive whole of physical form elements can be conceptualized in a way that preserves the coupling of urban form. Parcels collectively constitute a unit; therefore, within a unit, discontinuous components should not exist, as the coupling of elements in physical form at smaller, fundamental scales provides the basis for cohesion in larger-scale structures [Mohajeri, 2006]. To examine the geometric coupling of physical form, parcels with identifiable irregular structures are analyzed, while the coupling of mass and space and the extent of solid and void spaces resulting from construction activities are used to assess built form [Purevtseren et al., 2018].
This study seeks to demonstrate the existence of nested and complex relationships and emphasizes the necessity of transforming perspectives on spatial planning by redefining the concept of “relationships” in order to achieve an integrated approach to planning urban structures. Accordingly, by understanding the relational nature of physical form and considering geometric coupling in interregional interactions, a process can be identified based on the connectivity among physical form elements (streets, parcels, and buildings) that leads to an orderly organization. In the strategic–structural plan of Shiraz, the city is regarded as a whole with an internal structure and reciprocal links to environmental conditions; however, the role of recognizing the city’s geographical elements and the complex relationships among components in the urban planning process has been overlooked. In this article, considering the city’s complex network, we define the relational nature of Shiraz’s physical urban form. The aim of this research is to explain the cohesion of Shiraz’s physical urban form based on a connectivity-oriented model. Accordingly, this study seeks to answer the following question: from an urban planning perspective, what is the source of the cohesive form of the city of Shiraz?
Methodology
This quantitative study was conducted using surface feature data, including the parcel layer and the urban block layer (comprising multiple parcels bounded by streets), derived from the 2006 base map of Shiraz. In addition, information layers from the revised detailed development plan maps of 2014 including functional zoning layers and transportation networks were utilized for the year 2021. All spatial data were extracted and processed using ArcGIS software. Documentary and archival studies were employed to obtain the required background information and references.
The service boundary of Shiraz, based on the latest administrative divisions, consists of 11 municipal districts, covering an area of 22,731 hectares and comprising 77 subdistricts. The largest municipal district is District 10, with an area of approximately 3,563 hectares, while the smallest is the historical–cultural district, with an area of 377 hectares. Given the available data, the Guttman scalogram method was used to identify homogeneous areas within Shiraz. In this method, areas are grouped based on their degree of similarity, resulting in the identification of homogeneous zones. The districts were classified according to their levels of economic, social, cultural, and physical indicators by calculating the mean values and the deviation from the mean for each indicator. As a result, Districts 8 and 11 were classified as deprived or underdeveloped; Districts 2, 3, 5, 6, and 7 as semi-developed or moderately endowed; and Districts 1, 4, 9, and 10 as developed or well-endowed.
Currently, urban planning in Shiraz is carried out according to the regulations defined in the revised zoning system of the city. The fundamental emphasis is placed on only one dimension of the part–whole relationship between each element and other elements. In other words, zoning regulations are aligned with access networks, and building regulations are aligned with parcel size. Land uses are determined based on their compatibility or incompatibility with adjacent uses. In the revised detailed zoning framework of Shiraz, construction regulations for parcels are defined by considering the quality of spatial planning for society (based on human-centered criteria) and place (based on efficiency criteria). For each parcel, indicators such as compatibility (the correspondence between form and function), accessibility (the quantity and diversity of uses that can be accessed), identity (the distinction of one space from another), and meaning (what a place conveys, i.e., the meaningfulness of the visual environment) are specified. Consequently, the fixed position of each parcel within a block, as defined by its zoning code, has led to the aggregation of diverse buildings and the enclosure of spaces based on height regulations. As a result, the primary concern of urban planners has been limited to the provision of land-use areas and per capita service levels, the observance of hierarchical access levels, and compliance with density and site coverage regulations in each district.
What is overlooked in the zoning system is the failure to account for parcel heterogeneity within the unity of the physical form relative to the whole. Heterogeneity in urban physical form arises either from the physical shape of existing parcels, resulting from land subdivision processes, or from functional zoning and land-use categories. Since urban blocks are integral components of the city’s spatial structure and inseparable from the overall structure, this study addresses localized heterogeneity occurring in different parts of the physical form by recognizing macro–micro relationships within functional zones and land uses and by calculating the fractal dimensions and compactness of parcels in each district. This approach provides a response to the observed heterogeneity based on connectivity. Such conditions indicate the neglect of relational patterns among elements of the city’s physical form. Urban planners often regard intra-urban interactions as being influenced solely by geometric structure, which stems from overlooking the role of interconnected multi-scale structures in shaping interactions. To revise planning approaches within the zoning system and to propose an optimal structural model based on continuity and functional efficiency, appropriate indicators reflecting the relational patterns among physical form elements must be incorporated into urban planning.
To explain the concept of physical form cohesion from a connectivity perspective in Shiraz, two assumed characteristics of the “urban block”, namely, the block’s position within the hierarchy of connectivity and its boundary number were employed as the fundamental units of physical form across three stages.
Stage 1: The Nature of the Connectivity Pattern in Shiraz
The complex network system present in Shiraz provides a necessary framework for defining blocks with cohesive functions and structures. Distinct patterns that converge at similar elevation levels generate new patterns with different properties at higher hierarchical levels. Connectivity emerges from the relational structure among blocks and their mutual influences. This characteristic relates to the position of each block within hierarchical levels defined by block size in the city’s complex network. Using visualization tools (head–tail breaks), upper and lower thresholds at each hierarchical level of block size were classified, and contour curves derived from elevation points obtained in subsequent steps were used for further categorization.
Stage 2: Rules of the Connectivity Pattern in Shiraz
In this study, the “boundary number of each block” was used as an indicator of “connectivity distance.” For each block, a boundary number was defined based on its distance from the city boundary (the officially approved urban limit). Accordingly, the greater the distance of a block from the city boundary, the higher its boundary number. Boundary numbers represent discrete boundaries and indicate the connectivity status of each block. In other words, blocks with different boundary numbers appear as a “whole” at different levels within the hierarchical classification of urban block connectivity.
Moreover, at each classification level, there exist centers, not necessarily geometric centers, but focal points that influence connectivity characteristics within the complex network. Relationality indicates that all blocks, from the smallest to the largest scale, play roles within the hierarchy. Considering the functional zoning system used to define block functions in the detailed plan, centers located in blocks with different boundary numbers establish a property of interconnectedness within a hierarchical structure.
After determining the position of each block within the connectivity hierarchy, the priority of influence of each district on the centers present in the relational pattern was identified. Each center interacts with its surrounding environment, and the relationship between the center and its periphery is determined by the center’s sphere of influence. Based on block connectivity characteristics and simultaneous processes of concentration and decentralization in relation to functional zones, macro–micro connectivity interactions within the spatial structure were examined in relation to each functional zone (G, M, R, S) as micro-level connectivity, and in relation to all functional zones collectively as macro-level connectivity.
Given the variation among blocks in terms of built and open spaces across different districts, the fractal dimension was used to determine heterogeneity in the spatial filling of urban areas. This measure reflects the degree of complexity in parcel shapes within the urban fabric, indicating the formation of irregular structures (higher fractal dimensions correspond to greater structural irregularity). Additionally, the compactness ratio of parcels was employed to assess the extent of development (built spaces). An increase in the compactness index indicates an increase (or decrease) in the intensity of construction within the study area.
Stage 3: Integrated Analysis of the Outputs of Each Stage
In this stage, the concept of cohesion in the city’s physical form was explained from a connectivity perspective at the analytical level of Shiraz’s urban districts. By examining the degree of compatibility in the connectivity status of districts, based on the derived priorities (including the sphere of influence of block boundary numbers, influence on centers within the complex network and connectivity hubs, the formation of irregular structures, control and enhancement of construction activity, population distribution, and levels of economic, social, cultural, and physical indicators), the Kendall’s Coefficient of Concordance was calculated. This analysis assessed the mutual influence of different districts on one another and, consequently, their impact on the cohesion of the city’s physical form.
Findings
Streets constitute the primary element of physical form and, as the city’s complex network, generate urban blocks. Block size, which reflects the nature of their relational connectivity, indicates the coexistence of smaller blocks alongside larger ones. To identify the nature of relational connectivity in the physical form of Shiraz, the analysis began with a planimetric map by calculating the mean block length of the city (156 m). Blocks with lengths below 156 m were classified as the lower tail, while those exceeding 156 m formed the upper head at the first hierarchical level. In the subsequent step, the mean length of blocks in the upper head of the first level was calculated. Blocks shorter than this mean constituted the next lower tail, and those longer than it formed the upper head at the second hierarchical level. This set of streets, considered as a whole, was divided into an upper head (values above the mean) and a lower tail (values below the mean) using the head–tail breaks approach. This recursive process continued until the condition distinguishing poorly connected streets from well-connected ones was no longer violated, proceeding until the proportion of the upper head fell below 40%. Overall, the blocks of Shiraz were distributed across five hierarchical levels of connectivity.
Subsequently, using the concept of the boundary number (as discrete boundaries) for each block, the connectivity distance of each block from the city boundary was determined, thereby clarifying the connectivity status of blocks within repetitive relational patterns. Accordingly, a boundary number was assigned to each block based on its distance from the administrative boundary of Shiraz, such that greater distances corresponded to higher boundary numbers. This decomposition of the complex network into blocks with varying boundary numbers produced nested rings, with the smallest ring formed by the block with boundary number 21. Each block possesses a range of boundary numbers depending on its position relative to the city boundary: blocks with boundary number 1 have a single boundary, whereas the block with boundary number 21 encompasses boundaries from 1 to 21. The correspondence between contour lines and boundary numbers from 1 to 21 indicates that blocks located at similar elevation levels tend to be more strongly interconnected. By measuring distances from the central block to the centers of other blocks, the centers associated with boundary numbers 1 to 21 were identified.
Boundary number 21 encompassed all blocks across the city of Shiraz, and the block with this boundary number functioned as the primary center of urban connectivity. In the next step, the distances between the reference point (the central block with boundary number 21) and the centers of other blocks (centers of the complex network) were calculated. By defining the nature of relational connectivity in the physical form of Shiraz and identifying the hierarchical position of each block, the priority of influence of different districts on the existing centers was determined. The priority of influence of connectivity centers on the complex network followed the sequence 4 > 1 > 3 > 5 > 6 > 9 > 11, while the priority of influence of the city’s complex network centers on the eleven municipal districts followed the sequence 4 > 2 > 5 > 7 > 1 > 9 > 10.
Blocks sharing similar boundary numbers were interconnected across different hierarchical levels. Blocks with boundary numbers from 1 to 3 appeared across all hierarchical levels and elevation points.
According to the approved revised detailed plan, the function of each block is defined within the zoning system. It is therefore possible for blocks with different boundary numbers that converge at various hierarchical levels and elevation classes to be functionally complementary. Within each district, blocks, despite having discontinuous boundary numbers across different hierarchical levels, may exhibit either similar or distinct functions relative to one another. Consequently, any intervention in the city’s physical form must consider the locational position, functional role, and connectivity of blocks within the broader spatial structure. Blocks with varying boundary numbers occupy different hierarchical levels, and blocks with both smaller and larger boundary numbers recur across these levels. The hierarchical scaling of blocks across levels constitutes identifiable wholes. In effect, the boundary number not only indicates a block’s position relative to others but also serves as both a differentiating and a linking mechanism among blocks.
Connectivity among blocks existed across all hierarchical levels of elevation points. In the city’s complex network, the boundary number was defined as the connectivity distance of blocks from the outermost boundary relative to the urban network, and boundary numbers were used to identify the city’s connectivity centers. Both connectivity centers and complex network centers were present at multiple hierarchical levels. The intensity of influence exerted by centers was also dependent on the distribution of built and open spaces within their spheres of influence. Each center interacts with its surrounding environment, and the relationship between center and periphery is determined by the extent of this influence. By considering variable block boundaries within the primary elements of the physical form pattern, nodes, paths, and areas, the sphere of influence associated with each boundary number was identified. In the city’s physical form, the prioritization of boundary numbers with the greatest influence within their coverage radii followed the sequence: 1 > 2 > 4 > 5 > 8 > 6 > 7 > 11 > 13 > 9 > 14 > 16 > 17 > 12 > 13 > 10 > 15 > 18 > 20 > 19.
The position of urban blocks within the hierarchy of elevation points and the relationships among connectivity centers and complex network centers function as recursive rules, from whole to part and from part to whole, by accounting for locational similarity to preserve functional order and form within the connectivity of centers across their coverage areas. Blocks identified as connectivity centers or complex network centers interact with other blocks. The conflicts and heterogeneity arising from differences in form and function within specific spatial contexts can be clarified by considering connectivity across hierarchical elevation levels. By maintaining relationships between primary connectivity centers and surrounding blocks through similarity, larger centers can be formed.
Based on accessibility, population density, and the provision of service areas and per capita facilities, functional zones in the revised detailed plan have been allocated across the city. Overlaying these functional zones onto the relational pattern of the complex network allows for the assessment of how changes in blocks with specific functions affect their connected blocks. Given that functional zoning patterns recur across different scales, any modification to a block with a particular function must consider not only the scale of the zone but also the block’s connectivity capacity.
The relationship between each block and its surrounding environment indicates that any change in the number of blocks at the city scale affects the boundary numbers of other blocks. Each block occupies a defined space within the city’s spatial structure and contains parcels that likewise occupy specific spatial extents. Moreover, blocks emerge from the city’s complex network, underscoring the tangible occupation of space by this network. Under the revised functional zoning framework, blocks with similar zones tend to exhibit relatively comparable conditions in terms of building height, number of floors, balance between built and open spaces, building density, and permitted land uses. Although changes driven by urban needs and pressures may introduce heterogeneity in form and function, the diversity and hierarchical structure inherent in the zoning system can be employed to organize the spatial structure. Considering the varied needs of residents and broader socio-economic conditions, unnecessary functions may be removed and appropriate ones introduced to establish functional equilibrium.
Differences observed in the form and function of parcels, blocks, and complex networks reflect the differentiation of elements within the spatial structure. Given the formation of hierarchies in functional zones and access networks under the revised detailed plan, alongside the connectivity hierarchy of urban blocks, it can be argued that contrast is an enduring feature of spatial structure. Recognizing this reality enables urban planners to provide reasoned responses to differences arising from land-use changes.
To identify macro–micro relationships within the spatial structure of Shiraz’s eleven districts, the interaction of macro- and micro-level connectivity was examined for each district, considering its sphere of influence, based on parcel connectivity characteristics and concurrent processes of concentration and decentralization relative to functional zones. Interactions with each functional zone (G, M, R, S) were treated as micro-level patterns, while interactions with all functional zones collectively were treated as macro-level patterns. Each of the eleven districts, while functionally independent, forms part of a larger surrounding spatial system, simultaneously shaping and being shaped by it. Accordingly, the feedback effects of physical and functional changes in any district must be considered in relation to other districts.
Blocks generated by the complex network occupy specific portions of the spatial structure in a manner that, through their hierarchical positioning across elevation scales, shapes the arrangement and ordering of connectivity centers and complex network centers, as well as related symmetrical systems within the city’s spatial structure. The functional attributes or forms of blocks within areas sharing identical or differing boundary numbers may be altered by urban planners according to prevailing conditions.
The alternating repetition of connectivity centers and complex network centers across urban blocks forms identifiable wholes due to their distinct forms. This repetition relies on the consistent configuration of recurring blocks and the parcels situated among them. The arrangement of parcels within blocks contributes to the emergence of legible forms.
The presence of parcels with clearly defined boundaries results in simple, visible, and well-defined shapes. This absolute and fixed space is measurable. To identify parcel heterogeneity, two parcel characteristics—fractal dimension and compactness—were calculated, enabling the identification of areas requiring enhancement or control to facilitate the formation of centers and the organization of smaller hierarchical centers. By considering both regular and irregular structures, as well as built and open spaces across districts, urban planners can create environments that enhance connectivity among connectivity centers and complex network centers.
The fractal dimension indicates the degree of complexity and subdivision of parcels within the urban fabric. Districts exhibiting higher fractal dimensions reflect more irregular structures. The priority ranking of irregular urban fabric across the eleven districts was 8 > 7 > 3 > 5 > 2 > 9 > 10 > 11 > 4 > 1 > 6, with District 8 exhibiting the greatest irregularity and District 6 the least. Compactness reflects the extent of construction activity: higher compactness indicates increased development, whereas lower compactness reflects a greater proportion of open space relative to built mass. Districts with high compactness require greater control, while those with lower compactness require enhancement and increased development. Based on this, districts were categorized into priority classes for control and for enhancement.
Using Kendall’s Coefficient of Concordance calculated in SPSS 22, the study examined whether the derived priorities indicate a statistically significant compatibility in connectivity among the districts of Shiraz. The results showed mean ranks of 4.05 for the sphere of influence of block boundary numbers, 4.10 for influence on connectivity centers, 6.55 for irregularity, 4.15 for construction control, 3.05 for construction enhancement, 6.65 for population, and 3.30 for levels of economic, social, cultural, and physical indicators. The highest mean rank corresponded to population prioritization. Kendall’s coefficient was 0.326, with a chi-square value of 22, 7 degrees of freedom, and a significance level of 0.002.
Since the calculated significance level was below 0.05, a statistically significant compatibility in connectivity among the districts of Shiraz was confirmed. Accordingly, by considering the positional status of areas within the derived connectivity priorities and the connectivity conditions reflected in the macro–micro interaction matrix of the eleven districts, a relational process among the elements of the physical form was defined—one that ultimately leads to an orderly spatial organization.
Discussion
In the planning process of Shiraz based on the revised detailed development plan, boundaries related to per capita land consumption, the spatial distribution of population (density), and daily intra-urban patterns, derived from population census data, have been taken into account. Physical elements (parcels and buildings) with defined forms are visible within each functional zone (R, S, M, G) of the city’s spatial structure and are interconnected through access networks. In other words, urban planning in Shiraz, as articulated in the revised plan, has sought to establish a state and quality of coherence among the elements of the city’s physical form by conceiving the city as an integrated whole with an internal structure and reciprocal interaction with environmental conditions. Through identifying major trends across the city’s vital dimensions, the plan has provided physical grounds for improving existing conditions and accommodating future transformations within the urban structure. However, the impact of recognizing the elements of the city’s physical form and the complex relationships among them has been largely overlooked in the urban planning process. This is because the spatial qualities of Shiraz have been considered to depend solely on spatial geometry (i.e., quantitative distances among elements), and urban planning has been grounded in Euclidean geometric thinking, which results in a structure lacking differentiation and adaptability. Therefore, to address this shortcoming, urban spatial qualities must be understood as dependent on relationships that also arise from interactions among the elements of physical form. Identifying spatial differences and similarities of proportions within these differences leads to the formation of a coherent structure that is hierarchically organized within a harmonious whole. Without consideration of this coherent whole, the city is perceived merely as a conventional assemblage.
Distinct from most previous theoretical studies, this research adopts an objective and applied perspective on the concept of coherence and seeks to demonstrate the effects of the manner in which urban blocks—considered the smallest geographical elements of the urban fabric, are combined with one another (i.e., the quality of coherence) within the urban planning process. This objective is examined at the analytical level of urban districts.
Based on the capacities provided by the revised detailed plan of Shiraz, it was demonstrated that it is connectivity within the physical form that generates urban wholeness. In other words, connectivity determines how the elements of the city’s physical form are combined, organized, and expanded in the service of the overall urban form. By contrast, previous studies have primarily sought to achieve coherence through regulations and rules intended to establish continuity among elements of the physical form. Mokhtarzadeh et al. (2018) consider the coherence of urban physical form to be the result of compatibility between buildings and streets, streets and land uses, and buildings, with an emphasis on scale and hierarchy. Similarly, Mohajeri (2006) defines coherence as the outcome of hierarchical and scalar connections, the diversity and integration of the street network, land-use diversity and mix, compatibility, balanced land-use distribution, proportional dimensions, and the connective integration of buildings and blocks.
In the present study, the “urban block”, that is, the smallest unit of the city enclosed by surrounding streets and regarded as the most basic unit of the urban fabric, was selected to examine the quality of their combination through connectivity based on the two principles of “scale” and “hierarchy.” In contrast, in the study by Mokhtarzadeh et al. (2018), the “street” is introduced as the most important element of form and the primary agent of connection among other elements. While both studies identify scale and hierarchy as the most important principles of linkage and integration, their distinction lies in the level of analysis: the urban block in the present study versus the street in Mokhtarzadeh et al.’s work.
The latent order and recurring pattern embedded within the city’s physical form emerge from the arrangement and relationships among urban blocks. By examining block size as the principal element of physical form in relation to surrounding blocks, the connectivity of each block within the hierarchy and within its sphere of influence was identified. This demonstrated the potential for blocks, as the main components of physical form, to be integrated into a unified whole (the city of Shiraz). The relational nature of connectivity among Shiraz’s blocks revealed that each block, as an independent element, is linked to other blocks within a hierarchical relational system. Accordingly, by considering the entirety of block relationships across the city, integration among elements of physical form can be incorporated into the planning process.
By recognizing both compatibility and differentiation within the physical form through an understanding of connectivity relationships among parcels, buildings, and zoning areas across districts, it becomes possible to identify processes that systematically organize the elements of Shiraz’s physical form. Compatibility was examined by assessing how changes in physical form interact with the surrounding environment through macro–micro connectivity interactions within each district. The results indicated that changes in any of the eleven districts of Shiraz not only affect the physical form of their immediate surroundings but also influence the physical form of other districts. Differentiation in the size of equivalent occupied spaces of physical-form parcels was examined through the analysis of regular and irregular structures and of built and open spaces across the eleven districts, leading to a classification of districts for the systematic organization of physical form. In other words, by examining the distinctiveness of each block relative to others and its adaptation to the surrounding environment, the priority of influence of each district on others was identified through its connectivity sphere of influence. Consequently, any change in an element of physical form constitutes a process that functions as an input for the systematic organization of other related elements within the physical form.
Therefore, coherence is an attribute of Shiraz’s physical urban space, characterized by multiple interconnected and overlapping centers. The connectivity of physical form, manifested as unity and continuity in the geometry of physical-form utilization indicates that the physical form of Shiraz exists within a coherent structure, rather than the physical form itself constituting an inherently coherent structure, as suggested by Bahreini and Froughi-Far (2015). The findings of the present study are not aligned with those of Bahreini and Froughi-Far and instead present distinct results. Given the relational nature of connectivity, each urban block possesses a relational distance across hierarchical levels of connectivity, with distinct forms and functions within the integrated whole of Shiraz. These blocks recur as alternating and interconnected wholes, and the degree of coherence of Shiraz’s urban form can thus be explained through the connectivity of its physical elements. This study emphasized the necessity of an integrated perspective on the spatial structure of cities within the urban planning process, an approach aligned with the understanding of complexity, as emphasized by Alexander, Tavalaee, Chen, and Jiang (Tavalaee, 2002; Jiang, 2013; Chen, 2016). The impact of this perspective on the analysis of urban spatial structure formation, and consequently on spatial planning processes, underscores the central role of “relationships.” Although such relationships have been considered in spatial planning over the past century and are manifested in practice through per capita standards, land areas, densities, and land uses, they continue to be defined within a geographical framework influenced by the modernist tendency toward simplicity, treating planning as an engineering method grounded in pure Euclidean geometry. This research demonstrates that cities embody nested and complex relationships, thereby necessitating a transformation in planning paradigms through redefining “relationships” from Euclidean to fractal relationships in order to achieve an integrated approach to spatial planning. It was also demonstrated that connectivity signifies that the physical form of Shiraz exists within a coherent structure, rather than constituting a coherent structure in itself.
Based on the overall findings of this study, the urban planning process of Shiraz, without incorporating connectivity as the core of coherence, can be critiqued from three perspectives:
Conclusion
Connectivity indicates that the physical form of cities exists within a coherent structure, rather than the physical form itself constituting a coherent structure. Considering the defined boundary numbers of urban blocks and the interaction of macro–micro patterns within the spatial structure, a connectivity pattern exists among urban blocks if and only if two blocks with identical boundary numbers belong to the same hierarchical level of elevation points. Accordingly, in the context of urban planning, the coherent form of Shiraz emerges from its connectivity pattern.
Acknowledgments: There is nothing to report.
Ethical Permission: There is nothing to report.
Conflict of Interest: This article is derived from the PhD dissertation of the third author entitled “An Optimal Model of the Spatial Structure of Shiraz Based on the City’s Geographic Scalability” in the field of Geography and Urban Planning, conducted at Payame Noor University under the supervision of the first author and with consultation from the second author.
Authors’ Contributions: Ali Akbari E (First Author), Methodologist (25%); Mousakazemi SM (Second Author), Methodologist (25%); Gholami S (Third Author): Principal Researcher/Discussion Writer (50%)
Funding: The costs of this article were covered by the student using personal funds.
One of the major concerns in the field of urban spatial planning is the preparation of plans within the framework of objective urban planning regulations, particularly the provision of per capita service levels. This issue creates challenges regarding the priority or sequencing of social urbanization versus physical urban development. Urban development plans seek to restore dynamism and vitality to urban fabrics; however, neglect of existing structures and reliance on replicating previous plans have turned the definition of a sustainable urban form into a challenge for urban planners.
The social dynamism of a city depends on its spaces and places. Human interactions and social relationships take shape within the physical fabric of the city, while the physical form itself derives its identity from existing social life [Shakibaei Bidaruni et al., 2018]. The spatial structure of a city is closely related to the manner in which internal and external transportation corridors develop; the way these corridors are connected leads to the growth and development of different parts of the city [Abdollahi Torkamani et al., 2019]. In urban studies, form can be considered equivalent to physical structure. Kevin Lynch, in The Image of the City, have defined urban form as the “physical and visible manifestations of the city” [Mokhtarpour & Manteghi Fasaie, 2018]. In defining urban form, many scholars refer to the spatial pattern of large, immobile, and permanent physical elements (such as buildings, streets, rivers, and possibly trees) and define it as the spatial distribution pattern of human activities at a specific point in time [Mider, 2012]. Within urban form, a set of scales is interconnected through a hierarchical system of relationships [Jiang, 2013]. The city is composed of components and the relationships among them; the loss of these relationships, by preventing complementary land uses from fulfilling their roles in relation to one another, threatens the integrity of the city as a whole [Bahreini & Froughi-Far, 2015]. In recent years, comprehensive urban plans, by encouraging low-density growth through zoning regulations and the separation of major urban functions, have further fragmented urban structures [Ghoraba & Tabibian, 2017]. The spatial structure of a city refers to the distribution of residential areas and economic activities across space, shaped over long-term processes by locational preferences and public policies [Burgalassi & Tommaso, 2015].
Studies related to cohesive form indicate that more than 77% of scholars in this field have emphasized the composition of elements (streets, land uses, buildings) in analyzing form cohesion, while only 33% have defined cohesion based on the internal coherence of a single element [Mokhtarzadeh, 2018]. Raimbaut proposed an urban morphological model based on the interaction between access networks and built environments, showing that the existing spatial correlations between them reflect non-stationary and multi-scalar processes [Raimbaut, 2019]. Giannopoulou, in her research, demonstrates that measuring the degree of integration and connectivity in space syntax is an important tool for analyzing urban spatial configurations. According to this method, the relationship between connectivity and integration can indicate urban land value and accessibility, and these factors significantly influence the growth of areas by increasing accessibility under specific economic conditions [Giannopoulou et al., 2016]. Chen employed multiple fractal analysis indices to classify urban physical form patterns [Chen, 2016]. Shafieion and Zamani have examined urban form parameters (residential density, land-use mix, and connectivity) in relation to the walkability index in District 14 of Isfahan; the results show that variations in these indices and differences in urban form affect residents’ physical activity levels [Shafieion, 2021]. Nikpoor et al. assess the capacity of Babolsar’s neighborhoods based on the compact city model and found that compact neighborhoods perform better in physical, infrastructural, social, and economic terms, and due to their higher livability quality, show a greater tendency toward residential preference [Nikpoor et al., 2017]. Ghadami et al., aiming to propose a sustainable urban form for Sari, evaluate citizens’ travel tendencies using land-use mix, connectivity, and density indicators across compact, semi-compact, and sprawled forms [Ghadami et al., 2017]. Movahed et al. have examined different urban forms to explain the spatial expansion pattern of Saqqez from a sustainable urban form perspective and ultimately have proposed the compact growth pattern as the future development model for the city [Movahed et al., 2014]. Azizi and Araste have analyzed the process of urban sprawl and unsustainable development in Yazd by considering the effects of building density, population density, land prices, accessibility, and urban block size on urban form and spatial changes [Azizi & Araste, 2011]. Mohajeri, by examining complexity and cohesion in fractal urban form design, have compared physical sustainability in traditional Iranian cities with contemporary ones and introduced principles and criteria for urban physical sustainability [Mohajeri, 2006]. In the context of holistic urban planning, various aspects of urban cohesion have been examined in previous studies based on their respective research objectives; however, the existing gap and the rationale for this study lies in the limited presentation of a planning perspective capable of explaining a cohesive urban form and identifying the factors that generate it.
In growing cities where components continuously increase, urban form faces new challenges regarding the integration of these units into the larger urban system [Tavalaee, 2002]. If urban form is considered a combination of physical, natural, and functional factors along with the element of time, the prominent and stable elements of this set constitute the urban structure. Therefore, urban structure represents the main component of urban form, reflecting its overall characteristics and defining its structural framework [Daneshpoor & Roosta, 2012]. Structural cohesion emerges through the creation of interdependence within the city’s communication network. In fact, as each unit becomes embedded within a broader form, a close spatial relationship is established to preserve and strengthen the whole; thus, space as a cohesive element and the spatial network as a connecting element are of critical importance to urban function. Consequently, urban planning must recognize the characteristics of place and incorporate them into the planning process [Tavalaee, 2002]. Tsai, in a quantitative study of urban form at the micro-morphological scale, focused on the spatial distribution of population [Tsai, 2005]. Guerois and Paulus show that to understand the effects of independent and distinct units in a city, one may consider components of the built environment (morphology), urban functions, or administrative boundaries [Guerois & Paulus, 2002]. Poorjafar and Esmaelian have identified the main principles of urban cohesion as physical, functional, and identity dimensions [Poorjafar & Esmaelian, 2013]. Ana Julia et al., by considering physical and functional dimensions, have demonstrated that the cohesion of urban spaces is realized within the framework of network-based dimensions [Julia et al., 2010].
Different urban units are integrated through interfaces or boundary elements. These interfaces are responsible for establishing connections among various urban units [Mohajeri, 2006]. According to this principle, the boundary elements of one module connect to those of another, and some elements may interlock like pieces of a puzzle. Desirable boundaries in urban space can be achieved by considering appropriate visual principles derived from geometric rules [Roshani et al., 2017].
According to systems theory, any system can be divided into several subsystems, and each subsystem into multiple smaller components. Each of these constituent parts is considered a center or a distinct set of points in space [Nadimi et al., 2014]. Cohesion of physical form is a process that links physical form elements to one another through an orderly organization [Tavalaee, 2002]. By using the street network as the primary element, the entire physical space of the city can be scaled: the street network is decomposed into multiple blocks, with the size of each block representing its scaling characteristics. The recurring pattern of block sizes reveals the latent order embedded in the city’s physical form [Jiang & Liu, 2015]. This latent order indicates the interconnection among urban blocks, leading to the integration of physical form elements [Tavalaee, 2002].
Despite the relational nature of urban physical form, by identifying interactions between areas, a cohesive whole of physical form elements can be conceptualized in a way that preserves the coupling of urban form. Parcels collectively constitute a unit; therefore, within a unit, discontinuous components should not exist, as the coupling of elements in physical form at smaller, fundamental scales provides the basis for cohesion in larger-scale structures [Mohajeri, 2006]. To examine the geometric coupling of physical form, parcels with identifiable irregular structures are analyzed, while the coupling of mass and space and the extent of solid and void spaces resulting from construction activities are used to assess built form [Purevtseren et al., 2018].
This study seeks to demonstrate the existence of nested and complex relationships and emphasizes the necessity of transforming perspectives on spatial planning by redefining the concept of “relationships” in order to achieve an integrated approach to planning urban structures. Accordingly, by understanding the relational nature of physical form and considering geometric coupling in interregional interactions, a process can be identified based on the connectivity among physical form elements (streets, parcels, and buildings) that leads to an orderly organization. In the strategic–structural plan of Shiraz, the city is regarded as a whole with an internal structure and reciprocal links to environmental conditions; however, the role of recognizing the city’s geographical elements and the complex relationships among components in the urban planning process has been overlooked. In this article, considering the city’s complex network, we define the relational nature of Shiraz’s physical urban form. The aim of this research is to explain the cohesion of Shiraz’s physical urban form based on a connectivity-oriented model. Accordingly, this study seeks to answer the following question: from an urban planning perspective, what is the source of the cohesive form of the city of Shiraz?
Methodology
This quantitative study was conducted using surface feature data, including the parcel layer and the urban block layer (comprising multiple parcels bounded by streets), derived from the 2006 base map of Shiraz. In addition, information layers from the revised detailed development plan maps of 2014 including functional zoning layers and transportation networks were utilized for the year 2021. All spatial data were extracted and processed using ArcGIS software. Documentary and archival studies were employed to obtain the required background information and references.
The service boundary of Shiraz, based on the latest administrative divisions, consists of 11 municipal districts, covering an area of 22,731 hectares and comprising 77 subdistricts. The largest municipal district is District 10, with an area of approximately 3,563 hectares, while the smallest is the historical–cultural district, with an area of 377 hectares. Given the available data, the Guttman scalogram method was used to identify homogeneous areas within Shiraz. In this method, areas are grouped based on their degree of similarity, resulting in the identification of homogeneous zones. The districts were classified according to their levels of economic, social, cultural, and physical indicators by calculating the mean values and the deviation from the mean for each indicator. As a result, Districts 8 and 11 were classified as deprived or underdeveloped; Districts 2, 3, 5, 6, and 7 as semi-developed or moderately endowed; and Districts 1, 4, 9, and 10 as developed or well-endowed.
Currently, urban planning in Shiraz is carried out according to the regulations defined in the revised zoning system of the city. The fundamental emphasis is placed on only one dimension of the part–whole relationship between each element and other elements. In other words, zoning regulations are aligned with access networks, and building regulations are aligned with parcel size. Land uses are determined based on their compatibility or incompatibility with adjacent uses. In the revised detailed zoning framework of Shiraz, construction regulations for parcels are defined by considering the quality of spatial planning for society (based on human-centered criteria) and place (based on efficiency criteria). For each parcel, indicators such as compatibility (the correspondence between form and function), accessibility (the quantity and diversity of uses that can be accessed), identity (the distinction of one space from another), and meaning (what a place conveys, i.e., the meaningfulness of the visual environment) are specified. Consequently, the fixed position of each parcel within a block, as defined by its zoning code, has led to the aggregation of diverse buildings and the enclosure of spaces based on height regulations. As a result, the primary concern of urban planners has been limited to the provision of land-use areas and per capita service levels, the observance of hierarchical access levels, and compliance with density and site coverage regulations in each district.
What is overlooked in the zoning system is the failure to account for parcel heterogeneity within the unity of the physical form relative to the whole. Heterogeneity in urban physical form arises either from the physical shape of existing parcels, resulting from land subdivision processes, or from functional zoning and land-use categories. Since urban blocks are integral components of the city’s spatial structure and inseparable from the overall structure, this study addresses localized heterogeneity occurring in different parts of the physical form by recognizing macro–micro relationships within functional zones and land uses and by calculating the fractal dimensions and compactness of parcels in each district. This approach provides a response to the observed heterogeneity based on connectivity. Such conditions indicate the neglect of relational patterns among elements of the city’s physical form. Urban planners often regard intra-urban interactions as being influenced solely by geometric structure, which stems from overlooking the role of interconnected multi-scale structures in shaping interactions. To revise planning approaches within the zoning system and to propose an optimal structural model based on continuity and functional efficiency, appropriate indicators reflecting the relational patterns among physical form elements must be incorporated into urban planning.
To explain the concept of physical form cohesion from a connectivity perspective in Shiraz, two assumed characteristics of the “urban block”, namely, the block’s position within the hierarchy of connectivity and its boundary number were employed as the fundamental units of physical form across three stages.
Stage 1: The Nature of the Connectivity Pattern in Shiraz
The complex network system present in Shiraz provides a necessary framework for defining blocks with cohesive functions and structures. Distinct patterns that converge at similar elevation levels generate new patterns with different properties at higher hierarchical levels. Connectivity emerges from the relational structure among blocks and their mutual influences. This characteristic relates to the position of each block within hierarchical levels defined by block size in the city’s complex network. Using visualization tools (head–tail breaks), upper and lower thresholds at each hierarchical level of block size were classified, and contour curves derived from elevation points obtained in subsequent steps were used for further categorization.
Stage 2: Rules of the Connectivity Pattern in Shiraz
In this study, the “boundary number of each block” was used as an indicator of “connectivity distance.” For each block, a boundary number was defined based on its distance from the city boundary (the officially approved urban limit). Accordingly, the greater the distance of a block from the city boundary, the higher its boundary number. Boundary numbers represent discrete boundaries and indicate the connectivity status of each block. In other words, blocks with different boundary numbers appear as a “whole” at different levels within the hierarchical classification of urban block connectivity.
Moreover, at each classification level, there exist centers, not necessarily geometric centers, but focal points that influence connectivity characteristics within the complex network. Relationality indicates that all blocks, from the smallest to the largest scale, play roles within the hierarchy. Considering the functional zoning system used to define block functions in the detailed plan, centers located in blocks with different boundary numbers establish a property of interconnectedness within a hierarchical structure.
After determining the position of each block within the connectivity hierarchy, the priority of influence of each district on the centers present in the relational pattern was identified. Each center interacts with its surrounding environment, and the relationship between the center and its periphery is determined by the center’s sphere of influence. Based on block connectivity characteristics and simultaneous processes of concentration and decentralization in relation to functional zones, macro–micro connectivity interactions within the spatial structure were examined in relation to each functional zone (G, M, R, S) as micro-level connectivity, and in relation to all functional zones collectively as macro-level connectivity.
Given the variation among blocks in terms of built and open spaces across different districts, the fractal dimension was used to determine heterogeneity in the spatial filling of urban areas. This measure reflects the degree of complexity in parcel shapes within the urban fabric, indicating the formation of irregular structures (higher fractal dimensions correspond to greater structural irregularity). Additionally, the compactness ratio of parcels was employed to assess the extent of development (built spaces). An increase in the compactness index indicates an increase (or decrease) in the intensity of construction within the study area.
Stage 3: Integrated Analysis of the Outputs of Each Stage
In this stage, the concept of cohesion in the city’s physical form was explained from a connectivity perspective at the analytical level of Shiraz’s urban districts. By examining the degree of compatibility in the connectivity status of districts, based on the derived priorities (including the sphere of influence of block boundary numbers, influence on centers within the complex network and connectivity hubs, the formation of irregular structures, control and enhancement of construction activity, population distribution, and levels of economic, social, cultural, and physical indicators), the Kendall’s Coefficient of Concordance was calculated. This analysis assessed the mutual influence of different districts on one another and, consequently, their impact on the cohesion of the city’s physical form.
Findings
Streets constitute the primary element of physical form and, as the city’s complex network, generate urban blocks. Block size, which reflects the nature of their relational connectivity, indicates the coexistence of smaller blocks alongside larger ones. To identify the nature of relational connectivity in the physical form of Shiraz, the analysis began with a planimetric map by calculating the mean block length of the city (156 m). Blocks with lengths below 156 m were classified as the lower tail, while those exceeding 156 m formed the upper head at the first hierarchical level. In the subsequent step, the mean length of blocks in the upper head of the first level was calculated. Blocks shorter than this mean constituted the next lower tail, and those longer than it formed the upper head at the second hierarchical level. This set of streets, considered as a whole, was divided into an upper head (values above the mean) and a lower tail (values below the mean) using the head–tail breaks approach. This recursive process continued until the condition distinguishing poorly connected streets from well-connected ones was no longer violated, proceeding until the proportion of the upper head fell below 40%. Overall, the blocks of Shiraz were distributed across five hierarchical levels of connectivity.
Subsequently, using the concept of the boundary number (as discrete boundaries) for each block, the connectivity distance of each block from the city boundary was determined, thereby clarifying the connectivity status of blocks within repetitive relational patterns. Accordingly, a boundary number was assigned to each block based on its distance from the administrative boundary of Shiraz, such that greater distances corresponded to higher boundary numbers. This decomposition of the complex network into blocks with varying boundary numbers produced nested rings, with the smallest ring formed by the block with boundary number 21. Each block possesses a range of boundary numbers depending on its position relative to the city boundary: blocks with boundary number 1 have a single boundary, whereas the block with boundary number 21 encompasses boundaries from 1 to 21. The correspondence between contour lines and boundary numbers from 1 to 21 indicates that blocks located at similar elevation levels tend to be more strongly interconnected. By measuring distances from the central block to the centers of other blocks, the centers associated with boundary numbers 1 to 21 were identified.
Boundary number 21 encompassed all blocks across the city of Shiraz, and the block with this boundary number functioned as the primary center of urban connectivity. In the next step, the distances between the reference point (the central block with boundary number 21) and the centers of other blocks (centers of the complex network) were calculated. By defining the nature of relational connectivity in the physical form of Shiraz and identifying the hierarchical position of each block, the priority of influence of different districts on the existing centers was determined. The priority of influence of connectivity centers on the complex network followed the sequence 4 > 1 > 3 > 5 > 6 > 9 > 11, while the priority of influence of the city’s complex network centers on the eleven municipal districts followed the sequence 4 > 2 > 5 > 7 > 1 > 9 > 10.
Blocks sharing similar boundary numbers were interconnected across different hierarchical levels. Blocks with boundary numbers from 1 to 3 appeared across all hierarchical levels and elevation points.
According to the approved revised detailed plan, the function of each block is defined within the zoning system. It is therefore possible for blocks with different boundary numbers that converge at various hierarchical levels and elevation classes to be functionally complementary. Within each district, blocks, despite having discontinuous boundary numbers across different hierarchical levels, may exhibit either similar or distinct functions relative to one another. Consequently, any intervention in the city’s physical form must consider the locational position, functional role, and connectivity of blocks within the broader spatial structure. Blocks with varying boundary numbers occupy different hierarchical levels, and blocks with both smaller and larger boundary numbers recur across these levels. The hierarchical scaling of blocks across levels constitutes identifiable wholes. In effect, the boundary number not only indicates a block’s position relative to others but also serves as both a differentiating and a linking mechanism among blocks.
Connectivity among blocks existed across all hierarchical levels of elevation points. In the city’s complex network, the boundary number was defined as the connectivity distance of blocks from the outermost boundary relative to the urban network, and boundary numbers were used to identify the city’s connectivity centers. Both connectivity centers and complex network centers were present at multiple hierarchical levels. The intensity of influence exerted by centers was also dependent on the distribution of built and open spaces within their spheres of influence. Each center interacts with its surrounding environment, and the relationship between center and periphery is determined by the extent of this influence. By considering variable block boundaries within the primary elements of the physical form pattern, nodes, paths, and areas, the sphere of influence associated with each boundary number was identified. In the city’s physical form, the prioritization of boundary numbers with the greatest influence within their coverage radii followed the sequence: 1 > 2 > 4 > 5 > 8 > 6 > 7 > 11 > 13 > 9 > 14 > 16 > 17 > 12 > 13 > 10 > 15 > 18 > 20 > 19.
The position of urban blocks within the hierarchy of elevation points and the relationships among connectivity centers and complex network centers function as recursive rules, from whole to part and from part to whole, by accounting for locational similarity to preserve functional order and form within the connectivity of centers across their coverage areas. Blocks identified as connectivity centers or complex network centers interact with other blocks. The conflicts and heterogeneity arising from differences in form and function within specific spatial contexts can be clarified by considering connectivity across hierarchical elevation levels. By maintaining relationships between primary connectivity centers and surrounding blocks through similarity, larger centers can be formed.
Based on accessibility, population density, and the provision of service areas and per capita facilities, functional zones in the revised detailed plan have been allocated across the city. Overlaying these functional zones onto the relational pattern of the complex network allows for the assessment of how changes in blocks with specific functions affect their connected blocks. Given that functional zoning patterns recur across different scales, any modification to a block with a particular function must consider not only the scale of the zone but also the block’s connectivity capacity.
The relationship between each block and its surrounding environment indicates that any change in the number of blocks at the city scale affects the boundary numbers of other blocks. Each block occupies a defined space within the city’s spatial structure and contains parcels that likewise occupy specific spatial extents. Moreover, blocks emerge from the city’s complex network, underscoring the tangible occupation of space by this network. Under the revised functional zoning framework, blocks with similar zones tend to exhibit relatively comparable conditions in terms of building height, number of floors, balance between built and open spaces, building density, and permitted land uses. Although changes driven by urban needs and pressures may introduce heterogeneity in form and function, the diversity and hierarchical structure inherent in the zoning system can be employed to organize the spatial structure. Considering the varied needs of residents and broader socio-economic conditions, unnecessary functions may be removed and appropriate ones introduced to establish functional equilibrium.
Differences observed in the form and function of parcels, blocks, and complex networks reflect the differentiation of elements within the spatial structure. Given the formation of hierarchies in functional zones and access networks under the revised detailed plan, alongside the connectivity hierarchy of urban blocks, it can be argued that contrast is an enduring feature of spatial structure. Recognizing this reality enables urban planners to provide reasoned responses to differences arising from land-use changes.
To identify macro–micro relationships within the spatial structure of Shiraz’s eleven districts, the interaction of macro- and micro-level connectivity was examined for each district, considering its sphere of influence, based on parcel connectivity characteristics and concurrent processes of concentration and decentralization relative to functional zones. Interactions with each functional zone (G, M, R, S) were treated as micro-level patterns, while interactions with all functional zones collectively were treated as macro-level patterns. Each of the eleven districts, while functionally independent, forms part of a larger surrounding spatial system, simultaneously shaping and being shaped by it. Accordingly, the feedback effects of physical and functional changes in any district must be considered in relation to other districts.
Blocks generated by the complex network occupy specific portions of the spatial structure in a manner that, through their hierarchical positioning across elevation scales, shapes the arrangement and ordering of connectivity centers and complex network centers, as well as related symmetrical systems within the city’s spatial structure. The functional attributes or forms of blocks within areas sharing identical or differing boundary numbers may be altered by urban planners according to prevailing conditions.
The alternating repetition of connectivity centers and complex network centers across urban blocks forms identifiable wholes due to their distinct forms. This repetition relies on the consistent configuration of recurring blocks and the parcels situated among them. The arrangement of parcels within blocks contributes to the emergence of legible forms.
The presence of parcels with clearly defined boundaries results in simple, visible, and well-defined shapes. This absolute and fixed space is measurable. To identify parcel heterogeneity, two parcel characteristics—fractal dimension and compactness—were calculated, enabling the identification of areas requiring enhancement or control to facilitate the formation of centers and the organization of smaller hierarchical centers. By considering both regular and irregular structures, as well as built and open spaces across districts, urban planners can create environments that enhance connectivity among connectivity centers and complex network centers.
The fractal dimension indicates the degree of complexity and subdivision of parcels within the urban fabric. Districts exhibiting higher fractal dimensions reflect more irregular structures. The priority ranking of irregular urban fabric across the eleven districts was 8 > 7 > 3 > 5 > 2 > 9 > 10 > 11 > 4 > 1 > 6, with District 8 exhibiting the greatest irregularity and District 6 the least. Compactness reflects the extent of construction activity: higher compactness indicates increased development, whereas lower compactness reflects a greater proportion of open space relative to built mass. Districts with high compactness require greater control, while those with lower compactness require enhancement and increased development. Based on this, districts were categorized into priority classes for control and for enhancement.
Using Kendall’s Coefficient of Concordance calculated in SPSS 22, the study examined whether the derived priorities indicate a statistically significant compatibility in connectivity among the districts of Shiraz. The results showed mean ranks of 4.05 for the sphere of influence of block boundary numbers, 4.10 for influence on connectivity centers, 6.55 for irregularity, 4.15 for construction control, 3.05 for construction enhancement, 6.65 for population, and 3.30 for levels of economic, social, cultural, and physical indicators. The highest mean rank corresponded to population prioritization. Kendall’s coefficient was 0.326, with a chi-square value of 22, 7 degrees of freedom, and a significance level of 0.002.
Since the calculated significance level was below 0.05, a statistically significant compatibility in connectivity among the districts of Shiraz was confirmed. Accordingly, by considering the positional status of areas within the derived connectivity priorities and the connectivity conditions reflected in the macro–micro interaction matrix of the eleven districts, a relational process among the elements of the physical form was defined—one that ultimately leads to an orderly spatial organization.
Discussion
In the planning process of Shiraz based on the revised detailed development plan, boundaries related to per capita land consumption, the spatial distribution of population (density), and daily intra-urban patterns, derived from population census data, have been taken into account. Physical elements (parcels and buildings) with defined forms are visible within each functional zone (R, S, M, G) of the city’s spatial structure and are interconnected through access networks. In other words, urban planning in Shiraz, as articulated in the revised plan, has sought to establish a state and quality of coherence among the elements of the city’s physical form by conceiving the city as an integrated whole with an internal structure and reciprocal interaction with environmental conditions. Through identifying major trends across the city’s vital dimensions, the plan has provided physical grounds for improving existing conditions and accommodating future transformations within the urban structure. However, the impact of recognizing the elements of the city’s physical form and the complex relationships among them has been largely overlooked in the urban planning process. This is because the spatial qualities of Shiraz have been considered to depend solely on spatial geometry (i.e., quantitative distances among elements), and urban planning has been grounded in Euclidean geometric thinking, which results in a structure lacking differentiation and adaptability. Therefore, to address this shortcoming, urban spatial qualities must be understood as dependent on relationships that also arise from interactions among the elements of physical form. Identifying spatial differences and similarities of proportions within these differences leads to the formation of a coherent structure that is hierarchically organized within a harmonious whole. Without consideration of this coherent whole, the city is perceived merely as a conventional assemblage.
Distinct from most previous theoretical studies, this research adopts an objective and applied perspective on the concept of coherence and seeks to demonstrate the effects of the manner in which urban blocks—considered the smallest geographical elements of the urban fabric, are combined with one another (i.e., the quality of coherence) within the urban planning process. This objective is examined at the analytical level of urban districts.
Based on the capacities provided by the revised detailed plan of Shiraz, it was demonstrated that it is connectivity within the physical form that generates urban wholeness. In other words, connectivity determines how the elements of the city’s physical form are combined, organized, and expanded in the service of the overall urban form. By contrast, previous studies have primarily sought to achieve coherence through regulations and rules intended to establish continuity among elements of the physical form. Mokhtarzadeh et al. (2018) consider the coherence of urban physical form to be the result of compatibility between buildings and streets, streets and land uses, and buildings, with an emphasis on scale and hierarchy. Similarly, Mohajeri (2006) defines coherence as the outcome of hierarchical and scalar connections, the diversity and integration of the street network, land-use diversity and mix, compatibility, balanced land-use distribution, proportional dimensions, and the connective integration of buildings and blocks.
In the present study, the “urban block”, that is, the smallest unit of the city enclosed by surrounding streets and regarded as the most basic unit of the urban fabric, was selected to examine the quality of their combination through connectivity based on the two principles of “scale” and “hierarchy.” In contrast, in the study by Mokhtarzadeh et al. (2018), the “street” is introduced as the most important element of form and the primary agent of connection among other elements. While both studies identify scale and hierarchy as the most important principles of linkage and integration, their distinction lies in the level of analysis: the urban block in the present study versus the street in Mokhtarzadeh et al.’s work.
The latent order and recurring pattern embedded within the city’s physical form emerge from the arrangement and relationships among urban blocks. By examining block size as the principal element of physical form in relation to surrounding blocks, the connectivity of each block within the hierarchy and within its sphere of influence was identified. This demonstrated the potential for blocks, as the main components of physical form, to be integrated into a unified whole (the city of Shiraz). The relational nature of connectivity among Shiraz’s blocks revealed that each block, as an independent element, is linked to other blocks within a hierarchical relational system. Accordingly, by considering the entirety of block relationships across the city, integration among elements of physical form can be incorporated into the planning process.
By recognizing both compatibility and differentiation within the physical form through an understanding of connectivity relationships among parcels, buildings, and zoning areas across districts, it becomes possible to identify processes that systematically organize the elements of Shiraz’s physical form. Compatibility was examined by assessing how changes in physical form interact with the surrounding environment through macro–micro connectivity interactions within each district. The results indicated that changes in any of the eleven districts of Shiraz not only affect the physical form of their immediate surroundings but also influence the physical form of other districts. Differentiation in the size of equivalent occupied spaces of physical-form parcels was examined through the analysis of regular and irregular structures and of built and open spaces across the eleven districts, leading to a classification of districts for the systematic organization of physical form. In other words, by examining the distinctiveness of each block relative to others and its adaptation to the surrounding environment, the priority of influence of each district on others was identified through its connectivity sphere of influence. Consequently, any change in an element of physical form constitutes a process that functions as an input for the systematic organization of other related elements within the physical form.
Therefore, coherence is an attribute of Shiraz’s physical urban space, characterized by multiple interconnected and overlapping centers. The connectivity of physical form, manifested as unity and continuity in the geometry of physical-form utilization indicates that the physical form of Shiraz exists within a coherent structure, rather than the physical form itself constituting an inherently coherent structure, as suggested by Bahreini and Froughi-Far (2015). The findings of the present study are not aligned with those of Bahreini and Froughi-Far and instead present distinct results. Given the relational nature of connectivity, each urban block possesses a relational distance across hierarchical levels of connectivity, with distinct forms and functions within the integrated whole of Shiraz. These blocks recur as alternating and interconnected wholes, and the degree of coherence of Shiraz’s urban form can thus be explained through the connectivity of its physical elements. This study emphasized the necessity of an integrated perspective on the spatial structure of cities within the urban planning process, an approach aligned with the understanding of complexity, as emphasized by Alexander, Tavalaee, Chen, and Jiang (Tavalaee, 2002; Jiang, 2013; Chen, 2016). The impact of this perspective on the analysis of urban spatial structure formation, and consequently on spatial planning processes, underscores the central role of “relationships.” Although such relationships have been considered in spatial planning over the past century and are manifested in practice through per capita standards, land areas, densities, and land uses, they continue to be defined within a geographical framework influenced by the modernist tendency toward simplicity, treating planning as an engineering method grounded in pure Euclidean geometry. This research demonstrates that cities embody nested and complex relationships, thereby necessitating a transformation in planning paradigms through redefining “relationships” from Euclidean to fractal relationships in order to achieve an integrated approach to spatial planning. It was also demonstrated that connectivity signifies that the physical form of Shiraz exists within a coherent structure, rather than constituting a coherent structure in itself.
Based on the overall findings of this study, the urban planning process of Shiraz, without incorporating connectivity as the core of coherence, can be critiqued from three perspectives:
- Physical elements with defined forms, visible at multiple scales within the city’s spatial structure, are connected through access networks; however, in Shiraz’s zoning system, the allocation of functions and land uses is based on the context of their mutual impacts. What urban planners consider in terms of connectivity is limited to relationships among centers with similar functions or among centers with different functions, indicating a neglect of relationships among the broader elements of the city’s geographical space.
- The geometric order defined within Shiraz’s zoning system reflects rules and regulations that treat buildings as the primary basis for controlling development and density within each zone in relation to public services and transportation corridors. Construction activities are carried out solely according to regulations defined by functional zones. What is overlooked by urban planners is the coherence of form and context within the city’s spatial structure—coherence that generates beneficial relationships among structural elements and prevents disruption of the urban spatial structure.
- The zoning strategy in urban development plans is based on areas that are relatively similar in terms of building height, number of floors, proportions of built space, building density, and general land-use type or permitted uses. Consequently, urban elements within this zoning system are connected only through symmetry, similarity, and form-based relations, resulting merely in the orderly placement of urban centers within the spatial structure. What is neglected in the formation of spatial structure is the relationship between the density function (uniform distribution within the spatial structure) and increasing density intensity (the filling of space within the city).
- Developing hierarchical levels of heterogeneous scales for hierarchical urban systems;
- Formulating a general model of spheres of influence within hierarchical urban systems to identify existing deficiencies and needs, determine the future roles of these spheres, and examine their mutual influences across hierarchical levels;
- Identifying topological centers at various geographical, regional, sub-regional, and local levels, and recognizing the relationships among these centers in assessing the effectiveness of other socio-economic dimensions.
Conclusion
Connectivity indicates that the physical form of cities exists within a coherent structure, rather than the physical form itself constituting a coherent structure. Considering the defined boundary numbers of urban blocks and the interaction of macro–micro patterns within the spatial structure, a connectivity pattern exists among urban blocks if and only if two blocks with identical boundary numbers belong to the same hierarchical level of elevation points. Accordingly, in the context of urban planning, the coherent form of Shiraz emerges from its connectivity pattern.
Acknowledgments: There is nothing to report.
Ethical Permission: There is nothing to report.
Conflict of Interest: This article is derived from the PhD dissertation of the third author entitled “An Optimal Model of the Spatial Structure of Shiraz Based on the City’s Geographic Scalability” in the field of Geography and Urban Planning, conducted at Payame Noor University under the supervision of the first author and with consultation from the second author.
Authors’ Contributions: Ali Akbari E (First Author), Methodologist (25%); Mousakazemi SM (Second Author), Methodologist (25%); Gholami S (Third Author): Principal Researcher/Discussion Writer (50%)
Funding: The costs of this article were covered by the student using personal funds.
Keywords:
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