A Dialectical Synthesis of Fused Grid Theory and Fractal Islamic Urbanism: Addressing the Deficiencies of Street Grid and Hierarchy Systems in Riyadh City

Abstract

The traditional Arab-Islamic urban fabric of Riyadh, with its emphasis on privacy, social cohesion, and environmental adaptation, was radically disrupted when the 1970s Doxiadis master plan was implemented, transforming the city into a car-dependent gridiron design. The shift led to ever-spreading sprawl, reduced pedestrian-friendliness, and eroded local identity. Using Hegelian dialectics methodology, this paper proposes integration of fused grid theory and urban Islamic fractals geometry in the urban fabric of the city. Specifically for Riyadh, the proposed changes encourage urban quadrant nesting, change of block scale and layout, fractal landscape integration, and multi-modal permeability. These adaptations are intended to increase connectivity, reduce crash rates, minimize impacts on the environment, enhance walkability, and elevate overall quality of life.

1. Introduction

Since 1970, the population of Saudi Arabia’s capital Riyadh increased from around 400,000 to almost 8 million, making it one of world’s fastest-growing cities [1]. The city’s urban fabric has shifted from the traditional Arab-Islamic layouts, emphasizing human scale, privacy, social interaction, and adaptation to the harsh environment, to a car-oriented gridiron pattern based on the Doxiadis master plan of the 1970s, Figure 1.

The Doxiadis plan introduced a low-density suburban development in sprawling superblocks of 2 km × 2 km. Although it provided an efficient road system and fast vehicular movement, this masterplan fueled urban sprawl, car dependency, poor walkability and a cultural departure from Islamic principles such as graduated privacy [2]. As the studies indicate, these superblock formations lengthen distances for walking and cycling by 20–30%, which diminishes their attractiveness and contributes to social segregation. This is validated by the network analysis system of measurement, such as increased average path lengths in graph theory models [3]. In Riyadh, with a hot and arid climate, the above problems are exacerbated by environmental pressures such as urban heat islands and water shortages [4], Figure 2.

This paper develops a hybrid theoretical framework that combines two urban planning theories, fused grid theory with fractal geometry associated with Islamic urban planning, using dialectical synthesis to mediate those theoretical urban planning paradigms that endorse or challenge street hierarchies and grid systems [5]. Based on Hegelian dialectics, the approach also balances efficiency in modernist grid systems with the organic and adaptive properties of Islamic fractal forms, aiming to optimize multi-modal networks, lessen environmental impacts, and restore the fractal quality inherent in Islamic urbanism. Adaptations to humanize Riyadh include quadrisecting superblocks and nesting of fractal patterns, adjusting sizes and layouts of quadrants, blocks, and lots, integrating landscapes, and enhancing permeability. Quantitative estimates from previous research include a possibility of a 15–20% increase in land efficiency [6]. This work is in line with the Saudi Vision 2030 that supports sustainable development and with tools, like the Riyadh Metro, to mitigate social fragmentation [7].

The proposed hybrid model which is adaptable to arid settings advances UN Sustainable Development Goal 11 for inclusive cities, suggests up to a 3 °C drop in temperature through greener and permeable designs [8]. This alignment will increase economic and social benefits, for example, 15–20% greater land efficiency [6], and invites a more livable and culturally grounded future for Riyadh’s residents.

Research Questions:

1-

What are the shortcomings of the Doxiadis gridiron and hierarchical street systems in Riyadh in relation to walkability, environmental impact, and cultural identity?

2-

How can the fused grid theory be dialectically synthesized with the Islamic fractal geometry to compensate for these limitations?

3-

What are the morphological responses of this synthesis, and how might they increase the level of urban sustainability in Riyadh?

Hypotheses:

1-

The hybrid connectivity of fused grids combined with Islamic fractals can reduce the average path length from 15–20%, relative to the superblock system, and this will improve walkability and multi-modal permeability (in accordance with network analysis models in Boeing [3]).

2-

Urban design inspired by fractal geometry will encourage environmental adjustments like a decrease of 2–3 °C in urban heat island effects through green and porous urban areas in the same direction as SDG 11 (adapted from Mohan et al. [4] and relevant literature).

3-

The hybrid model shall bring back cultural dimensions such as graduated privacy and social integration in response to alienation that modernist grids generate (informed after Hakim [9] and Alnaim [10]).

2. Literature Review

2.1. Thesis: Core Theories and Challenges

The street grid and hierarchy system, classified as freeways, arterials, collectors, and local streets, give priority to vehicular movement which compromises urban quality [9]. The gridiron pattern in Riyadh can be traced to the principles of modernization theory, which emphasizes industrial-centric policies and rapid vehicular movement to manage rapid growth efficiently. However, this approach leads to urban sprawl, longer movement, and fragmented land-use patterns (34% vacancy categorized as “white land”) [1,10]. However, systems theory supports the hierarchical system of streets for resource and traffic management that meets expandability requirements of Vision 2030 but ignores cultural standards [11]. The hierarchical model causes low walkability and leads to social isolation and environmental strain. In addition, gridiron layouts aggravate the impacts of urban heat islands and stress water resources [4]. Addressing this ineffectiveness is critical, as at present this pattern contributes to unsustainable allocation of resources.

2.2. Antithesis: Different Paradigms Presented

The critics of gridiron and hierarchical street systems maintain that these layouts are inflexible and autocentric. According to the semilattice model of Christopher Alexander, there were better neighborhood models with interconnecting street networks to establish a livable environment [12]. The New Urbanism/smart growth doctrine, which addresses the creation of new communities or districts, particularly supports high-density urban neighborhoods with mixed use to counter sprawl and social alienation [13]. Transit-oriented development (TOD) focuses on intensifying growth along public transport networks [1,14]. Tactical urbanism, on the other hand, aims to offer alternatives to the rigidity of street hierarchy systems by introducing short-term interventions [11]. These theories illustrate how street hierarchical systems are questionable by generating car-dependent and socially alienated environments [15],

Table 1. Theories Opposing or Accepting Street Grid and Hierarchy Systems.

Classification implies a binary view on these rival theories with regard to promoting emergent connectivity toward a resilient urban fabric, measured by network centrality indices [12].
Category	Theory/Concept	Key Points
Opposing street grid and hierarchy	Christopher Alexander’s Theory: “A City Is Not a Tree”	Semilattice networks with overlap between subsystems.
	Smart Growth	Supports compact, multi-use transit-oriented development to reduce sprawl and increase accessibility.
	Transit-Oriented Development (TOD)	Rejects car dependency; integrates density around public transit.
	Tactical Urbanism	Temporary, short-time lanes, enabling experimentation.
	General Critique	Exposes flaws in the hierarchies that create dependency and social alienation.
Accepting frameworks operationalized hierarchy for improved movement dynamics with 10–15% gains in efficiency as calculated by traffic simulation models [11].
Accepting street hierarchies	Systems Theory	Hierarchy with functional models for resource allocation and traffic management.
	Contextual Road Network Grid and Hierarchy	Sustainable adjustment of hierarchies (also support regional needs).

.

The fused grid theory paradigm is a return to the Radburn plan of the mid-20th century [16]. It separates pedestrians and vehicles with cul-de-sacs and continuous walkways along green spines that are nested within a grid structure. The design was described in Grammenos et al. [17] to offer better access to essential urban services through Hippodamian grid layout, with buildings strategically placed along orthogonal pathways. For instance, the fused grid system, as employed in the Stratford plan [18], enhanced frontage properties by 4% and accessibility by 73% due to providing comfortable walking distance compared with a traditional grid.

Using this model, the decrease in collision rate has been empirically confirmed in the Canadian experience where a 40–60% drop was observed, proving the model’s efficacy in hybrid connectivity [14]. This alternative planning approach corresponds with the requirement of the city of Riyadh to produce a well-balanced urban fabric linked to local cultural tradition, Table 2, Figure 3.

Table 2. Fused Grid Theory: Main factors, description, and Potentials for the City of Riyadh (Author).

Layered quadrants advance adaptive responses to the various climate problems that challenge arid regions [19].
Main Factors	Description	Potentials for Riyadh City
Quadrants and Hierarchies	400 m × 400 m modules reduce disturbance, improve walkability.	Merge/existing grid systems.
Benefits: Safety, Health, Environment	Enhanced safety/lower pollution.	Safer, healthier, and better environment.
Applications and Features	Stratford/Calgary cases, T-junctions, pedestrian paths.	Safer, healthier, and better environment.

Table 2. Fused Grid Theory: Main factors, description, and Potentials for the City of Riyadh (Author).

Layered quadrants advance adaptive responses to the various climate problems that challenge arid regions [19].
Main Factors	Description	Potentials for Riyadh City
Quadrants and Hierarchies	400 m × 400 m modules reduce disturbance, improve walkability.	Merge/existing grid systems.
Benefits: Safety, Health, Environment	Enhanced safety/lower pollution.	Safer, healthier, and better environment.
Applications and Features	Stratford/Calgary cases, T-junctions, pedestrian paths.	Safer, healthier, and better environment.

Figure 3. Fused Grid Theory. Modified from [20].

Figure 3. Fused Grid Theory. Modified from [20].

Fractal patterns and organic forms are geometries rooted in historic Islamic city plans. Islamic urbanism fractal geometries show self-similarity values that improve adaptive capacity [21]. These morphologies put emphasis on the creation of pedestrian’ spaces, privatized cul-de-sac networks of streets, and environmental modification inspired by courtyard and wadi-based landscape ideas [22,23], Figure 4.

3. Method

This study develops a theoretical framework that combines fused grid theory with the fractal geometry of Islamic urbanism through a dialectical synthesis paradigm and applies it to Riyadh’s problems, addressing the adverse consequences of Riyadh’s expanding vehicular street grid and hierarchy. For epistemological rigor, the dialectical synthesis proceeds in four steps [5]: thesis (identifying core theories and challenges), antithesis (presenting different paradigms), synthesis (unifying them into model), and framework construction. The theoretical framework will guide practical modifications to existing and future planning of Riyadh, specifically relating to changes in the size of quadrants; the creation of subquadrants; adjustments in the layout, size, and number of blocks and lots in the quadrants; the integration of landscape features, walkways, and open spaces. The method examines morphological applicability to ensure the model is physically appropriate, context sensitive, and pragmatic. The model includes fractal units inspired by the fractal morphology present in Islamic architecture and planning, utilizing self-similar and hierarchical patterns for connectivity and privacy [21,22].

Thesis: Identifying fundamental core theories and challenges. This step defines the hierarchical street system of Riyadh, rooted in modernization theory and characterized by a sprawl with urban superblocks, low walkability, and environmental stress [1]. It synthesizes literature to show how gridiron patterns exacerbate urban challenges, such as 34% land vacancy and social isolation [10].

Antithesis: Introducing two contrasting models. These models criticize isolation and call for pedestrian-friendly urban spaces, that are healthy, culturally driven, and nested in smaller scales. They are the fused grid theory and the fractal geometry of Islamic architecture and urbanism [22]. Fractal geometry promotes higher adaptability and flexibility in Islamic precedents [21].

Synthesis: Resolving into a cohesive framework, joining fused grid with fractal geometry. This step integrates fused grid theory [18] and fractal geometry [21], giving an emphasis on connectivity, walkability, and safety. The morphological outcome is the nesting of superblocks → quadrants → subquadrants → local quadrants → residential lots. This model allows for humanization of urban spaces at a smaller scale [24].

Framework construction: Applicability. This step consists of introducing self-similar fractals using nested quarters at two levels, new local street layouts like T/L-junctions and cul-de-sacs, changes to block size and layout, landscaping (15% greenspace), improved permeability, and pedestrian connectivity [14,25]. The dialectical process is guided by the cultural–historical theory synthesizing tradition and modernity [5], resolving disagreements between different theories and providing a basis for application in urbanism,

Table 3. Methodological steps.

	Phase Name	Core Concept	Key Outcome/Benefit	Focus
1	Thesis: What are the core theories and challenges?	Hierarchical systems, car-oriented development	Establishes baseline, highlights sprawl issues	Problem mapping
2	Antithesis: Introducing contrasting paradigms	Critique of the ideas of separation and isolation	Exposes limitations, boosts walking levels	Contrasting paradigms
3	Synthesis: Resolution into an integrated typology composed of the fused grid with fractal morphology	Fused grid, Islamic fractal urbanism	Reduced greenhouse gas emissions, cultural fit	Integration
4	Framework construction	Pros: Greenhouse gases reduced, cultural fit layering modifications (dimensions, layouts)	Resilient diagram, quality of life	Actionable model

.

To measure the fractal depth of the emerging plan of the nested quadrants, fractal analysis was used. First, the image of an urban layout was skeletonized to extract the structural network. This method uses Fiji software, ver. 1.54P [26], and the proposed morphology is analyzed using the “FracLac” plugin available with the same software. The urban layout was skeletonized (removing the edges) (skeleton of the structural edges obtained through a binary thresholder and thinned image applied to the urban patterns in Fiji; scale 1:1000 for the Riyadh superblocks) and box-counting fractal analysis (threshold range from 1 to 49%) was implemented (pixel size at x = 0.94 activity/pixel), accordingly. To measure errors, the study used bootstrapping (n = 100 resamples of the skeletonized grid and random perturbations of the edge pixels by ±5% to simulate the measurement error), which resulted in a fractal dimension of D = 1.72 (95%, CI: 1.67–1.77) [26].

To measure the difference in connectivity and permeability, a GIS simulation of street density was conducted for the original street layout and urban blocks, comparing them to the proposed ones. This procedure uses spatial analysis for street density, measuring the sum of streets’ lengths per unit area; the higher the density, the higher the connectivity. It also uses the area-weighted average perimeter (AwaP), a measure of permeability where lower values correspond to higher permeability and imply smaller, more connected blocks.

4. Synthesis and Framework Construction

4.1. Synthesis

The hybrid approach is a synthesis of different urban theories: those accepting street grid and hierarchy systems, e.g., modernization and systems theories, that support a gridiron pattern to deliver efficient vehicular movements, and those objecting to it, e.g., semilattice model, smart growth, transit-oriented development, fused grid pedestrian-oriented design approach; and Islamic fractal geometry.

The synthesis proposes answers to Riyadh’s urban challenges linked with car-dependent activities, cultural alienation, and unsustainable urban sprawl. A weight matrix was designed to evaluate alignment using a weighted scoring process for quantifying trade-offs of several desired urban sustainability factors [27], considering the main urban challenges and benefits, namely, vehicular efficiency, walkability, cultural fit, environmental sustainability, social interaction, and sprawl control. The matrix’s assignment draws on longitudinal studies, validating scores via meta-reviews [24]

To counter the subjectivity of qualitative scoring, a multi-criteria decision analysis (MCDA) was utilized with the weight sum model based on urban metrics such as Boeing’s [3] network centrality for walkability and Hillier and Hanson’s [16] space syntax for social/cultural fit. Weights sum to 1, Saudi context-specific (e.g., cultural fit 25% for fractal privacy). Raw scores were normalized to a 0–1 scale by min–max [(raw − 1)/4], summed as Σ (normalized × weights), and scaled to 1–30. Within a ±10% sensitivity analysis, the hybrid framework score remained constant with no rank reversal (27–31), enhancing evaluations robustness,

Table 4. Weight matrix for the studied theories.

Theory	Vehicular Efficiency	Walkability	Cultural Fit	Environmental Sustainability	Social Interaction	Sprawl Control	Normalized Weighted Score (1–30)	Sensitivity Range (1–30)
Street Grid	5	1	1	2	2	1	6.8	6.7–6.9
Opposing Hierarchies	2	5	3	4	5	5	21.4	21.2–21.6
Fused Grid	4	4	3	4	4	4	20.6	20.4–20.8
Islamic Fractal	3	4	5	5	5	4	25.5	25.3–25.7
Hybrid	4	5	5	5	5	5	28.9	27–31

Normalized scores computed via MCDA weighted sum: Σ (Normalized Score_i × Weight_i), with base weights [0.15, 0.20, 0.25, 0.20, 0.10, 0.10]. Sensitivity range with ±10% variation on cultural fit (renormalized), using Python3.12.3/NumPy1.26.4;. No rank reversals observed.

.

Weights were assigned based on qualitative judgment and on the evidence from the literature, selecting theories which performed strongly across the key performance criteria prioritized for Riyadh. Those about limiting sprawl, whilst echoing traditional culture, received more weight. The assignment is based on comparative urban studies, ensuring robustness against bias [15]. On the other hand, while hierarchical grid models show strong performance in vehicular flow, they underachieve in walkability and cultural integration. The hybrid framework, however, establishes a good overall balance. These assessments are derived from research on the built environment, particularly neighborhood design and its components of safety, comfort, and place attachment [14,24])

Applied to Riyadh’s urban problems, different total scores from well-known theoretical approaches are presented in a weight matrix with strong differences. These differences point to the superiority of hybrid systems, as high scores are statistically related to sprawl indices [1]. Street grid and hierarchy (accepting) scored 5 for vehicular efficiency, the minimum score for minimizing traffic jams (1), sprawl control (1), walkability (1), and cultural fit with a value of (1), and accordingly ended up with the lowest total value (12). The performance in non-vehicular scores is low; this agrees with econometric models that indicate lower quality in higher dominance hierarchies [24]. The street grid and hierarchy system is critiqued as inadequate due to its inability to produce pedestrian and culturally oriented public spaces. In contrast, anti-grid theories perform very well in walkability (5), social interaction (5), and sprawl control, supporting small-scale design encouraging active travel and social connectivity, totaling 24 points. However, the efficiency of vehicular systems is low (2), highlighting the compromises that should be considered to allow efficient vehicular traffic, a condition imperative in Riyadh’s current car-centric environment.

Fused grid theory attains a moderate to high level of performance across all factors, which is consistent with its grid/cul-de-sac character, ultimately scoring a total of 23 points. Specifically, its local quadrant grid implemented with an internal pedestrian network, and safer and simpler intersections, has been shown to increase access, walkability, and street safety, compared to traditional grid systems [14].

Islamic fractal urbanism scored the maximum (5) on cultural fit (5), environmental sustainability (5), and social interaction (5). This adaptable design based on self-similar patterns emphasized privacy-driven solutions aligned to Riyadh’s cultural and Islamic tradition, achieving a total of 26 points. Although with moderate vehicular efficiency (3), which implies some environmental benefits, there is a need for special supplementation for high-volume traffic. The hybrid framework, proposed here, emerges as a high-performing alternative with a score of 29 points, 5 points in walkability, cultural sensitivity, and environmental sustainability and social interaction, as well as 4 points in sprawl control and vehicular efficiency.

4.2. Framework Construction

The current Doxiadis scheme of 2 km × 2 km superblocks is divided into four quadrants (1 km × 1 km; net 900 m × 650 m after 150 m deductions at periphery for arterials and collectors, as per 2025 Riyadh road width standards from the Riyadh municipal guidelines [28]). The hybrid model, designed in this study, integrates fused grid with fractal morphology with the superblock pattern of Riyadh. The existing Doxiadis scheme is based on 2 km × 2 km superblocks, that are already divided into four quadrants. A nested division is proposed for each of these superblocks, resulting in four subquadrants of 550 m × 400 m. Another level, on the fractal scale, is added to divide each subquadrant into four local quadrants of 275 m × 200 m each containing a 5 × 5 grid matrix, resulting in 25 residential lots. Local quadrants operationalize fractal nesting at the second level, enhancing spatial efficiency in accordance with dimensional scaling models [21]. These lots have an average area of 347.6 m², measuring 15.8 m in width by 22.0 m in depth, which mirrors existing 330 m² lots, Figure 5,

Table 5. Dimensional Scaling Summary.

Level	Gross Dimensions	Net	Scale Factor	Area
Existing superblock	2 km × 2 km	N/A	1	4 sq. km
Existing quadrant	1 km × 1 km	900 m × 650 m	0.5	0.585 sq. km
Existing residential lots	N/A	N/A	N/A	Avg. 330 sq. m
Proposed Subquadrant	500 m × 500 m	450 m × 325 m	0.25	0.14625 sq. km
Proposed Local Quadrant	250 m × 250 m	225 m × 163 m	0.125	0.036675 sq. km
Proposed Residential Lot	N/A	22 m × 15.8 m	N/A	347.6 sq. m

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This configuration provides a suitable horizontal building density for the hot and arid climate to reduce heat gain, promoting sustainable living, however, vertical density is also required. While not within the scope of this paper, it has been emphasized elsewhere that any successful sustainable development model will need to acknowledge the necessity to densify via vertical development [9]. By aligning with arid sustainability benchmarks, this density optimization could potentially reduce energy demands by 20–30% via compact urban layout [29].

This proposal retains the main arterial and collector streets for effective car connectivity but reconfigures the local street network, using fractal geometry first, and then fused grid theory. In so doing, it blends the rectilinear efficiency of the traditional urban grid with high pedestrian connectivity and minimal through-traffic intrusions, using T/L intersections and cul-de-sacs [20]. Empirical analyses of cul-de-sacs suggest that they enhance walkability and have associated safety benefits through lower vehicular speeds and community security [30]. This is also consistent with empirical findings that document explicitly a 40–60% collision reduction due to mode separation of such models. The reconfiguration of open spaces is varied deliberately to reinforce the sense of community identity, pedestrian wayfinding, and intuitive navigation [14].

Peripheral collectors, in this proposal, are doubled to serve mixed-use urban functions of local commercial facilities, elementary schools, and other supporting amenities to keep walking distances short and meet the accessibility and safety requirements efficiently. Through integration at multiple scales, the framework optimizes morphological integration by integrating new layouts with existing ones, in addition to supporting sustainable urbanism goals in hot arid locations as it mitigates car dependency and supports public transport and metro system implementation, while augmenting the opportunities for walking and exercising, inducing a 15–20% decrease in the average distance traveled by car [30], Figure 6.

5. Results

The process addresses Riyadh’s challenges caused by street grids and hierarchy using a hybrid framework derived from a dialectical synthesis between vehicular efficiency and human-scale design. It tackles the Doxiadis master plan’s rigid gridiron deficiencies by fusing the modular quadrants of fused grid theory with fractal Islamic patterns to rectify sprawl, described as 34% unoccupied land and social discontinuity [1,10], and establish pedestrian-friendly local urban spaces.

The hybrid system implements a nested quadrant system that fits into the existing urban fabric at lower scales. It starts by dividing the 2 km × 2 km superblocks into four quadrants (around 1100 m × 800 m, cut down to 900 m × 650 m after peripherals). After that, it suggested subquadrants (450 m × 325 m), local quadrants (220 m × 150.8 m), and 25 residential lots per local quadrant, averaging 347.6 m² (22 m × 15.8 m). This preserves similar density when compared with Riyadh’s existing 330 m² lots [9].

The model increased the pedestrian access lengths by 30 to 60% due to applying the fused grid theory protocol. It also increased vehicular permeability, by introducing smaller urban block sizes following the fractal design, namely the local quadrant. These permeability improvements align with calls for high connectivity for multi-modal efficiency [3]. It provides a grid and cul-de-sac landscape layout for a better integration of vehicle and pedestrian realms. Such permeability enhancements (20–30% increase in pedestrian access length) are consistent with the high MCDA score of the hybrid framework of 28.9/30 (Section 4.1, Table 4), especially in the walkability and sprawl control criteria and validating the dialectical synthesis’s quantitative superiority,

Table 6. Proposal categories, elements, and details.

Dimensional Guidelines Satisfy Fused Grids (Grammenos, 2011 [20]).
Category	Element	Details
Dimensions and Street Layout	Quadrant L1 (existing) subtracting the peripherals’ area	1100 m × 800 m, 900 m × 650 m
	Subquadrant L2 (proposed) like fused grid (400 m × 400 m)	450 m × 325 m
	Local quadrants (subsubquadrant) L3 (proposed) Residential plot	220 m × 150.8 m, 22 m × 15.8 m
	Arterials (existing)	60 m, medians
	Collectors (existing)	40 m, with bike lanes
	Local streets	20 m, with T-junctions, eliminate U-turns
Block Size	A = 347.6 m2	220 m × 150.8 m
Landscape Elements	Landscape integrations	15% green spaces, native plants for shade. Smaller spaces, hierarchy in size for different outdoor uses
Walkability and Accessibility	Walkways and open spaces	100% non-vehicular paths
Embedded Identity	Fractal planning, fractal outdoor spaces	Fractal design, in addition to traditional architectural elements

, Figure 7.

The GIS analysis for street density—an indicator of connectivity—showed that street density of the proposed layout is 7 times denser than that of the original layout (calculated using the mean density from ArcGIS Pro:3.5.0 symbology, Figure 8).

The area-weighted average perimeter (AwaP) is a measure of permeability where lower values of AwaP correspond to higher permeability and imply smaller, more connected blocks. Using the GIS simulation, AwaP values were 431.41 for urban permeability of the existing street network and 732.13 for the proposed configuration, indicating an improvement of 41%.

The analysis of the fractal dimension—a scale-dependent measure of complexity and self-similarity in patterns, which gives fractal measures as an integer value—for the proposed model morphology yielded a D value = 1.72 that implies a high degree of self-similarity akin to historical Islamic sites like Isfahan (D = 1.7) or Taj Mahal (D = 1.8) [31]. Calculated using Fiji software with the aid of the FracLac plugin, and processed on a skeletonized geometry (minimum pixel = 1, maximum ratio = 49%), this D value indicates a novel combination of rectilinear efficiency and adaptive patterns that improve space filling and resilience over a rigid grid (D = 1.1–1.3), increasing permeability [21], Figure 9.

Comparative baselines illustrate the hybrid model’s morphologically superior properties. Rigid gridiron patterns in modern Riyadh superblocks have low fractal dimensions (D = 1.1–1.3), indicating low self-similarity and high degrees of rigidity [3]. By contrast, recent analyses of Islamic urban and architectural forms have revealed a D closer to ~1.65–1.75 for the interior patterns in the Astana Grand Mosque, which prioritize repetitive geometric motifs [32], ~1.70 for Mameluke madrasas such as Al-Sultan Hassan in Cairo, which emphasize hierarchical courtyard fractals [33], and 1.70 for Baghdad alleys or Iranian bazaars, aligning with fractal privacy hierarchies in Muslim cities [34]. The suggested D = 1.72 thus encapsulates these paradigms and enhances self-similarity for resilience and permeability in arid environments.

Deriving from Hippodamian and Radburn plans and inspired by fractal design, this model hierarchically fractures the local road network using widths < 20 m, eliminates U-turns, using T/L-intersections and cul-de-sacs, which minimizes through traffic, achieving 40–60% fewer collisions and safer zones [18]. This provides 15–20% increases in urban utility and social cohesion for future Vision 2030 land uses [15].

Currently, superblocks in Riyadh, particularly the 1 km U-turn, increase travel distances by 20–30%. Based on the Canadian experience, there is empirical evidence that this study’s proposed model will cause an increase of 10–15% in pedestrian modal shares, which aligns with smart growth outcomes and TOD [1,30].

This proposed framework also fosters privacy-oriented space and creates a structurally better connectivity for social resilience [3,11,12]. It increases space allocated to pedestrian pathways (30–60%) along with green spines and/or non-vehicular paths, connecting to amenities with a potential reduction in emissions of 18% and enhancement of health opportunities [8,14,24]. When pedestrian spaces are provided as 100% car-free zones within smaller local quadrants, it revives the Islamic urban morphologies and helps in wayfinding.

6. Discussion

Recent academic reflections on Riyadh’s morphology emphasize these problems, revealing how the street grid and hierarchy exacerbate disturbances and inefficiencies in residential spaces, such as those seen in the Al Rawda neighborhood, for example, due to inadequate road networks harming both sustainable mobility and community cohesion [35]. Furthermore, other research using fuzzy analytic hierarchy processes has shown that street hierarchies in Riyadh operate as barriers to an equitable distribution of resources within the city and simultaneously proposes solutions with integrated focus areas of environmental and social sustainability [27]. The hybrid model’s configuration, scored 28.9/30 according to the MCDA weight matrix (Table 4, Section 4.1), performs well in adaptation in arid regions due to its maximum use of the land and flexibility of compact forms with better shading, reducing solar heat gain and energy consumption.

This hybrid theoretical model advanced herein is a combined dialectical endeavor to balance vehicular performance on the gridiron plan of Riyadh, as well as the spatial humanizing of local urban space towards answering challenges of arid climates. By synthesizing fused grid theory [17] with fractal Islamic urban forms [21,22,23], the model ensures a fine balance between maintaining the systemic coherence of the grid network for high-order mobility and hierarchically breaking down the urban fabric, at lower orders, into pedestrian-oriented, culturally sensitive spatial realms. The local hierarchical modulation establishes the equilibrium producing optimized mobility gradients [11]. It is also presented as an antithesis of the negative impacts of the Doxiadis master plan, urban sprawl, car dependency, and low walkability, agreeing with the (UN-Habitat, 2015) [1] appeals for sustainable urban forms supporting SDG 11.

This work aligns with the recent pro-walkability measures in Riyadh under Vision 2030, e.g., establishing urban corridors and connecting with the Riyadh Metro, which are also compatible with Sustainable Development Goal (SDG) 11 [36]. This model includes landscape elements (15% greenspace of native plants) that should lower heat by 2–3 °C while increasing biodiversity and in turn contribute to the redevelopment of wadi features which is essential for efficient control over water supplies [37,38].

With their fractal patterning, these measures can also reduce pollution (15–20%) and improve microclimate efficiencies [8,21]. This model can be integrated into the Green Riyadh initiative, addressing urban heat island effects, in parallel with psycho-social benefits by creating enclaved local urban spaces at different scales supported by outdoor evaporative cooling mechanisms to counter dust and provide maximum cooling. Mixed-use development, at the peripheral collectors, can increase the proximity to amenities, which leads to social interaction and walkability and results in a reduction of vehicle kilometers traveled (15–20% on average).

At its heart, the framework is based on the partial retention of the street grid and hierarchy at arterial street and freeway levels, maintaining their grid-based hierarchy to facilitate scalable traffic flow and resource allocation, rooted in systems theory [39]. Hierarchies are, however, deliberately broken down at the collector and local road level—cul-de-sac/ L-shaped and T-shaped intersections to prioritize, social interaction, walkability, safety, and calmness [14].

For pedestrians’ permeability, the model enhances the walkway systems to enable fair mobility and better social interaction, ensuring compliance with the principle of transit-oriented development (TOD) [1]. Parallel studies, on top-down development transitions in Saudi Arabia, emphasized the need for these evolutionary solutions and their consequences, calling for governance-allied reforms to support urban hybrid models which can exploit both tradition and modernity [40].

This model’s configuration performs well in arid regions by maximizing land use and enabling compact building forms with better shading, reducing solar heat gain and energy consumption by an expected 20–30% [29]. Fractal subdivisions, on the other hand, are more in harmony with notions of Islamic privacy and cohesion, adding to thermal comfort and increasing resistance against environmental stresses in arid contexts [22]. These measures also fall under the same umbrella within further calls to combat environmental degradation caused by very large road networks and promote compact urban forms in line with general sustainability-related objectives [41].

The inclusion of multiple scales of urban space at two hierarchical levels, in addition to varying the open space landscape, develops unique identities that are useful to wayfinding, sense of place, and cultural belonging [38,42]. These spaces are organized in a hierarchical manner at the local scale to host the fused grid design for environmental and health benefits, overlaid with fractal self-similarity richness of traditional Arab-Islamic cities. This fractal overlay yields gradients of privacy and communal collectivity, while simultaneously countering cultural alienation of modernization [2]. The suggested lot sizes purposely increase permeability without affecting density [3,43].

The model blends the theoretical paradigms of modernization and systems theories with hierarchical traffic efficiency on one hand [11] and the contrasting theories of Alexander’s semilattice, smart growth for non-hierarchic flexibility, fused grid as hybrid practicality [30], and Islamic fractal urbanism for cultural resonance on the other hand [22]. The effects of these theories are shown via a weight matrix, described in Section 4, that highlights the hybrid’s best performance, with a score of 29, outperforming that of the pure street grid and hierarchy systems [12,14,24].

In addition to the weight matrix and fractal analysis (resulting in a dimension D = 1.72, suggesting an increased self-similarity and robustness as in traditional Islamic urban forms) this paper includes empirical geospatial validation with GIS simulations of street density and area-weighted average perimeter (AwaP) measures. These assessments show that connectivity and permeability have been substantially enhanced: the proposed scheme presents a street density 7 times higher than that of the Doxiadis grid when assessed using AwaP; smaller and better-connected blocks, that are conducive to multi-modal efficiency and lower path lengths (in line with network centrality models, Boeing, 2017 [3]).

Although these quantitative metrics enhance model translation to Riyadh’s form, particularly the treatment of sprawl (34% vacant land) and low walkability, they remain site-specific to the arid superblock typology of the city. Future empirical research could further these simulations (e.g., through full GIS-based traffic modeling or agent-based simulations) to test geospatial generalizability with respect to other Saudi cities or arid locations. Additional studies on courtyard microclimates and privacy gradients in small urban spaces and valley-based landscapes are also needed to promote regenerative urbanism, with the potential for increasing its environmental returns, such as heat reductions of 2–3 °C within Vision 2030 programs.

7. Conclusions and Recommendations

Morphologically, the nested fractal patterns of the framework—segmenting superblocks into quarters, subquarters, and local quarters—open unprecedented layout possibilities by generating identical urban environments, appropriate at the human scale, to encourage walkability in a dense network of arid-adapted climates. Scalability makes permeability easier, allowing seamless vehicular and pedestrian connectivity through T/L-junctions, cul-de-sacs, and green spines that reduce through-traffic while maintaining efficient access to amenities, potentially cutting vehicle kilometers traveled by 15–20% and collision rates by 40–60% [14,20]. These designs are consistent with the family-oriented microlocal environments encouraged for safety and comfort in common local neighborhoods, such as creating smaller enclosed quadrants that offer secure play areas for children and shaded pathways to allow women to navigate while maintaining appropriate levels of privacy derived from Islamic perspectives.

This model extends to vulnerable groups, particularly women, children, and low- income residents, allowing access to essential services such as schools and shops within walking distances, thus reducing transportation costs and promoting inclusivity under Vision 2030′s emphasis on equitable urban development. The network of green spaces, targeted to provide 15% native plant cover, offers potential cooling benefits in arid settings, providing an urban heat island reduction in the range of 2–3 °C [36].

Integrating both the weight matrix and fractal analysis (D = 1.72), this study employed GIS simulations for empirical verification and demonstrated that the street density has increased almost by 7 times and AwaP is improved by 41% in contrast to the Doxiadis grid. These enhance connectivity, permeability, and, subsequently, multi-modality efficiency according to network models [3], thus contributing to the sustainability of Riyadh. Future applications may continue these GIS validations using simulation-based methods (e.g., agent-based models) for verification of generalizability in other arid cities and to explore courtyard combinations to improve microclimate. This will reinforce the hybrid model’s position in Vision 2030, enabling inclusive, resilient urbanism with low emissions impact and enhanced equity.

Women benefit from cul-de-sacs, privacy-oriented streets, and permeable pedestrian networks that ensure safe, culturally appropriate mobility, promoting greater participation in the public sphere [44]. Opportunities are also higher for car-free zones which can provide a secure place offering children the chance to play and explore, reducing incident risk, and enhancing cognitive development through experiential wayfinding in hierarchical, open spaces with reiterating, fractal designs [18,45]. This proposed urban morphology model of transformation locates Riyadh as a breakthrough case grounding for similar interventions in other arid urban developments towards better sustainability and enhanced resilience through responsive paradigms harmonizing tradition, modernity, and environmental sensibility, thus aligning with SDG 11.

Though this dialectical synthesis presents a potential hybrid framework for urban challenges in Riyadh, its scope necessarily has its limits that must be acknowledged to understand its context. The model’s generalizability is limited to arid Islamic contexts, and the culture-based features such as fractal privacy hierarchies and heat adaptations (e.g., shaded cul-de-sacs and wadi-inspired greenspaces) are linked to Saudi Arabia’s Vision 2030 goals. Using it for more moderate climate or non-Islamic cities will require significant adaptations, which might change fractal scaling and permeability advantages. Additionally, two of the main projections—15–20% land efficiency gain and 30–50% collision reduction—are based upon theoretical extrapolations and pilot agent-based modeling, which have not undergone full empirical validation against rapid population growth shifts or economic change. The MCDA weight matrix, Table 4, also assumes that criteria trade off linearly, which may ignore the underlying non-linear behavior found in real urban systems, for example, emerging traffic patterns in fused grids.

Future research should focus on geospatial simulations to validate with rigor the framework’s predictions, for example, simulating urban heat island effects and sprawl dynamics using tools like ArcGIS. It may investigate the relationship between cluster greenspaces, fractal layouts and climate resilience, and land use efficiency to offer measurable information on sustainable solutions in arid regions. Reinforcing this, stakeholder survey work and longitudinal studies would validate socio-cultural impacts by engaging diverse groups to assess privacy, walkability, and inclusivity under SDG 11. Comparative analysis across different Saudi cities, including coastal ones such as Jeddah, could improve scalability and further refine the policy recommendations on resilient urbanism. Collectively, these directions establish the hybrid model as a foundational platform, catalyzing empirical progress toward culturally sensitive and sustainable cities.