1.1 Introduction and the Rationale for the Research

1.1.1 The city of organized complexities

‘Cities happen to be problems in organised complexity, like the life sciences. They present situations in which half a dozen or several dozen quantities are all varying simultaneously and in subtly interconnected ways They are many but they are not helter skelter; they are interrelated into an organic whole(Jacobs, 1961; quoted in Batty, 2005, p.1).

‘There are several adaptive forces in society which, directly and indirectly, influence the life and shape of urban areas: there are demographic, economic, technological, and cultural forces They operate at all scales The problem in discussing each separately is that, in real life, most of these factors are complexly interlinked in a web of causes and effects (Gottmann, 1978, quoted in Larkham, 1996b, pp.37-38).

The city and its problems are the product of considerable diversity of socio-spatial processes, elements, variable problems, and several adaptive forces associated with politics, economics, technology, culture, climate, etc. There are also many factors playing a role in each of these processes and forces, which make the modern city more complex and its problems multi-factorial. These factors ‘operate at all scales in all settlements and throughout history and they are ‘complexly interlinked(Larkham, 1996b, p.37). Therefore, it should be obvious that the reductionist approaches to the city systems, which reduce their problems to their constituent parts with one-, two-, three-, and four-factors, cannot cope with the complex nature of problems posed by the modern city (Weaver, 1948; Jacobs, 1961; Batty, 2005). In this sense, cities, like the life sciences (e.g. biology), are recognised as ‘problems in organised complexity(Jacobs, 1961, p.432).

The difficulties of addressing this type of problems by purely reductionist approaches become even more apparent when considering the following two defining features: (a) City systems, like living organisms, are characterised by a complex organization, which results from a network of interactions involving a high degree of nonlinearity (b) they are open systems; that is, their form and function are in a state of permanent flux, continuously influencing and being influenced by their wider environment, exhibiting “emergent properties (Portugali, 2000; Walleczek, 2000). Figure 1.1 visualises the concept of a complex system with these two defining features. The whole structure is in a non-equilibrium state, emerging through the continuing interactions between micro and macro processes. In this sense, emergent properties or surprising events in a city like a living organism can be defined as properties that are possessed by a dynamic complex system as an organic whole, but not by its constituent parts alone (see also Chapter Three, section 3.2.2 and appendix A for definitions).

Figure 1.1: The dynamical interdependence between local (micro) interactions and the emerging global (macro) structure. (Walleczek, 2000, p.3)

However, cities have not generally been treated as complex systems. The architects, planners, urban designers, and builders of settlements treated them as simple predictable systems to be ordered and reduced to their components in order to facilitate urban modelling and to tackle city problems (Batty, 2005). In planning and design, the rise of the science of complexity has engendered a shift between the old view that sees cities as simple, ordered, structured, expressible by smooth lines and shapes towards a view that cities are complex organisms, evolving from the bottom up according to their local rules and conditions, which manifest greater order across many scales and times.

Jacobs (1961) was one of the first calling for the science of complexity in the effort to understand urban problems better and design solutions consistent with the way the city works. Alexander (1964, 1965) said much the same advocating the idea that the city should be gradually developed from the bottom up though slow adaptive processes, ‘but that since the Renaissance, and certainly since the Industrial revolution, this link had been broken(Batty, 2005, p.6). In his more recent work, Alexander (2002b, 2004) has brought forward the need for a theory that can cope with the nature of urban complexity:

‘We are surrounded by complexity. The modern city is immensely complex It would be natural to expect, therefore, that we must have a theory of complexity, that we have an effective and sensible way to create complexity. Faced with the need, growing everyday, to create successful complex structures all around us, one would expect that we have at least asked ourselves how, in general, a complex structure may become well-formed (Alexander, 2002b, p.180).

Alexander (2002b) argues that all the well-ordered complex systems we know in the world, at least those viewed as highly successful, are generated structures, not fabricated structures. According to him, this fundamental law is, to all intents and purposes, ignored in 99% of the daily “fabrication processesof society (see figure 2.25 in Chapter Two, and table 3.1 in Chapter Three). If our buildings and cities should reflect our worldviews, we must modify them to come closer to what we know about the organic universe ‘nonlinearity, emergence, complexity, and self-organization(Jencks, 1997, p.159). Otherwise, day by day we will build up an alienated environment with no living spatial characteristics.

1.1.2 The research background and the theoretical motivation

The motivation for this research stems from two parallel, but related, scientific events that happened over three decades ago. The first was the rise of chaotic dynamics in domains such as mathematics, cybernetics, and physics during the 1970s and 1980s (see Gleick, 1987; Prigogine and Stengers, 1984; see also Chapter Three, section 3.1). The second was the discovery of fractal geometry by Benoit Mandelbrot in the 1960s, and in his influential book, the Fractal Geometry of Nature, facilitating the study of many irregular and seemingly amorphous man-made and natural patterns (see Mandelbrot, 1983; see also Chapter Three, section 3.3). Both chaotic dynamics and fractal geometry have been employed in a wide range of sciences dealing with self-organised complex phenomena, including those related to urbanism (see table 4.1 in Chapter Four). In the following statements, Batty (2005, p.5) hints at the relationship between these new theories:

‘Processes that lead to surprising events, to emergent structures not directly obvious from the elements of their process but hidden within their mechanism, new forms of geometry associated with fractal patterns, and chaotic dynamics all are combining to provide theories that are applicable to highly complex systems such as cities./span>

From the mid 1990s, these two parallel paradigms began to merge under the new theory of complexity (see also Flood et al, 1993; Byrne, 1998; Wilson, 2000), which in the case of urban studies led to the proposition of the theory of fractal cities by Batty and Longley (1994). While the concern of chaotic dynamics is how a city as a complex system behaves, fractal geometry provides subtle views to the study of urban morphological complexity. Both subjects play a major role in the construction of this thesis, assisting in the understanding of the nature of urban functional and morphological evolution. However, as the title of the thesis suggests, the focus of the research is on the second paradigm fractal geometry as dealing with urban morphological complexity.

1.1.3 The fractal analysis of urban morphology and the research focus

‘Urban morphology refers to the study of physical (or built) fabric of urban form, and the people and processes shaping it(Larkham and Jones, 1991, p.55).

There is limited amount of ‘research on the physical form of cities(Larkham, 2006, p.118). Moreover, much of this work is on the physical urban form not the processes shaping it. ‘Fifty years ago, theories of how cities were structured in spatial terms hardly existed(Batty, 2005, p.2). The limited amount of research on physical form and urban evolution draws attention to the lack of appropriate theories, methods, and accurate tools in the hand of urban morphologists.

From the Renaissance architects (e.g. Leon Battista Alberti, 1404-1472) and their geometrical and mathematical analysis methods to the recent morphologists (e.g. Conzen, 1962, 1988) and their metrological and morphometric analysis methods, the linear principles of Euclidian geometry have been the common ground. These methods have been based on the detailed measurement of plot and building sizes with especial reference to relative proportions of width, length, and height (see Whitehand, 1981, 1987b, 2001; Slater, 1990a, 1999; Larkham 2004b, 2006; Steadman, 2008). Yet the inevitable linearity of Euclidean geometry associated with all of these methods does not allow them to explore the subtle complexity existing in urban forms and patterns (see section 2.2 in Chapter Two).

Over the last fifteen years, there have been a growing number of publications suggesting the application of fractal analysis in the study of urban morphological features. These include the study of building elevations by Bovill (1996), the analysis of street elevations, street patterns and street vistas by Cooper (2000, 2008), the research on skylines by Stamp (2002) and Cooper (2003), the work on urban boundaries by Batty and Longley (1994), the study of visual preference and structural landscape by Gotou et al (2002) and Hagerhall et al (2004), etc (see also table 4.1 for more examples). Some also explored the notion of finding a kind of fingerprint for the configuration of shapes and structures of a city (Webster, 1995, 2005; Haghani, 2004).

However, most of these suggest fractal measurement as a critical tool evaluating an urban morphological feature without reference to its change and evolution over time. In other words, there is a relative lack of research so far addressing the application of fractal analysis in measuring the change in urban morphological complexity. For instance, Cooper (2000, 2003, 2008) investigated the potential chaos and fractal analysis in examining urban elements at the street level for the city of Oxford. He proposed the fractal analysis method for evaluating urban snapshots, and his focus was on physical form of the city, not the processes of change and evolution over time. Therefore, this thesis examines this less-researched area. It aims to develop a fractal analysis tool to measure the processes of change in morphological complexity, and to that extent, it focuses on assessing the change in urban patterns.

1.1.4 The fractal analysis of planned and unplanned/organic urban patterns

‘All cities show some irregularity in most of their parts and are thus ideal candidates for the application of fractal geometry/span> (Batty and Longley, 1994, p.2).

Many analyses of urban form suggest that there are two types of urban patterns i>planned/i> and i>unplanned or organic/i>. While planned cities, or the planned parts of them, are cast in the geometry of straight lines (Euclidean geometry), the immediate application of fractal geometry is to the latter type. However, city geometry is often more complex, marrying the two pure types in modulated and refracted combination (for example see figure 1.2). The close fusion of planned and unplanned, regular and irregular, elements leads to the assumption that the great majority of towns grow by an organic, piecemeal, unplanned process. Conversely, some morphologists (e.g. Slater, 1990a, 1999) believe that, what seems to be organic or unplanned is often the conjunction of ‘many small phases of planning activity(Larkham, 1996b, p.35).

Figure 1.2: The plan of Bewdley. The analysis identifies six units of planned and unplanned phases of growth. (Slater, 1990a, reproduced in Larkham, 1996b, p.35)

Urban pattern analysis, in many cases, shows that what seems “unplannedis actually the result of many phases of planning, some of which are geometric and regular. Moreover, less-planned encroachments over several centuries have affected the appearance of many places (Larkham, 1996b). However, even the planned parts of a city (e.g. Unit IV in figure 1.2) are adapted to their context in more unplanned/organic ways once the plan is implemented; and they evolve gradually according to new needs and conditions. Thus, in any case, the extent to which urban form is ordered or planned is always a matter of degree (Batty and Longley, 1994). Furthermore, even when buildings are marshalled like troops along straight lines of an urban grid, the animation in their mass and height resulted in picturesque formations believed to be congenital to the unplanned/organic city (Kostof, 1991). Therefore, all cities show some irregularity in most of their parts, and as Batty and Longley (1994) claim, they are all ideal candidates for the application of fractal geometry (see Chapter Two, section 2.2).

Another important point seemingly terminological but actually based on the conceptual debate between urban morphologists is to find an appropriate term for the gradually grown and evolved urban patterns. Some authors (e.g. Lynch, 1981; Kostof, 1991) prefer the term “unplanned,as the term “organicmight have biological connotations. They argue that the visual and functional analogies between a city and an organism such as streets/veins, parks/ lungs, city centre/heart, etc can be misleading. The confusion stems from the distinction that they assume to be fundamental between the city, as an artificial system, and the human, as the driver of urban form and function. Lynch (1981, p.95) writes that ‘cities are not organisms They do not grow or change themselves, or reproduce or repair themselves According to him, human purpose drives the making of cities, whether planned or not.

The proponents of the term “organicemphasise the systematic rather than visual analogies between cities and organisms, considering cities as open living not artificial mechanical systems. Referring to the opening statements of this chapter (section 1.1.1), complexity theorists believe that there is a strong inter-linkage between a city, its constituent parts, the socio-spatial forces and factors by which they can hardly be understood apart. Human activity at local scales and the emergent properties of the city at macro scales should be understood together in an inter-dependent complex system (see again figure 1.1). If the human activities are seen as part of the whole system, it can be argued that city systems have a self-organising nature.

In this sense, the term “organicbetter represents the complex nature of urban change and its defining features (discussed earlier in section 1.1.1; see also Chapter Three, section 3.2.2). It also implies self-regulating, self-generating, and self-organising processes within city systems, while the term “unplanneddoes not. Finally, the term “organicconveys the notion of time and gradual change, which is the main property of naturally grown patterns. In this sense, “organic pattern,while perhaps may be not perfect, is the preferred term for the rest of this thesis referring to the parts of cities gradually grown or evolved over time.

1.2 Aims, Objectives and the Research Questions

1.2.1 Aims and objectives

‘Research aims are at the very heart of the thesis. Thus, they should be a thread, which links it together in expressing clearly and precisely the anticipated achievements of the original contribution to knowledge, which will be achieved (Oliver, 2004, p.121).

With the range of issues described earlier, the principal aims supply a broad indication of this study. These are:

a) Identifying the achievements and failures of the geometry of straight lines (linear Euclidean principles) as applied to the conventional top down planning, architecture, and urban design

b) Introducing the principles and applications of complexity theory and fractal geometry in order to examine their potential in urban morphological and functional analysis

c) Examining the potential of a fractal assessment methods to measure and map urban morphological complexity

The research objectives are:

a) Developing a fractal assessment tool to identify, classify, and analyse emergent urban patterns originating from both organic and planned types of growth

b) Selecting an area where historical data and record are available, and then assessing the fractal dimensions of its neighbourhoods to measure mathematically the change in its physical complexity

c) Producing a fractal map as a tool for architects, planners, and urban designers enabling them to reflect better on their design proposals and decisions before their real implementation

1.2.2 The research questions

Two set of questions will be explored to achieve the research principal aims and objectives. The first set is general but includes important questions related to complexity and the nature of urban morphological evolution. These questions will respond to the main aims of the research:

1. Why can Euclidean geometry and its linear principles not explain urban morphological complexity?

2. What does complexity theory mean? What is its relationship with chaotic dynamics and fractal geometry? What are the properties of complexity by which a complex system can be identified? Moreover, does a city system demonstrate these properties?

3. Is fractal geometry an essential substitute for Euclidean geometry as applied to architecture and urban design?

4. Why does the conventional top down approach to planning and urban design not conform to the nature of urban morphological evolution?

The research will then focus on the specific questions to achieve its objectives. The second set explores the applications of complexity theory and fractals as related to city form and function to devise a more accurate tool for spatial and morphological analysis. The questions are:

5. How may complexity theory and fractal geometry be applied to urban planning and design?

6. How could urban physical complexity be measured, visualised, and mapped?

7. How can fractal dimension be referred as a criterion to identify, classify, and analyse the change in complexity of urban patterns?

1.3 The Research Methodology

‘Quantitative research is considered to be hard-nosed, data-driven, outcome-oriented, and truly scientific(Yin, 2003b, p.33).

The research aims to develop a fractal analysis tool in order to assess the change in urban morphological complexity, not to evaluate them. Therefore, it follows a quantitative methodology rather than a qualitative one. Furthermore, since this research is of the data-driven, outcome-oriented type, a case study strategy is appropriate. Yin (2003a, p.1) writes:

‘Case studies are the preferred strategy when “howor “whyquestions are being posed, when the investigator has little control over events, and when the focus is on a contemporary phenomenon within some real-life context.

Therefore, among five different possible methods (experiment, survey, archival analysis, history, and case study) suggested by Yin (2003a), the “whyand “howquestions presented in the previous section are appropriate for the case study method. According to this type of strategy, the research should define an appropriate case study, and determine the relevant data to be collected and analysed.

1.3.1 The case study

Tehran, the capital city of Iran, provides good sample cases to be studied. Morphologically, the city is the product of two different patterns of growth. On the one hand, a fast large-scale expansion of the city imposed its regular grid-like pattern on the suburban areas. On the other, the gradual growth of the villages –formerly encircling the city gradually converted to be significant centres inside the city –generally produces organic patterns. This rapid growth, when merged with gradual transformation of the suburbs, provides very complex urban patterns in the neighbourhoods around these centres. Tajrish, the centre of Shemiran a district located in the north of Tehran has such characteristics, as it demonstrates the contradiction between both patterns of growth.

Chapter Five provides a detailed explanation of the criteria that have been considered for selecting an appropriate case study and the required sample cases. The fractal analysis method employed in this research aims to measure the degree of change in the complexity of urban patterns at different neighbourhoods in Shemiran. If this method is found to be useful for the selected sample cases, then the same method can be used for the entire city of Tehran and other cities too.

1.3.2 The thesis structure and the stages of the investigation

The research comprises three main stages, a) the literature review, b) the data collection and examination, and c) the data analysis. At each stage, the strategy is to narrow down the research according to its main aims, and to focus on the target specified by the research objectives. In this section, three stages of the investigation are briefly introduced. Figures 1.3, 1.4, and 1.5 illustrate the key elements of each stage. Stage I, the literature review:

This aims to investigate the traditional and conventional approaches towards urban form, providing the platform for the application of the fractal concept. Firstly, the review intends to identify the traditional views of urban form, and particularly, it discuses the role of the science of Euclidian geometry in shaping urban form throughout history (Chapter Two). Secondly, the properties of fractals, complexity, and chaos theories will be reviewed in order to identify how these new theories provide a more realistic insight into the study of urban form and change (Chapter Three). The advantages of fractal approach for understanding of urban complexity will be highlighted in order to shift our views from the top down deterministic planning and design tradition to the more realistic and flexible bottom up approach (Chapter Four).

By the end of the literature review, a number of approaches in the application of fractal theory in the study of urban form, growth, and change will be outlined to provide a backbone for the empirical stage, where the research aims to develop its own fractal analysis tool. As shown in figure 1.3, the research will be narrowed down, at this stage, from relatively a wide literature to a focused target, refining the research method for the empirical stage.

Figure 1.3: The first stage of the methodology; the literature review. The arrows indicate the overall strategy to narrow down the research and to formulate its target. Stage II, the data collection and examination:

Once the research has indentified its target, it follows three sequential steps at the empirical stage including case study selection (Chapter Five), pilot study, and case study examination (Chapter Six). The first step defines the relevant case study and sample cases to be examined according to the research target. The advantages of using remote sensing city images, as the data source, will be identified (Chapter Six, section 6.1.1). Then, the research develops its fractal assessment tool by using two different software programs in linkage. It employs Benoit 1.3 (fractal analysis software) to facilitate fractal dimension calculation and ArcMap 9.2 (GIS software) for its mapping, layer-overlapping capabilities. The latter software will convert numerical data into pictorial data in order to visualise spatial fractal dimensions in terms of the fractal map. The rationale for using this software is given in Chapter Six (see section

The important step at this stage is to test the reliability of the method before it is applied to the main case study. Therefore, at the second step, the pilot study carries out two different tests (Chapter Six, section 6.2). The first is the validity test, which aims to calibrate the adjustable parameters of the fractal analysis software. The second test is the sensitivity test, which checks urban elements within the image contents in terms of appropriateness, and the consistency of the pictorial data in terms of resolution, brightness, and contrast. The aerial photos of the selected case study are processed and refined based on the result of the pilot study and are prepared for the actual examination.

Figure 1.4: The second stage of methodology; the data collection and examination. The second stage of investigation includes the case study and sample selection, the pilot study; and the case study Examination.

The third step carries out the fractal measurement of the case study and the selected samples (Chapter Six, section 6.3). The aim is to assess the fractal dimensions of the selected areas from the neighbourhood local scales to the district and city scales. Since the focus of the research is at local scales, further examination will be carried out at neighbourhood level of the case study to measure the change in the complexity of their urban patterns for the period from 1956 to 2002 (determined by the availability of aerial photographs). The result of these measurements will be processed into the GIS software to be mapped. Figure 1.4 illustrates the main steps that are to be carried out at the stage II. Stage III, the data analysis:

The numerical data from the previous stage is transferred to GIS software (ArcGIS) in order to be visualised, mapped, and analysed (chapters Six and Seven). The map produced suggests a kind of fractal fingerprint for the examined neighbourhoods. This, together with the proposition of the fractal Identification code (FNID), provides the base for the pattern analysis at the third stage (Chapter Seven, section 7.1). The method will facilitate the pattern recognition and classification based on the degree of complexity that different neighbourhoods pose. The fractal map also identifies the homogeneity/heterogeneity of urban patterns and the areas that the urban patterns begin to be transformed or distorted (Chapter Seven, section 7.2).

Figure 1.5: The third stage of methodology, the data analysis. It includes the pattern recognition, classification and measuring the change over time.

Moreover, several maps from past to present are compared in order to measure the degree of change in physical complexity of the selected samples overtime (see Chapter Seven, section 7.3). This comparison will reveal the degree of impacts that urban interventions have imposed on physical complexity of selected case studies. Finally, the potentiality of proposed fractal technique in analyzing future morphological changes will be addressed. At this point, the fractal signature (FNID) of each neighbourhood provides a benchmark for testing different urban scenarios according to the current planning policies, possible architectural proposals, or urban design projects (see Chapter Seven, section Figure 1.5 illustrates the main ideas that will be discussed at data analysis stage.

1.4 Chapter Summary

The introductory chapter highlighted the research main theme and outlined the key researches supporting the topic, the less-researched areas, and the focus of the thesis. It also introduced the research aims and objectives by which two set of questions were formulated. As discussed in this chapter, the first set targets the research aims the potentials of fractal geometry as compared to Euclidean geometry in urban morphological analysis which are achievable through the literature review (Chapters Two, Three, and Four). However, the second set focuses on the research objectives the applicability of the fractal analysis tool which requires the case study examination (Chapters Five, Six, and Seven). Chapter Two, in particular, reviews the literature through a historical context to examine the role, strengths and weaknesses of the geometry of straight lines (Euclidean geometry) in shaping architectural and urban forms. The literature review, in general, aims to establish some reasons why understanding of urban morphological complexity and its evolution over time is beyond the principles of Euclidean geometry, and therefore, it requires some further knowledge in the light of complexity theory and fractal geometry