Develop an Analytical Framework for Studying Street Pattern; Comparative Study of Street Network Pattern in Self-Organized Districts of Tehran

 
Introduction:
The urban form can be considered as a set of elements of which the street network is one of the most important components. It is divided into two categories: self-organized and pre-designed networks. While the latter evolved by large-scale barriers of economic and social constraints in a short period of time, the former does not imposed by any central agency, but rather, sprouts out from the uncoordinated contribution of countless local agents during the time (Jacobs, 1961). Still today, self-organized street networks are often underestimated in their most fundamental values, and they are described as disordered (Porta et al, 2006a) complicated, and convoluted; but, the identification of common features and their regularities has become a field of research. Against this modernist stigmatization, some (like Jacobs) argued that, unlike the Euclidean geometry in the pre-designed networks, the marvelous complex order of the self-organized networks is not visible at a first glance. That order, is the order of life (Jacobs, 1961) which is such a complex order that, is common among other non-geographical biologic, social, or natural systems. These claims led to a wave of studies from the early 1960s on the analysis of the patterns of the street network and its components using the graph theory framework, which sought to identify the characteristics of the street network of old self-organized neighborhoods and the complex order embedded in them.
With this introduction, the current research has been done to find similarities and dissimilarities in street network patterns of self-organized districts that have emerged without any premeditated designs over time. This article also seeks to develop an analytical framework composed of different indicators that target various aspects of the street network patterns, to enable the recognition of these similarities and differences. For this reason, first, three concepts: 1) configuration, 2) composition, and 3) constitution has been distinguished in studying street patterns. Then, the corresponding measures have been introduced and evaluated in 15 self-organized districts in Tehran, which meticulously have been selected as case, and their street networks have been drawn. In the third stage, values have been compared with a three-plot analysis, and street network similarities and dissimilarities have been traced. 
 
Methodology:
The quantitative method is used in this research and to compare and analysis of the street network pattern in self-organized districts of Tehran. Based on the background of the research and theoretical framework, this comparison has been done using three types of indices which are 1) topological, 2) morphological, and 3) metric indicators which correspond to the three concepts of the street networks:
Topological indicators (corresponds to the configuration): Refers to featuring links and nodes that are associated with abstract topology, which is related to the process of formation: their ordering (relative position), adjacency, continuity, and connectivity.
Morphological indicators (corresponds to the composition): Refers to the absolute geometric layout which is related to the product of formation: absolute position, lengths, areas, and orientation.
Metric indicators (corresponds to the constitution): Refers to those characteristics obtained from the ratio between a geometric to a topological component or vice versa and are used to indicate the relationship between the product and the process of formation.
Results and discussion:
Similarities: The results show that not only the configuration of the street network in all studied self-organized districts is similar to each other (T-tree) which is different from other configurations in the grid (X-cell), loop and cul-de-sac (X-tree), and fused grid (T-cell) networks but also the Three-plot analysis confirms the similarity of the street network composition and construction in these areas:

In most of the districts, along with the increase in the relative beta (Rβ) index, the relative degree means of the vertices (RDM) increases at a similar rate.
In most of the districts, along with the increase in the relative shape factor index of the blocks (RShF(n)), the relative average area of the blocks (RCellAM) also increases at a relatively similar rate.
In most of the districts, along with the increase in the relative vertices density (RVD) index, the relative density of links (RLD) also increases at a relatively similar rate.

Differences: Despite the many similarities, some differences were also traced between these districts, which in order to better understanding, the 15 studied districts are classified into three categories as follows:

Consisting relatively large and serrated blocks, with scattered and long links, low number of intersections, and many dead cul-de-sac like Ozgol (J) and Dezashib (K) districts;
Consisting relatively small and simple blocks, with dense and short links, more intersections, and a low number of dead cul-de-sac like Emamzadeghasem (A) and Farahzad (H) districts;
Consisting other districts that have a combination of simple and serrated blocks of medium size and a number of dead-end and open links.

Conclusion:
The very similarity between the pattern of the street networks in the studied self-organized districts, which are evolved gradually over time in uncoordinated contribution and without any premeditated plan, is not accidental but displays a complex and surprising order. This order shows the behavioral rules that result in preferential attachment in different environmental conditions. These subconscious patterns are the product of a dynamic process in which empirical skills gradually mature through transfer and repetition and results in a self-organizing structure that continuously regulates the interaction of form and context. This interaction creates a pattern of the street network that exhibits the same order in different geographical districts.