Fractal Geometry, Complexity, and the Nature of Urban Morphological Evolution:
Developing a fractal analysis tool to assess urban morphological change at neighbourhood level

During the last three decades, an increasing amount of evidence suggests that the new theories of complexity and fractals are building up realistic views to study complex nature of urban forms and functions from micro to macro scales. Such works are based mainly on the concept that cities are evolving and changing from the “bottom up” according to their local rules and conditions at micro city scales by which more morphological and functional orders emerge at macro city scales. From a morphological point of view, it can be interpreted that urban forms and patterns emerge at macro scales of a city based on the sequence of changes occurring in micro scale urban units (buildings) within it. While complexity theorists are questioning the deterministic top down approach in current urban planning and design, the problem is that there are still gaps in formulating how the complexity theory may be applied in practice, particularly where it relates to city shapes, forms and patterns. This research addresses the lack of feasible tools for measuring changes in the physical complexity of urban morphological features and focuses on change analysis in urban patterns at local and neighbourhood scales.

The research, therefore, has sought to develop a fractal analysis tool to measure the complexity of urban patterns by calculating fractal dimensions of them. It proposes Fractal Neighbourhood Identification codes (FNID) as a kind of digital signature of a city structure, which reveal the level of physical complexity that urban patterns demonstrate at neighbourhood and local scales. Furthermore, the research has succeeded to produce a ‘fractal map’ of a city for the first time. It has employed fractal calculation software (Benoit) in linkage with GIS software (ArcMap) to convert numerical data into pictorial data and to visualise spatial fractal dimensions in terms of the fractal map. This map could then provide a basis for fractal identification and classification of urban patterns and, more importantly, the analysis of pattern changes over both space and time.

A district in the north of Tehran (Shemiran) has been selected as the case study for this research. The proposed fractal analysis tool has been found to be useful for the fractal interpretation of urban patterns, suggesting a realistic way of pattern identification and classification. Two sample cases within Shemiran, one originated from a gradual organic growth and the other from a rapid planned development, were selected to test the potentiality of the method in identifying homogeneity and heterogeneity that the patterns exhibits over different places. The same method was employed to measure the changes occurring over different periods. The aerial photos of Tajrish, the centre of Shemiran, between 1956 and 2002 were analysed to examine quantitatively the degree of changes that the urban pattern related to each neighbourhood experienced during this period. The research suggests that the same method can be applied to the entire metropolitan city of Tehran and more generally to any other cities.

The fractal assessment method suggested in this research can also be employed by urban designers, planners, and decision makers to predict mathematically the degree of changes that architectural design proposals or any other kind of urban interventions may impose to the physical complexity of an existing urban fabric, before their real implementation. In this sense, the proposed fractal assessment technique could contribute a more flexible appraisal method for urban conservationists who are keen to preserve urban characteristics while allowing innovations and recreations in the context of an historic urban district. Finally, the research also took another step forward in developing a practical tool for planners who believe that the current top down deterministic planning and design routine should be revised by flexible bottom up approaches.