Mapping and The Geometry of Form and Function of Cities Dissertation

Mapping and The Geometry of Form and Function of Cities - Dissertation Example However, these models fail to address the very issues related to urban form. The development of these contemporary models does not take into account the urban development geometry. Instead, these are developed at an aggregate level. Batty and Longley (p. 72, 1994) comment ‘The best way to begin describing fractals is by example. A coastline and a mountain are examples of natural fractals, a crumpled piece of paper an example of an artificial one. However, such irregularity which characterizes these objects is not entirely without order and this order is to be found in fractals in terms of the following three principles. First, fractals are always self-similar, at least in some general sense. On whatever scale, and within a given range you examine a fractal, it will always appear to have the same shape or same degree of irregularity. The 'whole' will always be manifest in the 'parts'; look at a piece of rock broken off a mountain and you can see the mountain in the part. Look at the twigs on the branches of a tree and you can see the whole tree in these, albeit at a much reduced scale.’ Although, it has been observed that there is an acceptable level of consistency between such models and urban form but when it comes to the geometrical considerations of urban development, these are not dependent upon the processes and mechanisms (Bertuglia et al, 1987). The urban system models which are theoretical in nature, like the urban economics models, have shown a dependency upon the urban form through a set of assumptions. However, urban form has been defined by these models in terms of treating urban space as quite simple (Thrall, 1987). Hence, building a model which links a given form to statics and dynamics is very difficult because the relevance of form is considered as given and not something that arises out of the forces in action. As a consequence of this, all the research that has been conducted in urban form is considered to be highly idiosyncratic. However, as a result of some major developments during the last decade the science of form has seen some significant changes, especially within the areas of mathematics and physics. These developments have been brought about by the requirement to establish a connection between urban form and growth processes. In addition to this, another driving force has been the analysis of natural forms on the basis of the occurrence of the geometry of the irregular. Remarkable developments in the area of computer graphics have initiated the mathematical description and visualization of the urban forms. Making use of mathematical principles on fragmented structures, visualization has achieved a milestone (Mandeibrot, 1983). The developments have come about in terms of simulating natural forms (like landscapes) in a simple, yet realistic manner. This majorly involves addition of fractal ideas to produce simulations which are more conventional. This gets further deepened into theoretical ideas whi ch involves the generation of fractal structures through physical processes. The physics of critical