Evaluation and assessment of compression rate and the distribution of cities form by using quantitative models

Essential element required for admission compact city vision and smart urban growth, is measuring in the amount of compression and distribution of city that is purpose of this research. for achieve this goal, first with introducing five patterns that contribute to the richness of the scientific literature in planning, (Entropy 1 and 2, Ginni, Moran and Gary), degree of compaction, and distribution for the metropolis of Tehran (with 22 regions of the council) and metropolis of Sydney in Australia (with forty and two local government) has been calculated. For understand form of two cities that studied, and study the amount of quantity (distribution of compression) methods and different models: density, physical size metropol, balanced distribution degree (using entropy and Ginni coefficients), degree of accumulation (with coefficients and Gary and Moran) has been used. In this study, has been used of library and field methods, statistical methods, quantitative, qualitative, the GIS software and etc. The results of these calculations show that the form of metropolis Sydney is "single center". (High population and employment are concentrated in the central and with distance from the downtown population density decreases - sprawl). But for Representation form of Tehran metropolis, all the evidence, methods and models applied show that the expression of physical development of Tehran in all courses was very fast and this leads to the horizontal distribution of the city and close to the random pattern in periods of 65 to 75, and went to tendency to compact and focus in after periods by 1385 year.