Introduction
Here regarding sustainable urban spatial model as a basic necessity in urban development plans indicated the importance of this issue in strengthening the cultural, social and physical aspects of city". In this direction, Kashan is also not exempt from problems caused by urban development and researches showed that the physical structure of Kashan in recent decades grown up in unplanned form and physical development does not match with growth and increase of population. As a result, these changes Cause to ongoing, sporadic and unorganized development of city that do not follow a special structure discipline. So, the aim of this research has first examined the physical development of urban spatial Kashan using quantitative models such as Shannon entropy, Holdren Model and Gary and Moran coefficient, the Gini coefficient. To continue, meantime explains the main causes of changes in the growth pattern of this city and its spatial dispersion, to compile appropriate strategies to achieve the proportional-physical model with sustainable development.
Materials and Methods
The purpose of the research is operational and based on research method and nature is descriptive - analytical. in continuance, for measurement of dispersion and compression of Kashan cities and systematic analysis of urban physical growth pattern is used quantitative methods and models such as balanced distribution degree consists of (model Shannon entropy, Gini coefficient), Holdren model and the size – density rule of city in different periods and for analysis spatial patterns of urban growth parameters of coefficient analysis i.e. correlation of spatial Atokroleyshen techniques (including Gary and Moran coefficient) with using Arc GIS software. This was used. In addition, in order to show urban development in different decades, were prepared with using of Arc GIS software and employment of existing map and aerial photos or satellite images, growth and urban physical development map in different historical periods.
Discussion and Results
Based on assessment of physical pattern of Kashan by using of urban form's assessment models, it can be said that the spatial-physical growth pattern of Kashan is kind of urban sprawl pattern. This factor had the main role in unstable development of Kashan and it caused negative results of diffused growth in Kashan.So based on the gaining results and the gaining numbers of each models the introduced assumption was approved that: physical growth of Kashan during the recent 3.5 decades (1977-2012) followed the urban sprawl patterns and it didn't conform to stable development pattern.
Conclusion
This research examines the spatial-physical growth evolutions of Kashan. Its findings show that:
A) the gross population aggregation of Kashan decrease significantly during 1977-2012, so that the number of people in each hectare decrease from 140 people in 1977 to 29.1 people in 2012. This decrease expresses the horizontal expanding of city in this period.
B) Assessment of physical pattern of Kashan based on urban form measuring models show that the spatial-physical growth pattern of Kashan is urban diffused pattern. The gaining numbers and coefficients of each model show this fact well. As the calculated entropy Shannon number during 1987-2007 show the sprawl growth (spiral) of physical expanding. Also, we conclude from assessment of the analogy between city expanding and population growth during (1977-2007) by using of Holdren model that 46 % of city expanding was accordant with population growth and 54% of physical expanding resulted from awkward and discordant (spiral) development of city. This problem result from having no supervision and control over city expanding and lack of ordered program and plan for physical expanding of city. The gaining results of Gini coefficients during 1987-2007 show the inequality and imbalanced population distribution in city. Also the sum of gaining numbers from accumulation degree (Moran coefficient) during the related period show the imbalanced and inequality distribution of people in the city and low degree of accumulation and focus. It means that these coefficients express that city population follow the accident pattern and checkered (diffused) pattern.(table 8 show the results of  measuring the urban form patterns of Kashan).