A spatial analysis on the way how the city shapes have been formed.

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A city is a compound of various elements. It has been constructed dynamically in search of an ideal urban form, which satisfies the Pareto efficiency of the people of each ages, such as economy, defense, culture and so on. In order to examine dynamic conditions of a city of ages, a methodology-Urban Entropy coefficient-will be proposed. The Urban Entropy Coefficient is defined as a measure of estrangement between "Global and Local"" which are concepts of Space Syntax.Conclusion 1 : Theoretical resultsThe main result of this research is to show that almost 90% links of a minimum spanning tree are composed by the links of the shortest neighbor and the second shortest neighbor. More concretely, exactly 69% links of a minimum spanning tree are made up of the nearest links, and about 22% links are made up of the second nearest neighbor and 9% links are made up of the third nearest and so on. From this information, if N points-facilities are located uniformly randomly in a 1 x 1 square, we can estimate the lower bound for the length of the minimum spanning tree on these N points far better than it has been. So that we can prove that the length of minimum spanning tree is greater than 0.64√<N> when N points are located randomly in 1 x 1.Conclusion 2 : Applied results:The second purpose of this study is to make clear the property of the complicated street networks in English historic towns. It does so by measuring what degree we can reconstructed the networks by using the network patterns that are constructed by the rationality of the shortest distance. We take out Chester, Canterbury, Norwich, Cambridge and Bath in English historic towns. If we construct the model networks by Exodic-tree and measure the re-production rate by comparing with the real network, we got a high re-production rate in the experimental results. We can estimate that the rationality of the shortest distance is acting even in the historic towns.