利用隨時間變化的碎形理論探討人口密度與城鎮規模變遷的相關研究－桃園地區之實證分析探討

人口數量與都市城鎮規模大小的關係為都市研究的一項重要課題，而區域內城市規模與城市人口變化和地區發展有密切的關係。在同一區域內城市規模之劃分，已有多項研究依據人口數量進行分級探討。本研究則以人口密度的變化探討區域內城鎮規模的大小，前研究者發現在同區域內城市人口相類同等級城鎮的發展，其規模亦有相似性，也因符合碎形維度（fractal dimension）的相似原理，所以本研究利用碎形維度原理探討城市規模與人口密度的關聯。本文先進行人口密度與都市城鎮規模相關的探討，再針對碎行維度隨時間變化的理論作推導，並以桃園地區為個案，分析區域中城鎮人口密度與城市規模及其發展的變化，以驗證碎形維度對城市規模分佈與人口密度變化之相關性。桃園地區因工商發展快速，但人口密度之發展及變遷具有特定性，並非均勻發展，因此本文利用碎形維度的數學模式將定性描述轉為定量計算，並分析其與隨時間演變動力機制的關聯性。研究結果顯示發現隨時間變化的碎形維度理論，確可由量化方式探討城市規模發展的變化及人口變遷的動態過程，且顯示運用於研析城市規模與人口密度變化是一有效的量測指標。

關鍵字

碎形維度；城市規模；人口密度

並列摘要

The relation between urban population and magnitude is an important subject of urban research. Also, the urban magnitude and population change in an urban system are closely related to the regional development. It is found that cities in the same region with same population level have similar magnitude, in accordance with the similarity property of the fractal dimension. In this research, we investigate the urban magnitude with respect to population density change and discuss related connection by using a time dependent fractal dimension theory. We first investigate the relation between the urban population density and magnitude, and develop the theory of time varying fractal dimension by taking Taoyuan area as an example. In Taoyuan area there is a special trend for the transportation of population density, which is not quite uniform. In contrast to formal qualitative description, we use the mathematical model of fractal dimension to quantitatively analyze the dynamic process. Our result validates the mathematical model that it's possible quantitatively to explore the dynamic process on the change of urban magnitude and variation of population density, and demonstrate the available index for probing the urban magnitude and population density.

並列關鍵字

Fractal Dimension ； City Size ； Population Density

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