本研究之目的在以碎形維度量測都市計畫區外圍之非都市土地建成區的蔓延程度，相較於傳統空間分析指標，碎形維度更能描述都市蔓延在空間上之分布形態。研究範圍為臺南市主要計畫區與相鄰都市計畫區的最外圍邊界，向內、外各擴張1 km之環域範圍，所使用資料為各都市計畫土地使用分區資料及國土利用調查之土地使用現況。本研究先以空間限制集群分析法將研究範圍依照都市發展情形與空間相鄰特性劃分為16個研究單元；再以盒計數法計算各研究單元中非都市土地建成區之碎形維度值，並以建成區的空間分布形態、土地使用現況、道路路口密度等變量來驗證碎形維度所代表之空間意義，以此探討建成區的蔓延情形；另再分析非都市土地碎形維度與相鄰都市土地使用情形的相關性，以探討都市蔓延的成因。結果顯示碎形維度可反應不同的都市蔓延形態；且都市計畫區邊緣的土地使用類型與相鄰非都市土地之都市蔓延有顯著的相關性，研究成果可做為都市規劃、國土計畫等政策擬定之依據。

This study measured urban sprawl on the urban fringe of Tainan using fractal dimensions. Unlike conventional indexes such as area and density, the fractal dimension can describe the scattering patterns of urban sprawl areas. The research area is the buffer zone 1 km inside and 1 km outside of the boundary of the urban planning areas around Tainan city center. Data analysis included data from the Land Use Investigation of Taiwan and from land use zoning information in urban plans. The research area was divided into 16 spatial analysis units using the contiguity-constrained clustering technique. The box counting method was used to measure the fractal dimension of the built-up areas for each spatial analysis unit outside the boundary of the urban planning areas. Bivariate correlation analysis was used to describe relationships between fractal dimension measurements and conventional urban development indexes (sizes of built-up areas, distances between traffic intersections, residential uses, commercial uses and industrial uses). The analytical results show that fractal dimensions are able to depict urban sprawl patterns. In addition, the fractal dimension measurements had significant positive correlations with commercial uses, residential areas and built-up areas within the urban planning boundary, but had significant negative correlation with agricultural uses. The outcomes of this study can be applied to land use planning.