Fractal Formation of Settlement Forms in Taiwan

台灣聚落型態的碎形研究

10.29790/JTGIS.200504.0001

蔡博文(Bor-Wen Tsai)；李介中(Chieh-Chung Lee)

碎形幾何 ； 聚落型態 ； 地理資訊系統 ； fractal ； settlement form ； GIS

臺灣地理資訊學刊

2期（2005 / 04 / 01）

1 - 10

英文

碎形幾何(fractal geometry)近年被廣泛運用於都市、生態、GIS的研究上，有些研究運用於地物形狀(shape)的分析，有的運用於地物的分佈(distribution)探究，本研究採盒計法(box-counting method)分析台灣近百年的聚落分佈型態及其變遷；同時進行與人口密度、聚落面積的相關分析，分析結果並與Shen(2002)的美國20個主要都市的研究結果進行比較。 研究結果顯示：1)碎形維度值D介於1與2之間，顯示台灣地區的聚落型態合於碎形幾何的特性；2)北、南、東區域的聚落分佈型態與富田方郎(1934)的研究吻合，即北部以散村為主、南部與東部多集村；3)台灣的聚落型態與Shen(2002)研究的美國20個主要都市的型態非常相似，與人口及聚落面積的關係也相當一致。

Fractal geometry has recently caught great attention in urban, ecology, and GIS research. This paper employs box-counting method to measure the settlement forms of twenty jurisdictions in Taiwan. The computed fractal dimensions are then linked to population density and ratio of urban area to total land area for each jurisdiction. The results are compared to Shen's study (2002) to investigate the difference between the development of settlements in the U.S. and that in Taiwan. The conclusions are: 1) the fractal measures satisfies the inequality of 1＜D＜2 and can be regarded as proof of urban fractal that has been studied by several researchers, 2) the computed fractal measures coincides with the pattern of the spatial distribution of various settlements, that is, scattered in northern Taiwan, compact in the southern and the eastern regions, and 3) similar characteristics exist between settlements in Taiwan and cities in the US in terms of their spatial forms and population and urban area parameters.

1. Batty, M.,Longley, P. A.(1988).The morphology of urban land use.Environment and Planning B,15,461-488.
2. Batty, M.,Longley, P. A.(1986).The fractal simulation of urban structure.Environment and Planning A,18,1143-1179.
3. Batty, M.,Xie, Y.(1996).Preliminary evidence for a theory of the fractal city.Environment and Planning A,28,1745-1762.
4. Berube, D.,Jebrak, M.(1999).High precision boundary fractal analysis for shape characterization.Computers & Geosciences,25,1059-1071.
5. Cheng, Y. C.,Lee, P. J.,Lee, T. Y.(1999).Self-similarity dimensions of the Taiwan Island landscape.Computers & Geoscience,25,1043-1050.
6. Deng, D. P.,Lin, Y. P.(2000).Exploration of fractal dimension of built-up patterns in Central Taiwan.People and Land,209,55-61.
7. Frankhauser, P.,Fotheringham, A. S.,Wegener, M. (eds.)(2000).Spatial Models and GIS: New Potential and New Models.London:Taylor & Francis.
8. Li, B. L.(2000).Fractal geometry applications in description and analysis of patch patterns and patch dynamics.Ecological Modelling,132,33-50.
9. Lin, F. T.(1991).A semi-fractal indicator for spatial complexity measurement.Journal of Building and Planning,6,9-17.
10. Lin, Z. G.(1998).National Chung Hsing University.
11. Longley, P. A.,Mesev, V.,Donnay, J. P.,Barnsley, M. J.,Longley, P. A. (eds.)(2001).Remote Sensing and Urban Analysis.London:Taylor & Francis.
12. Mandelbrot, B. B.(1982).The Fractal Geometry of Nature.San Franciso:Freeman.
13. Shen, G.(2002).Fractal dimension and fractal growth of urbanized areas.International Journal of Geographical Information Science,16(5),419-437.
14. Sue, D. Z.(1998).GIS-based urban modelling: practices, problems, and prospects.International Journal of Geographical Information Science,12(7),651-671.
15. Tomita, Y.(1934).Settlement Research in Taiwan.Taipei:Taiwan News.

1. 林世強(2013)。金門島嶼型災害特性及規模設定方法之探討。地理學報，69，1-24。