基于分形的中国沿海省区海岸线复杂程度分析

Analysis on the Complication-degree for Coast Line of the Chinese Provinces Along the Sea Based on the Fractal Theory

海岸线是分形领域最早的研究课题,但是到目前为止,尚没有人系统而全面地就一个地区或一个国家的全部边界进行过系统的分形维数的研究。为此从海岸线的分形维数着手,利用两种经典的分形维数计算方法,设计程序,分析计算普通印刷地图和电子地图的省区海岸线分形维数,提出海岸线复杂性分析的方法和原则,首次对不同比例尺、不同计算方法、不同模式的地图海岸线复杂程度的计算进行对比分析,在此基础上得出关于中国沿海各省区海岸线复杂程度的重要结论。

Coastline was one of the earliest object in the fields of fractal research. However, the fractal dimension of coastline in one country has not been studied systematically so far. In this paner, programs are designed to calculate two kinds of fractal dimensions—box-counting dimension and divider dimension. Meanwhile, the method and the principle by which the complexity of the coastline is analyzed have been put forward through computing the fractal dimension of the common printing map and the electronic map. And for the first time, the complexities of the coastline computed by different scales, computational methods and modes of map are compared and analyzed. On this base, conclusions of the complexity of the coastline of the Chinese maritime provinces are drawn . The fractal dimensional value calculated by divider method is always bigger than that by box-counting method. The variety of the geographical constitution and aboriginal physiognomy from north to south is approximately consistent with the variety trend of the fractal dimension. To the electronic maps with the same precision and different scale, the fractal dimension goes along with the scale.