Chen Yanguang
Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China.
Entropy (Basel). 2019 Apr 30;21(5):453. doi: 10.3390/e21050453.
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archetypes, we can reveal the causes and effects of the diversity of fractal dimension estimation results by analogy. The main factors influencing fractal dimension values of cities include prefractal structure, multi-scaling fractal patterns, and self-affine fractal growth. The solution to the problem is to substitute the real fractal dimension values with comparable fractal dimensions. The main measures are as follows. First, select a proper method for a special fractal study. Second, define a proper study area for a city according to a study aim, or define comparable study areas for different cities. These suggestions may be helpful for the students who take interest in or have already participated in the studies of fractal cities.
分形几何为城市的无标度空间分析提供了一个强大的工具，但分形维数的计算结果总是取决于研究区域的方法和范围。这种现象一直困扰着许多研究人员。本文致力于讨论分形维数估计的不确定性问题及其潜在的解决方案。以规则分形为原型，我们可以通过类比揭示分形维数估计结果多样性的因果关系。影响城市分形维数值的主要因素包括预分形结构、多尺度分形模式和自仿射分形增长。该问题的解决方案是用可比较的分形维数替代实际的分形维数值。主要措施如下。首先，为特定的分形研究选择合适的方法。其次，根据研究目的为城市定义合适的研究区域，或者为不同城市定义可比较的研究区域。这些建议可能对那些对分形城市研究感兴趣或已经参与其中的学生有所帮助。
