城镇体系空间结构的分形维数及其测算

城镇体系空间结构的分形维数及其测算

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Initial contribute: 2018-12-04

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Affiliation:  
岳天祥编著
Email:  
yue@lreis.ac.cn
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城镇体系空间结构的分形维数及其测算

(1)聚集维数基本模型:

1)城镇数目与相应半径的关系:

 

式中,N(r)为半径为r的圆周内的城镇数目;Df为分维。

2)平均半径与城镇个数的关系:

 

式中,Rs为平均半径;ri为第i个城镇到中心城市的欧氏距离;S为城镇个数;〈…〉表示平均;D为分维。

3)城镇体系的空间分布密度与相应半径的关系:

 

式中,ρ(r)为城镇体系的空间分布密度;欧式维数取d=2

(2)网格维数基本模型:

1)网格数与网格尺寸的关系

 

式中,N(ε)为被城镇占据的网格数;ε为网格尺寸;α为分维。

2)信息量与网格数的关系:

 

式中,I(ε)为信息量;I0为常数;D1为信息维。

(3)关联维数基本模型:

1)空间关联函数:

 

式中,r为码尺;dij为两城镇的欧氏距离;θHeaviside函数;

2)空间关联函数与相应半径的关系:

 

式中,α为分维。

 

参考文献

刘继生,陈彦光:城镇体系空间结构的分形维数及其测算方法。地理研究,1999,18(2)

How to Cite

《资源环境数学模型手册》 (2018). 城镇体系空间结构的分形维数及其测算, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/2197ba63-286b-4b06-9f4f-0295938663c1
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Last modifier : 
wu kai
Last modify time : 
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Contributor

Initial contribute: 2018-12-04

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Authorship

Affiliation:  
岳天祥编著
Email:  
yue@lreis.ac.cn
Homepage:  
View
Is authorship not correct? Feedback

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Last modifier : 
wu kai
Last modify time : 
2020-12-17
Modify times : 
View History

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