人文经济地理空间分数维的认知基础——兼论分形技术的应用  

COGNITION BASIS OF FRACTIONAL DIMENSION IN HUMAN ECONOMIC GEOGRAPHICAL SPACE:THE APPLICATION OF FRACTAL TECHNOLOGY

作　　者：宋志军 SONG Zhi-jun(The College of Geography and Environmental Science,Henan University,Kaifeng 475004,China;Key Laboratory of Geospatial Technology for the Middle and Lower Yellow River Regions,Ministry of Education,Henan University,Kaifeng 475004,China)

机构地区：[1]河南大学地理与环境学院,开封475004 [2]河南大学黄河中下游数字地理技术教育部重点实验室,开封475004

出　　处：《人文地理》2023年第4期121-130,共10页Human Geography

基　　金：国家自然科学基金项目(42071156)。

摘　　要：人文经济地理系统是复杂的开放巨系统,传统数理方法常无法描述其看似混乱的存在形式、运行过程。实际人文经济地理空间是社会经济系统相变、临界现象的终端表现,自身充满了非线性的特征和过程,所以分数维的空间形态是其本质性的系统属性。由此本文介绍了人文经济地理空间分数维的表现形式、认识过程、基本的数理描述,并对其度量方法——分形的理论基础、计算方法、应用“情境”、研究进展进行了综述和讨论。而本文对人文经济地理事物的空间分数维及分形技术所进行的溯源和应用基础讨论,其目的就是要为科学描述人文经济地理空间的复杂性、合理利用分形技术提供基础性的理论支持。Human economic geographical system is a complex open giant system.Traditional mathematical methods cannot explain and describe its seemingly disordered existence form and running process.In general,the monomer is in the process of change,the grassroots level shows chaos,and the macro level shows certain certainty or regularity,which constitutes the basic characteristics of the human economic geographical reality space.Compounded together,they not only enhance the complexity of the spatial system,but also become a source of fractal dimension.In fact,human economic geographical space is a final performance of phase transitions and criticality phenomenon in social economic system,and the fractal dimension is the reflection of the self-similar feature.To deeply understand this complex system full of nonlinear features and processes,this paper introduces the performance form,cognitive process and basic mathematical description of human economic geographical system.Also,this research has a summary and discussion for its measurement methods:Fractal of theoretical basis,calculation method,application"circumstance"and research development.From the mathematical point of view,fractal is mainly through the analysis of quantitative indicators with scale-free characteristics such as system singularity,evolution intensity,evolution dominance or subjectivity,to reflect irregular and difficult to measure spatial pattern changes and their evolution details.

关 键 词：分数维 分形 临界现象 相变 人文经济地理空间 

分 类 号：K909[历史地理—人文地理学]