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一种广义自相似曲线分形建模方法
供稿: 金毅;刘仙鹤;张朔;张玥夕子 时间: 2018-09-29 次数:

作者:金毅刘仙鹤张朔张玥夕子

作者单位:河南理工大学资源环境学院中原经济区煤层(页岩)气协同创新中心

摘要:借助经典Koch曲线的构建思路,依据狭义分形拓扑理论发展了一种广义分形曲线的构建方法,并实现了随机、自相似和多尺度行为的统一定义。在此基础上,推导了分形曲线的长度计算模型并验证了其正确性。结果表明,新方法提供了对分形行为的本质解释,显著降低了尺度不变几何分形模拟的难度。另外,广义分形曲线构建方法严密分离了原始复杂性与行为复杂性,这使得尺度不变属性的定量表征易于实现。

基金:国家自然科学基金资助项目(41472128,41772104);山西省煤层气联合基金资助项目(2012012002,2015012010);河南省高校科技创新人才项目(16HASTIT023);河南省高校科技创新团队项目(17IRTSTHN025);

关键词:狭义分形拓扑;自相似;分形曲线;分形模拟;

Abstract:Following iterative process in classical Koch curve, a generalized approach was developed to model arbitrary fractal curves by using the newly emerged “special fractal topography”theory. In this approach, the definitions of deterministic or stochastic, self-same or self-similar, single-scale or multi-scale properties were unified. The length model of fractal curves was derived and its validity was verified. The study indicates that the new approach reduces the complexity of modeling fractal curves significantly because the essential understanding of scale-invariant properties are provided by special fractal topography. Furthermore, the complexity in fractal curve is decomposed into original one wrapped in scaling object and behavior complexity. It is easy to realize the quantitative characterization of scale-invariant properties.

Keyword:special fractal topography;self-similarity;fractal curve;fractal modeling;

DOI:10.16186/j.cnki.1673-9787.2018.05.24

分类号:O415.5

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