一种广义自相似曲线分形建模方法

A general approach to model arbitrary self-similar fractal curves

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。

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 u-nified. 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 understand-ing of scale-invariant properties are provided by special fractal topography. Furthermore, the complexity in frac- tal curve is decomposed into original one wrapped in scaling object and behavior complexity. It is easy to real-ize the quantitative characterization of scale-invariant properties.