Numerical Examination for Fractal Extension
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摘要: 由于仅用一个分维值难以区分不同的形态,首先需要对原分维概念予以扩充,即把原来仅局限于无标度区内的呈直线形分布的常数分维扩充为包括无标度区上下界以外区域在内的,呈反S形分布的变量(函数)分维,使分维方法的应用不受观测尺度的限制;其次,要研究表达扩充分维的数学模型。文中论述了反S形扩充分维的数值实现方法和增强描述复杂现象的能力。Abstract: Because of the difficulty in description of geo-features with a single value of fractal dimension,it is necessary to perform extension from the original constant dimension value which is independent upon measure step lengths to variable one which can be considered as a function depended upon measure step lengths. In this paper the author proposed principles and methods to establish the inverse S shaped curve function and to examine the suitability of this model for enhancing the ability to describe complexed phenomena.
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