Abstract

The method of numerical Fourier analysis is used to investigate the fractal properties of 2D objects with micrometer–centimeter sizes. This numerical method simulates the small-angle light scattering experiment. Different geometric 2D-regular fractals, such as the Sierpinski carpet, Sierpinski triangle, Koch snowflake, and Vishek snowflake, are studied. We can divide 2D fractals, by analogy with 3D fractals, into “plane” and “boundary” fractals with fractal dimensions lying in the intervals from 1 to 2 and from 2 to 3, respectively. For an object with a smooth boundary, i.e., a circle, the model small-angle scattering curve decreases according to the power law q^–3, where q is the momentum transferred.

中文翻译：

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关于二维空间中的分形和非分形对象的分类

摘要

傅里叶数值分析方法用于研究具有微米-厘米大小的二维物体的分形特性。该数值方法模拟了小角度光散射实验。研究了不同的二维二维规则分形，例如Sierpinski地毯，Sierpinski三角形，Koch雪花和Vishek雪花。与3D分形类似，我们可以将2D分形分为“平面”分形和“边界”分形，分形维数分别在1到2和2到3的区间内。对于具有光滑边界（即圆）的对象，模型小角度散射曲线根据幂定律q ^–3减小，其中q是传递的动量。