On Optimal Thickness of the Curve at Calculating the Fractal Dimension Using the Box-Counting Method
On Optimal Thickness of the Curve at Calculating the Fractal Dimension Using the Box-Counting Method
复制标题
计盒法计算分形维数时曲线的最佳粗细
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
D. Tumakov
中科院分区：
文献类型：
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作者：
I. Pershin;D. Tumakov
分形曲线在科学技术的各个领域都有应用，分形曲线的维数计算是一个实际的方向。分形维数（FD）是用来描述用曲线填充平面的度量。曲线厚度的选择
Fractal curves are found in various fields of science and technology, and the calculation of the dimensions of the curves is an actual direction. The fractal dimension (FD) is a metric used to characterize the filling of a plane with a curve. The choice of the thickness of the curve
line at calculating its FD using the box-counting method (BCM) is not obvious. This is the subject of the present paper. First, we consider a straight horizontal line with different thicknesses, and calculate FD for different thicknesses, using BCM. Using the exact dimensional value for a
straight line, the initial conclusion is made about the thicknesses that give a correct FD. In the next step, the dimensions of straight lines rotated by a certain angle in the range from to 90 degrees are calculated. At any angle of inclination of the line, the FD values should also remain
equal to unity. The range of FD values depending on the rotation angle is analyzed. The result is an “optimal” line thickness equal to 3 px. At this value, the FD values are the closest to one for any angle of inclination. As a result it is received that at dimensional calculation
by means of BCM, it is enough to choose the initial image of 200 on 200 pixels, and boxes to choose the sizes from 2 to 50 pixels with step of 2 pixels. The stability of dimension calculations on the grid offset has been verified. The algorithm’s error is estimated on the example of
the calculation of FD for the Koch fractal.