Comparison of two fractal interpolation methods

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	Comparison of two fractal interpolation methods
	Fu Y(傅洋); Zheng ZY(郑泽宇); Xiao R(肖睿); Shi HB(史海波)
刊名	Physica A: Statistical Mechanics and its Applications
	2017
卷号	469 页码:563-571
关键词	Fractal surface modeling The midpoint displacement method The Weierstrass–Mandelbrot method Autocorrelation analysis
ISSN号	0378-4371
通讯作者	傅洋 ; 郑泽宇
产权排序	1
中文摘要	As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass–Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass–Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass–Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass–Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass–Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass–Mandelbrot fractal function method has strong periodicity, which is suitable for simulating periodic surface.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Physics, Multidisciplinary
研究领域[WOS]	Physics
关键词[WOS]	TIME-SERIES ; COMPLEXITY ; PROFILES ; GEOMETRY ; SURFACE ; MODEL ; SEA
收录类别	SCI ; EI
语种	英语
WOS记录号	WOS:000392793500055
内容类型	期刊论文
源URL	[http://ir.sia.cn/handle/173321/19719]
专题	沈阳自动化研究所_数字工厂研究室
推荐引用方式 GB/T 7714	Fu Y,Zheng ZY,Xiao R,et al. Comparison of two fractal interpolation methods[J]. Physica A: Statistical Mechanics and its Applications,2017,469:563-571.
APA	Fu Y,Zheng ZY,Xiao R,&Shi HB.(2017).Comparison of two fractal interpolation methods.Physica A: Statistical Mechanics and its Applications,469,563-571.
MLA	Fu Y,et al."Comparison of two fractal interpolation methods".Physica A: Statistical Mechanics and its Applications 469(2017):563-571.