Average Distance of Sierpinski-Like Carpet

Ma, Ying; Wang, Qin; Zhang, Kai

doi:10.1142/s0218348x21500912

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…In recent years, complex networks [1][2][3][4][5][6] have been widely researched because they are closely related to life and various disciplines. Real networks in life are abstracted into many interesting network models in unique iterative ways, such as Sierpinski gaskets [7][8][9], Vicsek fractals [10][11][12] and Koch curves [13,14]. The topological property [15,16] is the most basic and important content in the study of complex networks, which includes several features: average shortest path, clustering coefficient and degree distribution.…”

Section: Introductionmentioning

confidence: 99%

Scaling of average receiving time and average weighted shortest path on weighted-crystal network

Li¹,

Li²,

Sun³

2021

J. Stat. Mech.

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In this paper, we focus on a network with even nodes named the weighted-crystal network, which is different from the regular iterative rules. By employing the self-similarity of the crystal network, we study and calculate the average receiving time (ART) and average weighted shortest path (AWSP) after dividing the network into n + 1 blocks. In particular, we pay attention to the hexagon crystal network in order to obtain exact results. The obtained scaled results show that ART grows linearly or sublinearly with the iterative and increases with the weight factor r. Meanwhile, the results of AWSP indicate that AWSP exhibits a sublinear dependence on the network order when r = 1. Otherwise, AWSP tends towards constants when 0 < r < 1.

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Section: Introductionmentioning

confidence: 99%

Scaling of average receiving time and average weighted shortest path on weighted-crystal network

Li¹,

Li²,

Sun³

2021

J. Stat. Mech.

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Scaling Region of Weierstrass-Mandelbrot Function: Improvement Strategies for Fractal Ideality and Signal Simulation

Feng

Zhang

et al. 2022

Fractal Fract

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Fractal dimension (D) is widely utilized in various fields to quantify the complexity of signals and other features. However, the fractal nature is limited to a certain scope of concerned scales, i.e., scaling region, even for a theoretically fractal profile generated through the Weierstrass-Mandelbrot (W-M) function. In this study, the scaling characteristics curves of profiles were calculated by using the roughness scaling extraction (RSE) algorithm, and an interception method was proposed to locate the two ends of the scaling region, which were named corner and drop phenomena, respectively. The results indicated that two factors, sampling length and flattening order, in the RSE algorithm could influence the scaling region length significantly. Based on the scaling region interception method and the above findings, the RSE algorithm was optimized to improve the accuracy of the D calculation, and the influence of sampling length was discussed by comparing the lower critical condition of the W-M function. To improve the ideality of fractal curves generated through the W-M function, the strategy of reducing the fundamental frequency was proposed to enlarge the scaling region. Moreover, the strategy of opposite operation was also proposed to improve the consistency of generated curves with actual signals, which could be conducive to practical simulations.

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Average Distance of Sierpinski-Like Carpet

Abstract: The geodesic structures on self-similar fractals are interesting. One feature of geodesic structures is average distance on fractal. We investigate the Sierpinski-like carpet and obtain the average distance in terms of self-similar measure.

Cited by 2 publications

References 12 publications

Scaling of average receiving time and average weighted shortest path on weighted-crystal network

Scaling of average receiving time and average weighted shortest path on weighted-crystal network

Scaling Region of Weierstrass-Mandelbrot Function: Improvement Strategies for Fractal Ideality and Signal Simulation

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