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Journal articles on the topic 'Sierpinski carpet'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

BERKOVE, ETHAN, and DEREK SMITH. "GEODESICS IN THE SIERPINSKI CARPET AND MENGER SPONGE." Fractals 28, no. 07 (2020): 2050120. http://dx.doi.org/10.1142/s0218348x20501200.

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In this paper, we study geodesics in the Sierpinski carpet and Menger sponge, as well as in a family of fractals that naturally generalize the carpet and sponge to higher dimensions. In all dimensions, between any two points we construct a geodesic taxicab path, namely a path comprised of segments parallel to the coordinate axes and possibly limiting to its endpoints by necessity. These paths are related to the skeletal graph approximations of the Sierpinski carpet that have been studied by many authors. We then provide a sharp bound on the ratio of the taxicab metric to the Euclidean metric,

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2

Wang, Xu, and Jun Wang. "Statistical Behavior of a Financial Model by Lattice Fractal Sierpinski Carpet Percolation." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/735068.

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The lattice fractal Sierpinski carpet and the percolation theory are applied to develop a new random stock price for the financial market. Percolation theory is usually used to describe the behavior of connected clusters in a random graph, and Sierpinski carpet is an infinitely ramified fractal. In this paper, we consider percolation on the Sierpinski carpet lattice, and the corresponding financial price model is given and investigated. Then, we analyze the statistical behaviors of the Hong Kong Hang Seng Index and the simulative data derived from the financial model by comparison.

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3

Joe D, Allin, and Thiyagarajan Krishnan. "A modified sierpinski carpet antenna structure for multiband wireless applications." Scientific Temper 14, no. 02 (2023): 398–404. http://dx.doi.org/10.58414/scientifictemper.2023.14.2.25.

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Multiband patch antenna has a very important part in the communication devices and systems. The benefits in designing and testing of Sierpinski carpet geometries for a low profile, cost effective multiband microstrip patch antenna for wireless standards is reviewed in this paper. The basic structure of the patch antenna is designed using the FR4 substrate with a thickness of 1.3 mm. The designed patch antenna structure is excited using the microstrip feed system. The Sierpinski carpet antenna structure is designed and simulated using High Frequency Structural Simulator (HFSS) software. The ava

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4

YANG, YUN, YUTING FENG, and YANHUA YU. "THE GENERALIZATION OF SIERPINSKI CARPET AND MENGER SPONGE IN n-DIMENSIONAL SPACE." Fractals 25, no. 05 (2017): 1750040. http://dx.doi.org/10.1142/s0218348x17500402.

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In this paper, we generalize Sierpinski carpet and Menger sponge in [Formula: see text]-dimensional space, by using the generations and characterizations of affinely-equivalent Sierpinski carpet and Menger sponge. Exactly, Menger sponge in [Formula: see text]-dimensional space could be drawn out clearly under an affine transformation. Furthermore, the method could be used to a much broader class in fractals.

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5

Ercai, Chen. "Chaos for the Sierpinski Carpet." Journal of Statistical Physics 88, no. 3/4 (1997): 979–84. http://dx.doi.org/10.1023/b:joss.0000015182.90436.5b.

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6

Lyamshev, L. M., and I. A. Urusovskii. "Sound diffraction at Sierpinski carpet." Acoustical Physics 49, no. 6 (2003): 700–703. http://dx.doi.org/10.1134/1.1626183.

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7

Jha, Mani Chandra, and Anne E. B. Nielsen. "Properties of Laughlin states on fractal lattices." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 5 (2023): 053103. http://dx.doi.org/10.1088/1742-5468/acd104.

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Abstract Laughlin states have recently been constructed on fractal lattices and have been shown to be topological in such systems. Some of their properties are, however, quite different from the two-dimensional case. On the Sierpinski triangle, for instance, the entanglement entropy shows oscillations as a function of particle number and does not obey the area law despite being topologically ordered, and the particle density is non-uniform in the bulk. Here, we investigate these deviant properties in greater detail on the Sierpinski triangle, and we also study the properties on the Sierpinski

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8

HAMBLY, B. M., and T. KUMAGAI. "ASYMPTOTICS FOR THE SPECTRAL AND WALK DIMENSION AS FRACTALS APPROACH EUCLIDEAN SPACE." Fractals 10, no. 04 (2002): 403–12. http://dx.doi.org/10.1142/s0218348x02001270.

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We discuss the behavior of the dynamic dimension exponents for families of fractals based on the Sierpinski gasket and carpet. As the length scale factor for the family tends to infinity, the lattice approximations to the fractals look more like the tetrahedral or cubic lattice in Euclidean space and the fractal dimension converges to that of the embedding space. However, in the Sierpinski gasket case, the spectral dimension converges to two for all dimensions. In two dimensions, we prove a conjecture made in the physics literature concerning the rate of convergence. On the other hand, for nat

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9

Pei, Anqi, and Jun Wang. "Volatility Behaviors of Financial Time Series by Percolation System on Sierpinski Carpet Lattice." Fluctuation and Noise Letters 14, no. 02 (2015): 1550015. http://dx.doi.org/10.1142/s0219477515500157.

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The financial time series is simulated and investigated by the percolation system on the Sierpinski carpet lattice, where percolation is usually employed to describe the behavior of connected clusters in a random graph, and the Sierpinski carpet lattice is a graph which corresponds the fractal — Sierpinski carpet. To study the fluctuation behavior of returns for the financial model and the Shanghai Composite Index, we establish a daily volatility measure — multifractal volatility (MFV) measure to obtain MFV series, which have long-range cross-correlations with squared daily return series. The

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10

Mohsin, Moslim, Adil AL Rammahi, and Furkan Rabee. "An Innovative Topologies Based on Hypercube Network Interconnection." European Journal of Information Technologies and Computer Science 3, no. 4 (2023): 7–13. http://dx.doi.org/10.24018/compute.2023.3.4.92.

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A parallel processing system's most crucial part is a network interconnection that links its processors. The hypercube topology has interesting features that make it a great option for parallel processing applications. This paper presents two innovative configurations of interconnection networks based on fractal Sierpinski and a hypercube. These are called the Sierpinski Triangle Topology (STT) and Sierpinski Carpet Topology (SCT). Compared to a hypercube, the Sierpinski Triangle topology (STT) noticed a significant decrease in the number of nodes and links as large networks grew. Hence, it is

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11

KANG, HYUNG SUK, DUANE DENNIS, and CHARLES MENEVEAU. "FLOW OVER FRACTALS: DRAG FORCES AND NEAR WAKES." Fractals 19, no. 04 (2011): 387–99. http://dx.doi.org/10.1142/s0218348x1100549x.

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An experimental study of interactions between a high Reynolds number fluid flow and multi-scale, fractal, objects is performed. Studying such interactions is required to improve our current understanding of wind or ocean current effects on vegetation elements, which often display fractal-like branching geometries. The main objectives of the study are to investigate the effects of the range of scales (generation numbers) of the fractal object and of the incoming flow condition on the drag force and drag coefficient, and to observe flow features in the near wake region resulting from the interac

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12

Dian, Widi Astuti, Wahyuni Intan, Muslim, and Alaydrus Mudrik. "Lowpass Filter with Hilbert Curve Ring and Sierpinski Carpet DGS." TELKOMNIKA Telecommunication, Computing, Electronics and Control 16, no. 3 (2018): 1092–100. https://doi.org/10.12928/TELKOMNIKA.v16i3.7722.

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Good performance and compact size are the paramaters which are vital when desiging a filter. One of the creteria of good performance is selectivity. This research, conducted by Hilbert Curve Ring and Siepinski Carpet, is used as defected ground structure to overcome filter selectivity. By using three cascadeds Hilbert Curve Ring defected ground structure cells and three steps Sierpinski carpet, a lowpass filter is designed and fabricated. The measurement result for lowpass filterwith Hilbert Curve Ring defected ground structure has sharper selectivity with the cut off frequency at 2.173 GHz an

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13

Mandrazhy, Oksana. "Amazing Properties of Fractal Figures." International Journal of Pure Mathematical Sciences 16 (March 2016): 37–43. http://dx.doi.org/10.18052/www.scipress.com/ijpms.16.37.

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This article describes the process of research of the properties of geometric fractals by high school students. The general formulas of calculating the length and the area of the Sierpinski carpet have been derived in the article. The total surface area and the volume of the Menger sponge have been calculated in the paper. The amazing facts of geometric fractals have been revealed. For instance, if n→∞, the length of the Sierpinski carpet is Ln→∞, and its area is Sn→0, similarly, if n→∞, the total surface area of the Menger sponge is Sts(n)→∞, and its volume is Vn→0.

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14

ZHAO, LUMING, SONGJING WANG, and LIFENG Xi. "AVERAGE GEODESIC DISTANCE OF SIERPINSKI CARPET." Fractals 25, no. 06 (2017): 1750061. http://dx.doi.org/10.1142/s0218348x1750061x.

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We obtain the average geodesic distance on the Sierpinski carpet in terms of the integral of geodesic distance on self-similar measure. We find out the finite pattern phenomenon of integral inspired by the notion of finite type on self-similar sets with overlaps.

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15

De Nicola, Francesco, Nikhil Santh Puthiya Purayil, Davide Spirito, et al. "Multiband Plasmonic Sierpinski Carpet Fractal Antennas." ACS Photonics 5, no. 6 (2018): 2418–25. http://dx.doi.org/10.1021/acsphotonics.8b00186.

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16

Jia, Baoguo. "Maximum density for the Sierpinski carpet." Computers & Mathematics with Applications 57, no. 10 (2009): 1615–21. http://dx.doi.org/10.1016/j.camwa.2009.02.032.

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17

Simpelaere, Dominique. "Multifractal decomposition of the Sierpinski carpet." Chaos, Solitons & Fractals 5, no. 11 (1995): 2153–70. http://dx.doi.org/10.1016/0960-0779(94)00224-e.

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18

Fangyue, Chen, and Xie Tingfan. "Hausdorff measure of fractal-Sierpinski carpet." Approximation Theory and its Applications 16, no. 2 (2000): 45–51. http://dx.doi.org/10.1007/bf02837392.

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19

Lu, Ying, Qingcheng Zeng, Jiajun Xu, and Lifeng Xi. "Geodesic distance on Sierpinski-like carpet." Journal of Mathematical Analysis and Applications 550, no. 1 (2025): 129541. https://doi.org/10.1016/j.jmaa.2025.129541.

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20

Xian-Yin, Zhou. "On the recurrence of simple random walks on some fractals." Journal of Applied Probability 29, no. 2 (1992): 454–59. http://dx.doi.org/10.2307/3214582.

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In this paper, the recurrence or transience of simple random walks on some lattice fractals is investigated. As results, we obtain that the simple random walk on the pre-Sierpinski gasket inddimensions is recurrent for alld≧ 2, and on the pre-Sierpinski carpet inddimensions it is recurrent ford= 2 and transient for alld≧ 3.

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21

Liu, Qing-Hui, Li-Feng Xi, and Yan-Fen Zhao. "DIMENSIONS OF INTERSECTIONS OF THE SIERPINSKI CARPET WITH LINES OF RATIONAL SLOPES." Proceedings of the Edinburgh Mathematical Society 50, no. 2 (2007): 411–27. http://dx.doi.org/10.1017/s0013091505000428.

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22

Han, Dan, Wenyang Ding, Xinyu Wang, and Lin Cheng. "Tunable thermal transport in a WS2 monolayer with isotopic doping and fractal structure." Nanoscale 11, no. 42 (2019): 19763–71. http://dx.doi.org/10.1039/c9nr02835h.

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23

Xian-Yin, Zhou. "On the recurrence of simple random walks on some fractals." Journal of Applied Probability 29, no. 02 (1992): 454–59. http://dx.doi.org/10.1017/s0021900200043205.

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In this paper, the recurrence or transience of simple random walks on some lattice fractals is investigated. As results, we obtain that the simple random walk on the pre-Sierpinski gasket in d dimensions is recurrent for all d ≧ 2, and on the pre-Sierpinski carpet in d dimensions it is recurrent for d = 2 and transient for all d ≧ 3.

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24

LUO, LIANG, BOMING YU, JIANCHAO CAI, and XIANGFENG ZENG. "NUMERICAL SIMULATION OF TORTUOSITY FOR FLUID FLOW IN TWO-DIMENSIONAL PORE FRACTAL MODELS OF POROUS MEDIA." Fractals 22, no. 04 (2014): 1450015. http://dx.doi.org/10.1142/s0218348x14500157.

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The tortuosity is a very important parameter for description of fluid flow in porous media, and it has been shown that porous media in nature have the fractal characteristics. The Sierpinski carpet is an exactly self-similar fractal model, which is often used to simulate fractal porous media. In this work, the tortuosity of different generations of Sierpinski carpet is calculated and analyzed by the finite volume method. A simple linear relation between the generations and tortuosity in pore fractal model of porous media is obtained. The results are compared with the available conclusions and

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25

Al-Shara’a, Iftichar M. T., and Hassanein Q. Al-Salami. "Rational map has a Cantor Circle Julia set and a Sierpinski Carpet Julia set of degree m." Journal of Interdisciplinary Mathematics 26, no. 7 (2023): 1483–91. http://dx.doi.org/10.47974/jim-1569.

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This research aims to study complex dynamics, and one of the best examples of this concept is the Julia set, for this we will present new concepts specific to the Julia set of the rational map J(Gμ). We introduce the family of complex rational maps as: Gμ(z) = 2μm+1 z–m + z2m – μ3m+1 / zm (z2m – μm–1) , with m ≥ 2 and μ ϵ ℂ\{0}(ℂ complex numbers) such that μm+1 ≠ 1 and μ2m+2 ≠ 1. We prove J(Gμ) is a degenerate Sierpinski carpet or a Sierpinski carpet or a Cantor circle by condition one of the free critical points has an image for Gμ is diverge on ∞ or 0.

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26

Christie, Marian. "Iterations of Emptying." Journal of Humanistic Mathematics 11, no. 1 (2021): 441–44. http://dx.doi.org/10.5642/jhummath.202101.28.

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27

Saluja, Nitin, and Rajesh Khanna. "Design analysis and fabrication of novel coplanar waveguide -fed hybrid fractal-based Broadband antenna." International Journal of Microwave and Wireless Technologies 5, no. 6 (2013): 749–52. http://dx.doi.org/10.1017/s1759078713000706.

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In this paper, a new compact hybrid fractal antenna with ultrawideband (UWB) behavior is proposed. Two merged fractals shapes, i.e. Sierpinski carpet and Sierpinski Gasket fed with coplanar waveguide (CPW) feed make patch as multiband and broadband antenna. The antenna is optimized using particle swarm optimization for side length of Sierpenski Gasket fractal and bandwidth. The overall width of the patch is taken as a parameter for optimizing bandwidth. The total size of presented antenna is 59 × 29 mm2. The antenna resonates at 2–5.2 GHz, so that wideband operation is observed. Antenna with t

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28

Li, Xiao Chuan, Xiang Yong Huang, and Xiao Feng Cui. "Quantitative Characterization of 2-D Porous Channels by Using Fractal Random Walk Method." Advanced Materials Research 614-615 (December 2012): 234–38. http://dx.doi.org/10.4028/www.scientific.net/amr.614-615.234.

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An improved random walk mode is proposed based on fractal geometry and random walk theory to characterize the features of porous channels quantitatively. Three different types of fractal Sierpinski carpet structures are obtained by iterative method. The effective thermal conductivities and fractal dimensions are calculated by finite volume method and statistical fractal algorithm respectively. The influences of porosity and pore distribution on effective thermal conductivity are investigated. Results indicate that, the effective thermal conductivity may be different for various structures with

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29

Boichenko, Viktoriia, Nataliya Shchestyuk, and Anastasiia Florenko. "Interpolation problems for random fields on Sierpinski’s carpet." Mohyla Mathematical Journal 6 (April 18, 2024): 28–34. http://dx.doi.org/10.18523/2617-70806202328-34.

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The prediction of stochastic processes and the estimation of random fields of different natures is becoming an increasingly common field of research among scientists of various specialties. However, an analysis of papers across different estimating problems shows that a dynamic approach over an iterative and recursive interpolation of random fields on fractal is still an open area of investigation. There are many papers related to the interpolation problems of stationary sequences, estimation of random fields, even on the perforated planes, but all of this still provides a place for an investi

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30

TIAN JU-PING and YAO KAI-LUN. "VISCOUS FINGERING IN SELF-AFFINE SIERPINSKI CARPET." Acta Physica Sinica 48, no. 2 (1999): 193. http://dx.doi.org/10.7498/aps.48.193.

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31

Kwapisz, Jaroslaw. "Conformal dimension via p-resistance: Sierpinski carpet." Annales Academiae Scientiarum Fennicae Mathematica 45, no. 1 (2020): 3–51. http://dx.doi.org/10.5186/aasfm.2020.4515.

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32

Noor, A., and Z. Hu. "Wideband multilayer Sierpinski carpet array radar absorber." Electronics Letters 52, no. 19 (2016): 1617–18. http://dx.doi.org/10.1049/el.2016.2702.

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33

Manning, Anthony, and Károly Simon. "Dimension of slices through the Sierpinski carpet." Transactions of the American Mathematical Society 365, no. 1 (2012): 213–50. http://dx.doi.org/10.1090/s0002-9947-2012-05586-3.

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34

Zhou, Zuoling, and Min Wu. "The Hausdorff measure of a Sierpinski carpet." Science in China Series A: Mathematics 42, no. 7 (1999): 673–80. http://dx.doi.org/10.1007/bf02878985.

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35

Li, Wenxia, and Dongmei Xiao. "DIMENSIONS OF MEASURE ON GENERAL SIERPINSKI CARPET." Acta Mathematica Scientia 19, no. 1 (1999): 81–85. http://dx.doi.org/10.1016/s0252-9602(17)30614-8.

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36

Mohanamurali, R., and T. Shanmuganantham. "Sierpinski Carpet Fractal Antenna for Multiband Applications." International Journal of Computer Applications 39, no. 14 (2012): 19–23. http://dx.doi.org/10.5120/4888-7376.

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37

Noquez, Victoria, and Lawrence S. Moss. "The Sierpinski Carpet as a Final Coalgebra." Electronic Proceedings in Theoretical Computer Science 372 (November 1, 2022): 249–61. http://dx.doi.org/10.4204/eptcs.372.18.

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38

Simpelaere, Dominique. "The correlation dimension of the Sierpinski carpet." Chaos, Solitons & Fractals 4, no. 12 (1994): 2223–35. http://dx.doi.org/10.1016/0960-0779(94)90042-6.

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39

XUE, YUMEI, and DONGXUE ZHOU. "ASYMPTOTIC FORMULA ON AVERAGE PATH LENGTH OF A SPECIAL NETWORK BASED ON SIERPINSKI CARPET." Fractals 26, no. 03 (2018): 1850039. http://dx.doi.org/10.1142/s0218348x18500391.

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In this paper, we construct a special network based on the construction of the Sierpinski carpet. Using the self-similarity and renewal theorem, we obtain the asymptotic formula for the average path length of our evolving network.

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40

Lupera Morillo, Pablo, Gary Flores, and Amanda Montaluisa. "Antena UHF multifuncional del tipo fractal microstrip basada en la alfombra de Sierpinski." Revista de Investigación en Tecnologías de la Información 9, no. 17 (2021): 4–16. http://dx.doi.org/10.36825/riti.09.17.002.

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The use of multifunctional devices increases day by day. Mentioned devices, as smart tv, need appropriate and unified antennas which can meet required frequencies. Therefore, in this paper, a Sierpinski carpet microstrip fractal antenna in the second iteration is designed and fabricated for Digital Tv in UHF band and wireless wideband networks. It was verified that that the design of a fractal antenna based on the Sierpinski carpet is possible from a rectangular patch on iteration 0; however, it must be taken into account that the patch design must be carried out at a specific resonance freque

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41

Nasar, Mohammed Abdul, Midhun Chakkaravarthy, and B. Khaleelu Rehman. "Design of Sierpinski Carpet Fractal Antenna for Wireless Applications." International Journal of Microsystems and IoT 2, no. 5 (2024): 817–22. https://doi.org/10.5281/zenodo.12779125.

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In wireless applications the antenna plays a vital role. It acts as an electromagnetic wave transmitter and receiver. When wireless antennas emit electromagnetic waves, they will reflect when they come into contact with objects. The research work suggests an antenna producing multiple frequencies operating in the 1 GHz–8 GHz range including both C-band and S-band applications operating range. The antenna is designed for VSWR< 2 and return loss S<sub>11</sub> < 10 dB. A rectangular microstrip patch with a fractal Sierpinski carpet approach is used in the antenna's design. The actual

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42

CANNING, S., A. J. WALKER, and P. A. ROACH. "THE EFFECTIVENESS OF A SIERPINSKI CARPET-INSPIRED TRANSDUCER." Fractals 25, no. 05 (2017): 1750050. http://dx.doi.org/10.1142/s0218348x17500505.

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Piezoelectric ultrasonic transducers have the ability to act both as a receiver and a transmitter of ultrasound. Standard designs have a regular structure and therefore operate effectively over narrow bandwidths due to their single length scale. Naturally occurring transducers benefit from a wide range of length scales giving rise to increased bandwidths. It is therefore of interest to investigate structures which incorporate a range of length scales, such as fractals. This paper applies an adaptation of the Green function renormalization method to analyze the propagation of an ultrasonic wave

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43

GIBSON, LEE R., and MELANIE PIVARSKI. "ISOPERIMETRIC PROFILES ON THE PRE-FRACTAL SIERPINSKI CARPET." Fractals 18, no. 04 (2010): 433–49. http://dx.doi.org/10.1142/s0218348x10005111.

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We describe the relationships among several notions of isoperimetry on a class of pre-fractal Sierpinski Carpets that satisfy a set of geometric assumptions as well as on the graphs corresponding to these carpets. We compute the L1-isoperimetric profile at scale h, and we use this computation to determine both the classical isoperimetric profile and a profile computed using Jordan curve boundaries.

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44

Tamegai, Shu, Shohei Watabe, and Tetsuro Nikuni. "Spatial Search on Sierpinski Carpet Using Quantum Walk." Journal of the Physical Society of Japan 87, no. 8 (2018): 085003. http://dx.doi.org/10.7566/jpsj.87.085003.

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45

Ju-ping, Tian, and Yao Kai-lun. "Computer simulation of viscous fingering in Sierpinski carpet." Acta Physica Sinica (Overseas Edition) 7, no. 9 (1998): 681–87. http://dx.doi.org/10.1088/1004-423x/7/9/006.

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46

Simpelaere, Dominique. "Recurrence and return times of the Sierpinski carpet." Journal of Statistical Physics 77, no. 5-6 (1994): 1099–103. http://dx.doi.org/10.1007/bf02183155.

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47

Li, Jian-Hua, and Bo-Ming Yu. "Tortuosity of Flow Paths through a Sierpinski Carpet." Chinese Physics Letters 28, no. 3 (2011): 034701. http://dx.doi.org/10.1088/0256-307x/28/3/034701.

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48

Jia, Baoguo. "Bounds of the Hausdorff Measure of Sierpinski carpet." Analysis in Theory and Applications 22, no. 4 (2006): 362–76. http://dx.doi.org/10.1007/s10496-006-0362-0.

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49

Wong, S., and B. L. Ooi. "Analysis and bandwidth enhancement of Sierpinski carpet antenna." Microwave and Optical Technology Letters 31, no. 1 (2001): 13–18. http://dx.doi.org/10.1002/mop.1343.

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50

Kanwal, Samra, Chun Yun Kee, Samuel Y. W. Low, Muhammad Zubair, and L. K. Ang. "Capacitance for fractal-like disordered dielectric slab." Journal of Applied Physics 132, no. 2 (2022): 024104. http://dx.doi.org/10.1063/5.0100159.

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In this paper, we model a heterogeneous dielectric medium exhibiting fractal geometry or disordered random structures by applying non-integer dimensions to determine its capacitance between two parallel plates. The capacitance depends on the fractional dimensions of the fractal or disordered dielectric slab, which may be obtained from the theoretical fractal dimension or box-counting method. The findings are verified by CST Studio Suite (Electromagnetic field simulation software), experimental measurements, and the equivalent capacitance method. Five common types of fractals (Cantor bars/plate

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