Academic literature on the topic 'Koch Curve'

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Journal articles on the topic "Koch Curve"

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Prasad, Sanjeev Kumar. "Superior Koch Curve." International Journal of Artificial Life Research 2, no. 4 (2011): 24–31. http://dx.doi.org/10.4018/jalr.2011100103.

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In this paper, the author presents the design of Superior Koch Curve with different scaling factor, which has wide applications in Fractals Graphics. The proposed curve has been designed using the technique of superior iteration. The Koch curve is the limiting curve obtained by applying the self similar divisions to infinite number of times but in Superior Koch Curve scaling factor is based on superior iteration.
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Weixing, Zheng. "On generalized Koch curve." Approximation Theory and its Applications 15, no. 4 (1999): 6–14. http://dx.doi.org/10.1007/bf02848665.

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DARST, R. B., J. A. PALAGALLO, and T. E. PRICE. "GENERALIZATIONS OF THE KOCH CURVE." Fractals 16, no. 03 (2008): 267–74. http://dx.doi.org/10.1142/s0218348x08003971.

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We present an iterative method to define a two-parameter family of continuous functions fa,θ: I → ℂ such that f1/3,π/3 is the Koch curve. We consider the two-cases θ = π/3 and θ = π/4 of these generalized Koch curves fa,θ(I). In each case we determine the pivotal value of a, the largest value of a for which the corresponding curve is not simple. We give characterizations of the double points of the curve (points on the curve that have two inverse images). In the case where θ = π/3 double points are vertices of equilateral triangles. When θ = π/4 the double points form Cantor sets in the plane.
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Purnomo, Kosala Dwidja, Siti Fatimah, and Bagus Juliyanto. "Generation of Fractal Objects with Iterated Function System on the Developments of Trellis Ornament Designs." BERKALA SAINSTEK 13, no. 1 (2025): 1–7. https://doi.org/10.19184/bst.v13i1.25656.

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Fractals are one of a mathematical concept that provides artistic value and is therefore widely used to design various kinds of objects. The purpose of this study is to obtain various trellis ornament designs generated from fractal objects. Some fractal objects that will be used are Koch Snowflake (m,n,c), Koch Anti-Snowflake (m,n,c) and dragon curve. The basic trellis pattern is built from basic geometry, namely line segments, rhombuses and elliptical curved lines with certain sizes. In this study, the generation of fractal objects was carried out using the Iterated Function Systems (IFS) met
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Ungar, Šime. "The Koch Curve: A Geometric Proof." American Mathematical Monthly 114, no. 1 (2007): 61–66. http://dx.doi.org/10.1080/00029890.2007.11920392.

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Kabanava, Maryia. "Function spaces on the Koch curve." Journal of Function Spaces and Applications 8, no. 3 (2010): 287–99. http://dx.doi.org/10.1155/2010/940297.

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We consider two types of Besov spaces on the Koch curve, defined by traces and with the help of the snowflaked transform. We compare these spaces and give their characterization in terms of Daubechies wavelets.
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Paramanathan, P., and R. Uthayakumar. "Fractal interpolation on the Koch Curve." Computers & Mathematics with Applications 59, no. 10 (2010): 3229–33. http://dx.doi.org/10.1016/j.camwa.2010.03.008.

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Hwang, Sam Chung, and Hyun Seung Yang. "Discrete approximation of the Koch curve." Computers & Graphics 17, no. 1 (1993): 95–102. http://dx.doi.org/10.1016/0097-8493(93)90057-g.

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Ri, Song-Il, Vasileios Drakopoulos, and Song-Min Nam. "Fractal Interpolation Using Harmonic Functions on the Koch Curve." Fractal and Fractional 5, no. 2 (2021): 28. http://dx.doi.org/10.3390/fractalfract5020028.

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The Koch curve was first described by the Swedish mathematician Helge von Koch in 1904 as an example of a continuous but nowhere differentiable curve. Such functions are now characterised as fractal since their graphs are in general fractal sets. Furthermore, it can be obtained as the graph of an appropriately chosen iterated function system. On the other hand, a fractal interpolation function can be seen as a special case of an iterated function system thus maintaining all of its characteristics. Fractal interpolation functions are continuous functions that can be used to model continuous sig
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Jamil, Atif, Muhammad Rauf, Abdul Sami, Arsalan Ansari, and Muhammad Dawood Idrees. "A Wideband Hybrid Fractal Ring Antenna for WLAN Applications." International Journal of Antennas and Propagation 2022 (February 21, 2022): 1–8. http://dx.doi.org/10.1155/2022/6136916.

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We propose the design of a novel fractal antenna that is both unique and performance-driven. Two important antenna design features, miniaturization and wideband operation, are combined in this work. A ring-shaped antenna is designed using the well-known fractal geometry. This hybrid geometry is a fusion of meander and Koch curve shapes. The geometrical construction of the proposed antenna is compared to the standard Koch curve geometry. It is shown that combining the meander and Koch curve shapes increases the effective electrical length. The wider bandwidth is achieved by bringing the higher
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Dissertations / Theses on the topic "Koch Curve"

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Fetbrandt, Joshua Taylor. "Hölder Extensions for Non-Standard Fractal Koch Curves." BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/4097.

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Let K be a non-standard fractal Koch curve with contraction factor α. Assume α is of the form α = 2+1/m for some m ∈ N and that K is embedded in a larger domain Ω. Further suppose that u is any Hölder continuous function on K. Then for each such m ∈ N and iteration n ≥ 0, we construct a bounded linear operator Πn which extends u from the prefractal Koch curve Kn into the whole of Ω. Unfortunately, our sequence of extension functions Πnu are not bounded in norm in the limit because the upper bound is a strictly increasing function of n; this prevents us from demonstrating uniform convergence in
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Irgin, Umit. "Analysis Of Koch Fractal Antennas." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/2/12610644/index.pdf.

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Fractal is a recursively-generated object describing a family of complex shapes that possess an inherent self-similarity in their geometrical structure. When used in antenna engineering, fractal geometries provide multi-band characteristics and lowering resonance frequencies by enhancing the space filling property. Moreover, utilizing fractal arrays, controlling side lobe-levels and radiation patterns can be realized. In this thesis, the performance of Koch curve as antenna is investigated. Since fractals are complex shapes, there is no well&ndash<br>established for mathematical formulation t
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Evans, Emily Jennings. "Extension Operators and Finite Elements for Fractal Boundary Value Problems." Digital WPI, 2011. https://digitalcommons.wpi.edu/etd-dissertations/134.

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The dissertation is organized into two main parts. The first part considers fractal extension operators. Although extension operators are available for general subsets of Euclidean domains or metric spaces, our extension operator is unique in that it utilizes both the iterative nature of the fractal and finite element approximations to construct the operator. The resulting operator is especially well suited for future numerical work on domains with prefractal boundaries. In the dissertation we prove the existence of a linear extension operator, Π from the space of Hölder continuous functions o
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Leifsson, Patrik. "Fractal sets and dimensions." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7320.

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<p>Fractal analysis is an important tool when we need to study geometrical objects less regular than ordinary ones, e.g. a set with a non-integer dimension value. It has developed intensively over the last 30 years which gives a hint to its young age as a branch within mathematics.</p><p>In this thesis we take a look at some basic measure theory needed to introduce certain definitions of fractal dimensions, which can be used to measure a set's fractal degree. Comparisons of these definitions are done and we investigate when they coincide. With these tools different fractals are studied and com
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Книш, Максим Андрійович, та Maksym Knysh. "Інформаційно-вимірювальна система пристрою для автоматичного контролю розмірів еластичних деталей". Master's thesis, ТНТУ ім. І. Пулюя, 2020. http://elartu.tntu.edu.ua/handle/lib/33777.

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В даній кваліфікаційній роботі магістра здійснюється розробка та дослідження інформаційно-вимірювальної системи пристрою для автоматичного контролю розмірів еластичних деталей, зроблено опис конструкції та роботи системи, розглянуто будову основних вузлів, проведено їх розрахунок проведено математичний аналіз роботи приладу, Cтворено S-модель вузла переміщення контрольованого зразка на вимірювальну позицію. Розроблена інформаційно-вимірювальна система дозволить збільшити якість продукції шляхом підвищення точності автоматичного контролю розмірів еластичних деталей за допомогою технічних засобі
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Almeida, Ana Cláudia Pereira de. "De Brás cubas a curva de Koch : produção textual com base nas teorias da Complexidade." Universidade Catolica de Pelotas, 2015. http://tede.ucpel.edu.br:8080/jspui/handle/tede/480.

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Submitted by Cristiane Chim (cristiane.chim@ucpel.edu.br) on 2016-08-15T12:50:08Z No. of bitstreams: 1 ANA CLAUDIA.pdf: 11662033 bytes, checksum: 737a34a0d7b9c637e82eb334fc9fe1bf (MD5)<br>Made available in DSpace on 2016-08-15T12:50:08Z (GMT). No. of bitstreams: 1 ANA CLAUDIA.pdf: 11662033 bytes, checksum: 737a34a0d7b9c637e82eb334fc9fe1bf (MD5) Previous issue date: 2015-12-02<br>On studies about Education, it is quite common to notice that while some teaching methodos approach the subjects and the intended object in a direct and explicit way, other ones use theoretical supports that advocate
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Pellegrino, Tommaso. "Misura e dimensione di Hausdorff in R^n." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13555/.

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La tesi fornisce le principali nozioni riguardanti la misura e la dimensione di Hausdorff. Dopo averle definite e osservato le principali proprietà si analizza il suo rapporto con la misura di Lebesgue n-dimensionale. Vengono poi osservati dei risultati sulla misura di Hausdorff in relazione a funzioni Lipschitziane che serviranno per dimostrare come una curva rettificabile abbia dimensione di Hausdorff 1 e misura di Hausdorff 1-dimensionale uguale alla sua lunghezza indipendentemente dallo spazio in cui siamo immersi. In fine si osserva un esempio di curva con dimensione frazionaria, la curva
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Oelhafen, Jonathan Fabio [Verfasser], Klaus [Akademischer Betreuer] Drechsler, Klaus [Gutachter] Drechsler, and Alexander W. [Gutachter] Koch. "Cure and Viscosity Measurement of Thermosetting Epoxy Resin with Fresnel Reflectometer Sensors / Jonathan Fabio Oelhafen ; Gutachter: Klaus Drechsler, Alexander W. Koch ; Betreuer: Klaus Drechsler." München : Universitätsbibliothek der TU München, 2019. http://d-nb.info/1200098730/34.

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Wang, Nancy. "Fractal Sets: Dynamical, Dimensional and Topological Properties." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-233147.

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Fractals is a relatively new mathematical topic which received thorough treatment only starting with 1960's. Fractals can be observed everywhere in nature and in day-to-day life. To give a few examples, common fractals are the spiral cactus, the romanesco broccoli, human brain and the outline of the Swedish map. Fractal dimension is a dimension which need not take integer values. In fractal geometry, a fractal dimension is a ratio providing an index of the complexity of fractal pattern with regard to how the local geometry changes with the scale at which it is measured. In recent years, fracta
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Creddo, Martina. "La matematica dei frattali." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12015/.

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Questa tesi ha lo scopo di descrivere le proprietà matematiche degli insiemi frattali. Nell'introduzione è spiegato brevemente cosa sono i frattali e vengono fatti alcuni esempi di frattali in natura, per poi passare agli aspetti più matematici nei capitoli. Nel capitolo uno si parla della misura e della dimensione di Hausdorff e viene calcolata, seguendo la definizione, per l'insieme di Cantor. Poi nel secondo capitolo viene descrittà l'autosimilarità e viene enunciato un importante teorema che lega l'autosimilarità e la dimensione di Hausdorff. Nel terzo capitolo vengono descritti degli insi
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Books on the topic "Koch Curve"

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Goetz, Thomas. Remedy: Robert Koch, Arthur Conan Doyle, and the Quest to Cure Tuberculosis. Penguin Publishing Group, 2015.

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The remedy: Robert Koch, Arthur Conan Doyle, and the quest to cure tuberculosis. Gotham Books, 2014.

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Burnett, James Compton. Five Years Experience In The New Cure Of Consumption By Its Own Virus: Presumably On A Line With The Method Of Koch. Franklin Classics, 2018.

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Burnett, James Compton. Five Years Experience in the New Cure of Consumption by Its Own Virus: Presumably on a Line with the Method of Koch. Creative Media Partners, LLC, 2018.

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Burnett, James Compton. Five Years Experience in the New Cure of Consumption by Its Own Virus: Presumably on a Line with the Method of Koch. Franklin Classics Trade Press, 2018.

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Book chapters on the topic "Koch Curve"

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Uthayakumar, R., and A. Nalayini Devi. "Some Properties on Koch Curve." In Fractals, Wavelets, and their Applications. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08105-2_10.

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Xu, Zhengzhi, and Youhui Su. "Implementation of Koch Curves Based on Html5." In Recent Developments in Data Science and Business Analytics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72745-5_50.

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"Generalizations of the Koch curve." In Curious Curves. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814291293_0004.

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"The Koch curve and tangent lines." In Curious Curves. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814291293_0002.

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D'Agostino, Susan. "Consider the less traveled path, because of the Jordan Curve Theorem." In How to Free Your Inner Mathematician. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198843597.003.0031.

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“Consider the less traveled path, because of the Jordan Curve Theorem” offers a basic introduction to simple, closed curves and explains why the theorem asserting that every simple closed curve in the plane separates the plane into an “inside” and an “outside” is best appreciated when considering pathological curves. A pathological curve, such as a space-filling curve or the Koch snowflake, is one that lacks features of so-called well-behaved curves. The discussion is enhanced by numerous hand-drawn sketches and a reference to “The Road Not Taken” by poet Robert Frost. Mathematics students and
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Hwang, Sam Chung, and Hyun Seung Yang. "Discrete approximation of the Koch curve." In Chaos and Fractals. Elsevier, 1998. http://dx.doi.org/10.1016/b978-044450002-1/50032-1.

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D'Agostino, Susan. "Exercise your imagination, with fractional dimensions." In How to Free Your Inner Mathematician. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198843597.003.0046.

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“Exercise your imagination, with fractional dimensions” offers a basic introduction to fractional dimensional objects. Unlike a one-dimensional line, a two-dimensional piece of paper, or a three-dimensional box, the dimension of a fractional dimensional object may not be represented by a whole number. The fractional dimensional Koch curve, for example, has approximately 1.26185 dimensions. The discussion is enhanced with numerous hand-drawn sketches providing instruction on how to construct and compute the dimension of the Koch curve. Mathematics students and enthusiasts are encouraged to exer
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Gonzales Palacios, Orlando Francois, Ricardo Erick Diaz Vargas, Patrick H. Stakem, and Carlos Enrique Arellano Ramirez. "Koch Snowflake Fractal Antenna Design in the Deep Space Bands for a Constellation of Cubesat Explorers." In Proceedings of CECNet 2021. IOS Press, 2021. http://dx.doi.org/10.3233/faia210419.

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This paper presents the design and simulation of a Koch curve fractal antenna, developed according to the second iteration of the Koch snowflake fractal for S-band, C-band, X-band and Ku-band. The simulated antenna shows good performance for the operating frequencies and desirable gain, bandwidth and VSWR parameters. Being a compact antenna, it has a size, geometry and characteristics that go in accord with the CubeSat’s structure standards. The antenna was fabricated on a 1.5 mm thick FR-4 substrate. The VSWR achieved values are lower than 1.4 for the frequencies used (2.1 GHz to 2.4 GHz and
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"Cellular Automata, Gaskets, and Koch Curves." In Chaos and Fractals. Elsevier, 1998. http://dx.doi.org/10.1016/b978-044450002-1/50024-2.

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Anitha, R., and R. S. Sankarasubramanian. "Verifiable Encryption of Digital Signatures Using Elliptic Curve Digital Signature Algorithm and its Implementation Issues." In Web Services Security and E-Business. IGI Global, 2007. http://dx.doi.org/10.4018/978-1-59904-168-1.ch010.

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This chapter presents a new simple scheme for verifiable encryption of elliptic curve digital signature algorithm (ECDSA). The protocol we present is an adjudicated protocol, that is, the trusted third party (TTP) takes part in the protocol only when there is a dispute. This scheme can be used to build efficient fair exchanges and certified email protocols. In this paper we also present the implementation issues. We present a new algorithm for multiplying two 2n bits palindromic polynomials modulo xp–1 for prime p = 2n + 1 for the concept defined in Blake, Roth, and Seroussi (1998), and it is
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Conference papers on the topic "Koch Curve"

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Abbas, S. Muzahir, Muryum Mahmood, Nihala Khalid, K. S. Alimgeer, and Shahid A. Khan. "Radial analysis of fractal Koch curve antenna." In 2012 International Conference on Emerging Technologies (ICET). IEEE, 2012. http://dx.doi.org/10.1109/icet.2012.6375424.

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Haitao, Cui, and Zhao Xiqing. "The Mechanization of the Koch Snowflake Curve." In 2011 International Conference on Information Management, Innovation Management and Industrial Engineering (ICIII). IEEE, 2011. http://dx.doi.org/10.1109/iciii.2011.389.

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Tahir, Mustafa Khalid. "Four Arms Koch Curve Multiband Cross Antenna." In The 2007 International Conference on Next Generation Mobile Applications, Services and Technologies (NGMAST 2007). IEEE, 2007. http://dx.doi.org/10.1109/ngmast.2007.4343425.

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Karim, Mohd Nazri A., Mohamad Kamal A. Rahim, Mohamad Irfan, and Thelaha Masri. "Fractal Koch curve for UHF band application." In 2007 Asia-Pacific Conference on Applied Electromagnetics (APACE). IEEE, 2007. http://dx.doi.org/10.1109/apace.2007.4603894.

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Yang, Qiuchen, Runjie Liu, Jinyuan Shen, and Weixin Mu. "Formal Development of Non-recursive Algorithm for Koch Curve." In 2010 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2010. http://dx.doi.org/10.1109/iwcfta.2010.93.

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Lyu, Xiaojing, Zhonghua Ma, and Xiangdong Zhao. "A Comparison of Algorithms of Drawing the Koch Snowflake Curve." In the 3rd International Conference. ACM Press, 2019. http://dx.doi.org/10.1145/3331453.3361292.

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Joy, Sijin Mary, and S. Santhosh Kumar. "Triangular microstrip loop resonator bandpass filter using Koch curve approach." In 2013 IEEE Recent Advances in Intelligent Computational Systems (RAICS). IEEE, 2013. http://dx.doi.org/10.1109/raics.2013.6745483.

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Purnomo, Kosala Dwidja, Nanda Puspa Winda Sari, Firdaus Ubaidillah, and Ika Hesti Agustin. "The construction of the Koch curve (n,c) using L-system." In INTERNATIONAL CONFERENCE ON SCIENCE AND APPLIED SCIENCE (ICSAS) 2019. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5141721.

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Pandav, Subhasish, Gautam Sadhukhan, Tanmaya Kumar Das, Santanu Kumar Behera, and Madhusmita Mohanty. "Design of High Gain Koch-Curve Fractal Antenna for Wireless Applications." In 2021 2nd International Conference for Emerging Technology (INCET). IEEE, 2021. http://dx.doi.org/10.1109/incet51464.2021.9456127.

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Elavarasi, C., and T. Shanmuganantham. "SRR loaded crescent patch-koch curve fractal for dual band applications." In 2016 International Conference on Control, Instrumentation, Communication and Computational Technologies (ICCICCT). IEEE, 2016. http://dx.doi.org/10.1109/iccicct.2016.7987956.

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