Log in

Relevant bibliographies by topics / Koch Curve / Journal articles

To see the other types of publications on this topic, follow the link: Koch Curve.

Journal articles on the topic 'Koch Curve'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Koch Curve.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

2

Weixing, Zheng. "On generalized Koch curve." Approximation Theory and its Applications 15, no. 4 (1999): 6–14. http://dx.doi.org/10.1007/bf02848665.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

4

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

5

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

7

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

10

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

11

Kim, Sun-Woong, Gul-Bum Kim, Jung-Hyun Yun, and Dong-You Choi. "Design of Koch Curve Microstrip Patch Antenna for Miniaturization Structure." Journal of the Korea Institute of Information and Communication Engineering 18, no. 12 (2014): 2823–30. http://dx.doi.org/10.6109/jkiice.2014.18.12.2823.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Jamil, A., K. Rafique, M. D. Idrees, A. S. Rajput, A. Abdullah, and A. S. Saand. "Design and Geometric Transformations of Koch Curve Monopole Antennas." Engineering, Technology & Applied Science Research 12, no. 2 (2022): 8452–57. http://dx.doi.org/10.48084/etasr.4767.

Full text

Abstract:

In this paper, a modified Koch curve monopole antenna is proposed for the dual-band Wireless Local Area Network (WLAN) and its performance has been compared with the conventional printed Koch-curve monopole antenna. Both the antennas have been contrived, and their simulated return loss and radiation pattern results have been validated with the measurements. Antenna #1 is designed on the geometrical basis of a conventional Koch-curve monopole antenna. Moreover, the shape of antenna # 1 is bent with a two-step rotation process to yield antenna #2. There are two advantages to this geometrical mod

APA, Harvard, Vancouver, ISO, and other styles

13

CANTRELL, MICHAEL, and JUDITH PALAGALLO. "SELF-INTERSECTION POINTS OF GENERALIZED KOCH CURVES." Fractals 19, no. 02 (2011): 213–20. http://dx.doi.org/10.1142/s0218348x11005257.

Full text

Abstract:

We present a two-parameter family of curves Ka, θ that are modifications of the Koch curve. For each θ, there is a corresponding pivotal valuea(θ) of a, where Ka, θ is simple if a > a(θ), and Ka, θ is self-intersecting if a < a(θ). We find a(θ), for θ ∈ (0, π/3], then show that the pivotal-valued curves comprise two classes of self-intersecting curves that we characterize by whether or not θ = π/n for some even positive integer n>2.

APA, Harvard, Vancouver, ISO, and other styles

14

Luo, Hong, Ying Tan, and Shou Li Peng. "A Symbolic Dynamics Approach to Random Walk on Koch Fractal." Applied Mechanics and Materials 610 (August 2014): 17–22. http://dx.doi.org/10.4028/www.scientific.net/amm.610.17.

Full text

Abstract:

The paper presents a new symbolic dynamic approach to the research of the random walk andBrownianmotion(BM)on Koch fractal. From the symbolic sequence of Koch automaton, on the one hand, we obtained the geometric description of the Koch curve completely, and constructed the state space of the random walk with the symbolic sequence. And the precise arithmetic representation of Koch curve is provided by the deterministicRademachersequence. On the other hand, the arithmetic feature of the Koch automaton, the position numbers, forms a partition of integer , which is naturally a one-dimensional lat

APA, Harvard, Vancouver, ISO, and other styles

15

Younis, Mahasin. "Measurement Brownian Dimension of Von Koch Curve." AL-Rafidain Journal of Computer Sciences and Mathematics 12, no. 1 (2018): 37–43. http://dx.doi.org/10.33899/csmj.2018.163573.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Harangi, Viktor. "The Koch snowflake curve is tube-null." Proceedings of the American Mathematical Society 139, no. 04 (2011): 1375. http://dx.doi.org/10.1090/s0002-9939-2010-10712-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Epstein, Marcelo, and Jędrzej Śniatycki. "The Koch curve as a smooth manifold." Chaos, Solitons & Fractals 38, no. 2 (2008): 334–38. http://dx.doi.org/10.1016/j.chaos.2006.11.036.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Nagatani, Takashi. "Deterministic Avalanches on a Branching Koch Curve." Journal of the Physical Society of Japan 60, no. 8 (1991): 2571–75. http://dx.doi.org/10.1143/jpsj.60.2571.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

E. W. Dekking and F. M. Dekking. "Helge von Koch′s Snowflake Curve Revisited." American Mathematical Monthly 123, no. 2 (2016): 181. http://dx.doi.org/10.4169/amer.math.monthly.123.2.181.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Chen, Guolong, and Zheng Cao. "Quantitative evaluation of eddy current distribution by relative entropy and cross entropy." Measurement and Control 54, no. 3-4 (2021): 164–69. http://dx.doi.org/10.1177/0020294020984201.

Full text

Abstract:

Koch curve exciting coil of an eddy current probe can adjust the eddy current distributing in more directions at a small domain to enhance the sensitivity of eddy current probe for short defect detection. In this study, a relative entropy and a cross entropy of tangential intersection angle spectrum are proposed to evaluate the eddy current distributions in the different directions when the eddy current probe is positioned at different lift-off distances and excited by different exciting frequency alternative currents. The eddy current distributions induced by a circular and a fractal Koch cur

APA, Harvard, Vancouver, ISO, and other styles

21

Dimri, Priti, Dharmendra Kumar, and Ashish Negi. "New Escape Time Koch Curve in Complex Plane." International Journal of Computer Applications 58, no. 8 (2012): 19–24. http://dx.doi.org/10.5120/9302-3521.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Milošević, Nebojša T., and Dušan Ristanović. "Fractal and nonfractal properties of triadic Koch curve." Chaos, Solitons & Fractals 34, no. 4 (2007): 1050–59. http://dx.doi.org/10.1016/j.chaos.2006.03.117.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Lakhtakia, A., V. K. Varadan, R. Messier, and V. V. Varadan. "Generalisations and randomisation of the plane Koch curve." Journal of Physics A: Mathematical and General 20, no. 11 (1987): 3537–41. http://dx.doi.org/10.1088/0305-4470/20/11/052.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Suzukawa, Kazumi, Kazuki Tomoda, Tatsufumi Miyazaki, Yusuke Kawamura, and Yugo Kanai. "Power Number and Mixing Drag Coefficient of Koch Fractal Impellers used by Koch Curve." KAGAKU KOGAKU RONBUNSHU 47, no. 3 (2021): 57–63. http://dx.doi.org/10.1252/kakoronbunshu.47.57.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Kim, Sun-Woong, Dong-Seob Lim, Young-Gon Kim, and Dong-You Choi. "Design and Implementation of Koch curve Microstrip Patch Antenna for Antenna Miniaturization." Journal of the Korea society of IT services 12, no. 3 (2013): 323–30. http://dx.doi.org/10.9716/kits.2013.12.3.323.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Chen, Guolong. "Two Novel Information Entropy Indices for Analysis of the Eddy Current Distribution." Entropy 20, no. 9 (2018): 699. http://dx.doi.org/10.3390/e20090699.

Full text

Abstract:

The Koch curve exciting coil eddy current sensor is a kind of novel flexible planar eddy current probe. In this study, an intersection angle spectrum entropy index and a radial direction energy spectrum entropy were proposed to evaluate the eddy current distribution. Eddy current distributions induced by one turn of a circular coil and one turn of a second order Koch curve coil feed with different exciting frequency alternative currents and at different lift-off distances, were simulated and the eddy current distributions varying with lift-off distance in different exciting frequencies were co

APA, Harvard, Vancouver, ISO, and other styles

27

Zhikharev, L. "Application of the Koch Curve to Increase the Strength of Aircraft Parts." Geometry & Graphics 10, no. 4 (2023): 13–25. http://dx.doi.org/10.12737/2308-4898-2022-10-4-13-25.

Full text

Abstract:

Fractals are formed by iterative repetition of the construction algorithm at different scale levels. The use of such an algorithm, which increases the strength properties during the construction of the structure, will strengthen these properties with each iteration. The Koch curve principle is applied in the article. Replacing the compressible plate with four new ones connected at angles increases the stability of the structure. This article theoretically confirms the increase in the stability of the Koch plate both at the level of individual plates and at the level of fractal segments a

APA, Harvard, Vancouver, ISO, and other styles

28

Choukiker, Yogesh Kumar, and Jagadish Chandra Mudiganti. "Compact hybrid fractal antenna for wideband wireless applications." International Journal of Microwave and Wireless Technologies 9, no. 5 (2016): 1191–96. http://dx.doi.org/10.1017/s1759078716001318.

Full text

Abstract:

A compact size hybrid fractal antenna is proposed for the application in wideband frequency range. The proposed antenna structure is the combination of Koch curve and self-affine fractal geometries. The Koch curve and self-affine geometries are optimized to achieve a wide bandwidth. The feed circuit is a microstrip line with a matching section over a rectangular ground plane. The measured impedance matching fractal bandwidth (S11 ≤ −10 dB) is 72.37% from 1.6 to 3.4 GHz. An acceptable agreement is obtained from the simulated and measured antenna performance parameters.

APA, Harvard, Vancouver, ISO, and other styles

29

XIONG, SIYUE, and XUEYE CHEN. "A NOVEL 3D MICROMIXER WITH QUARTIC KOCH CURVE FRACTAL." Surface Review and Letters 28, no. 06 (2021): 2150049. http://dx.doi.org/10.1142/s0218625x21500499.

Full text

Abstract:

In this paper, we mainly study the mixing performance of the micromixer with quartic Koch curve fractal (MQKCF) by numerical simulation. Changing the structure of the microchannel based on the fractal principle can significantly improve the fluid flow state in the microchannel and improve the mixing efficiency of the micromixer. This paper discussed the effects of different fractal deflection angles, microchannel heights and different fractal times on the mixing efficiency under four different Reynolds numbers (Re). It is found that changing the deflection angle of the fractal can bring extrem

APA, Harvard, Vancouver, ISO, and other styles

30

Fonseca, Daniel, Feliphe Pereira, and Ulysses R. C. Vitor. "Study of Patch Antennas with Koch Curve Form Slots." Journal of Microwaves, Optoelectronics and Electromagnetic Applications 18, no. 3 (2019): 399–407. http://dx.doi.org/10.1590/2179-10742019v18i31672.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Jia, Baoguo. "Bounds of the Hausdorff measure of the Koch curve." Applied Mathematics and Computation 190, no. 1 (2007): 559–65. http://dx.doi.org/10.1016/j.amc.2007.01.046.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Sharma, Chetna, and Dinesh Vishwakarma. "Miniaturization of logarithmic spiral antenna with modified Koch curve." Microwave and Optical Technology Letters 60, no. 9 (2018): 2167–72. http://dx.doi.org/10.1002/mop.31321.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

RAMÍREZ, JOSÉ L., GUSTAVO N. RUBIANO, and BORUT JURČIČ ZLOBEC. "GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION." Fractals 23, no. 04 (2015): 1550047. http://dx.doi.org/10.1142/s0218348x15500474.

Full text

Abstract:

In this paper, we introduce the [Formula: see text]-circle inversion which generalizes the classical inversion with respect to a circle ([Formula: see text]) and the taxicab inversion [Formula: see text]. We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the [Formula: see text]-circle inversion.

APA, Harvard, Vancouver, ISO, and other styles

34

ALLOUCHE, J. P., and G. SKORDEV. "VON KOCH AND THUE-MORSE REVISITED." Fractals 15, no. 04 (2007): 405–9. http://dx.doi.org/10.1142/s0218348x07003630.

Full text

Abstract:

We revisit the relation between the von Koch curve and the Thue-Morse sequence given in a recent paper of Ma and Goldener by relating their study to papers written by Coquet and Dekking at the beginning of the 1980s. We also emphasize that more general links between fractal objects and automatic sequences can be found in the literature.

APA, Harvard, Vancouver, ISO, and other styles

35

ZANTEMA, HANS. "TURTLE GRAPHICS OF MORPHIC SEQUENCES." Fractals 24, no. 01 (2016): 1650009. http://dx.doi.org/10.1142/s0218348x16500092.

Full text

Abstract:

The simplest infinite sequences that are not ultimately periodic are pure morphic sequences: fixed points of particular morphisms mapping single symbols to strings of symbols. A basic way to visualize a sequence is by a turtle curve: for every alphabet symbol fix an angle, and then consecutively for all sequence elements draw a unit segment and turn the drawing direction by the corresponding angle. This paper investigates turtle curves of pure morphic sequences. In particular, criteria are given for turtle curves being finite (consisting of finitely many segments), and for being fractal or sel

APA, Harvard, Vancouver, ISO, and other styles

36

KELETI, TAMÁS. "WHEN IS THE MODIFIED VON KOCH SNOWFLAKE NON-SELF-INTERSECTING?" Fractals 14, no. 03 (2006): 245–49. http://dx.doi.org/10.1142/s0218348x06003234.

Full text

Abstract:

We prove that the modified von Koch snowflake curve, which we get as a limit by starting from an equilateral triangle (or from a segment) and repeatedly replacing the middle portion c of each interval by the other two sides of an equilateral triangle (and the corresponding von Koch snowflake domain), is non-self-intersecting if and only if c < ½. This answers a question of M. van den Berg.

APA, Harvard, Vancouver, ISO, and other styles

37

Zhang, Li Jun, and Li Chen. "Anti-Counterfeiting Ability Analysis of Color Koch Curve in Package Printing." Applied Mechanics and Materials 312 (February 2013): 904–8. http://dx.doi.org/10.4028/www.scientific.net/amm.312.904.

Full text

Abstract:

Currently, there are some illegal businessmen in society who usually use the methods of copying picture of goods package to fake famous goods, and cheat customers to get illegal profits. Traditional package pictures are often designed with simple graphics which are easy to be copied by other people. Because of the complexity of the color variation and graphics structure, the package pictures designed with fractal graphics are very difficult to be copied by simple methods and low-end scanners. Therefore, fractal graphics can be used for anti-counterfeiting in package printing field, and prevent

APA, Harvard, Vancouver, ISO, and other styles

38

Essex, C., M. Davison, C. Schulzky, A. Franz, and K. H. Hoffmann. "The differential equation describing random walks on the Koch curve." Journal of Physics A: Mathematical and General 34, no. 41 (2001): 8397–406. http://dx.doi.org/10.1088/0305-4470/34/41/301.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Miyazima, Sasuke, Yasuhito Oota, and Yutaka Hasegawa. "Fractality of a modified Cantor set and modified Koch curve." Physica A: Statistical Mechanics and its Applications 233, no. 3-4 (1996): 879–83. http://dx.doi.org/10.1016/s0378-4371(96)00159-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Zheng, Dafang, Youyan Liu, and Z. D. Wang. "Quantum conductivity exponent of a fractal non-branching Koch curve." Solid State Communications 98, no. 6 (1996): 527–29. http://dx.doi.org/10.1016/0038-1098(96)00089-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Ponomarev, Stanislav P. "On the logarithmic potential defined for a Van Koch curve." Siberian Mathematical Journal 50, no. 5 (2009): 898–906. http://dx.doi.org/10.1007/s11202-009-0100-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Li, Tianpeng, Guang-Ming Wang, Ke Lu, He-Xiu Xu, Zhi-Heng Liao, and Binfeng Zong. "NOVEL BANDPASS FILTER BASED ON CSRR USING KOCH FRACTAL CURVE." Progress In Electromagnetics Research Letters 28 (2012): 121–28. http://dx.doi.org/10.2528/pierl11082903.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Yang, Guangjun, Xiaoling Yang, and Ping Wang. "H&#246;lder Derivative of the Koch Curve." Journal of Applied Mathematics and Physics 11, no. 01 (2023): 101–14. http://dx.doi.org/10.4236/jamp.2023.111008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Morillo, Pablo Lupera, Gary Flores Cadena, and Ricardo Merizalde. "Design and Testing of Fractal Antenna Parameters based on the Koch Curve for Reception of Digital Terrestrial Television Signals in the UHF Band." Law, State and Telecommunications Review 11, no. 1 (2019): 159–72. http://dx.doi.org/10.26512/lstr.v11i1.24855.

Full text

Abstract:

Purpose – In this research paper, the electrical and radiation characteristics of a proposed fractal antenna based on the Koch curve in the second iteration for reception of digital terrestrial television signals are designed and analyzed by laboratory tests. Methodology/approach/design – The design is based on the concepts of fractal geometry and on a previously designed antenna, which is adapted to obtain a different frequency of operation; the designed antenna is constructed in three different ways, finally, they are tested in the lab using vector-network-analyzer, that allows to meas

APA, Harvard, Vancouver, ISO, and other styles

45

Zhang, Hetong, Yue Guo, Xiang Zhang, et al. "Enhanced Shielding Performance of Layered Carbon Fiber Composites Filled with Carbonyl Iron and Carbon Nanotubes in the Koch Curve Fractal Method." Molecules 25, no. 4 (2020): 969. http://dx.doi.org/10.3390/molecules25040969.

Full text

Abstract:

Layered carbon fiber composites (CFC) with enhanced shielding effectiveness (SE) were prepared with mixed fillers of carbon nanotubes (CNTs) and carbonyl iron powders (CIPs) in the form of a Koch curve fractal. In the layered composite structure, glass fiber (GF) cloth was used in the wave–transmissive layer (WTL), and the carbon fiber (CF) cloth was used in the supporting layer (SL). Between WTL and SL, CNTs and CIPs were distributed in epoxy resin in the form of a Koch curve fractal to act as an absorbing layer (AL), and copper foil was used as a reflective layer (RL) and bonded at the botto

APA, Harvard, Vancouver, ISO, and other styles

46

Rani, S., and A. P. Singh. "On the Design and Analysis of Modified Koch Curve Fractal Antenna." Journal of The Institution of Engineers (India): Series B 94, no. 4 (2013): 231–36. http://dx.doi.org/10.1007/s40031-013-0061-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Campos, D., J. Fort, and V. Méndez. "Propagation through fractal media: The Sierpinski gasket and the Koch curve." Europhysics Letters (EPL) 68, no. 6 (2004): 769–75. http://dx.doi.org/10.1209/epl/i2004-10284-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Camp, Dane R. "A Fractal Excursion." Mathematics Teacher 84, no. 4 (1991): 265–75. http://dx.doi.org/10.5951/mt.84.4.0265.

Full text

Abstract:

Recently, chaos theory and the related topic of fractal geometry have blossomed as creative fields of study in mathematics and physics. Fractals are shapes containing self-similarity on arbitrary magnification. One such object, the Koch curve, is generated by simple recursion on an equilateral triangle. The process used to produce the curve is a great way to introduce students to some concepts of fractal geometry.

APA, Harvard, Vancouver, ISO, and other styles

49

TSIANOS, KONSTANTINOS I., and RON GOLDMAN. "BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE." Fractals 19, no. 01 (2011): 67–86. http://dx.doi.org/10.1142/s0218348x11005221.

Full text

Abstract:

We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in

APA, Harvard, Vancouver, ISO, and other styles

50

Rani, Shweta, and Sushil Kakkar. "Modified Koch Fractal Antenna for Multi and Wideband Wireless Applications." ECTI Transactions on Electrical Engineering, Electronics, and Communications 19, no. 2 (2021): 182–89. http://dx.doi.org/10.37936/ecti-eec.2021192.242065.

Full text

Abstract:

This paper focuses on the design and development of modified Koch fractal antenna. Compared to traditional Koch curve antenna, the presented antenna possesses a greater number of frequency bands and better impedance matching. Furthermore, the bacterial foraging optimization (BFO) approach is implemented to enhance the impedance bandwidth. The developed technique has been verified by employing various numerical simulations. The design parameters generated from the optimization procedure have been utilized to manufacture the antenna and the respective experimental and simulated results compared.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!