Log in

Relevant bibliographies by topics / Fractal shapes / Journal articles

To see the other types of publications on this topic, follow the link: Fractal shapes.

Journal articles on the topic 'Fractal shapes'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 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 'Fractal shapes.'

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

Kediangan, Ilham Vanka Agustiawan, La Zakaria, and Agus Sutrisno. "Design 3D Wallpaper Motifs from Sierpinski Carpet Fractals Using Mathematica Applications." Journal of Mathematics: Theory and Applications 6, no. 2 (2024): 146–57. http://dx.doi.org/10.31605/jomta.v6i2.3569.

Full text

Abstract:

The development of geometric studies is very rapid, including fractal geometry. A fractal is a geometric shape that fulfills the properties of the fractal dimension. If you look at a fractal at first glance, it has an irregular shape, but if you look further, there is a regularity. One of the properties of fractals is self-similarity which occurs when a fractal is enlarged. The fractal form has a pattern obtained from iterating a function with infinite repetition. Among the fractal shapes there is the Sierpinski carpet shape. Fractals in 2D form can be transformed using geometric concepts into

APA, Harvard, Vancouver, ISO, and other styles

2

Sulistyawati, Eka, and Imam Rofiki. "Ethnomathematics and creativity study in the construction of batik based on fractal geometry aided by GeoGebra." International Journal on Teaching and Learning Mathematics 4, no. 1 (2022): 15–28. http://dx.doi.org/10.18860/ijtlm.v5i1.10883.

Full text

Abstract:

This study aims to describe geometric objects that used by students on constructing fractal batik using Geogebra, procedure that used to construct fractal batik design, and students creativity on the process of constructing fractal batik. The qualitative descriptive research was applies including data collection, data separation, data analysis and conclusions. The research data were obtained from 97 students of tadris mathematics IAIN Kediri. The research results showed that fractal batik was constructed from a single geometric shape and combination of 2, 3, and 4 single geometric shapes throu

APA, Harvard, Vancouver, ISO, and other styles

3

Buriboev, Abror Shavkatovich, Djamshid Sultanov, Zulaykho Ibrohimova, and Heung Seok Jeon. "Mathematical Modeling and Recursive Algorithms for Constructing Complex Fractal Patterns." Mathematics 13, no. 4 (2025): 646. https://doi.org/10.3390/math13040646.

Full text

Abstract:

In this paper, we present mathematical geometric models and recursive algorithms to generate and design complex patterns using fractal structures. By applying analytical, iterative methods, iterative function systems (IFS), and L-systems to create geometric models of complicated fractals, we developed fractal construction models, visualization tools, and fractal measurement approaches. We introduced a novel recursive fractal modeling (RFM) method designed to generate intricate fractal patterns with enhanced control over symmetry, scaling, and self-similarity. The RFM method builds upon traditi

APA, Harvard, Vancouver, ISO, and other styles

4

Retnaningsih, Retnaningsih. "Fractal Geometry, Fibonacci Numbers, Golden Ratios, And Pascal Triangles as Designs." Journal of Academic Science 1, no. 1 (2024): 51–66. http://dx.doi.org/10.59613/msd4n328.

Full text

Abstract:

Fractal geometry is a part of mathematics that discusses the shape of fractals or any form that is self-similarity. A fractal can be broken down into parts that are all similar to the original fractal. Fractals have infinite detail and can have self-similar structures at different magnifications. In many cases, a fractal can be generated by repeating a pattern, which is usually in a recursive or iterative process. In mathematics and art, two values are considered to be a golden ratio relationship if the ratio between the sum of the two values to the large value is equal to the ratio between th

APA, Harvard, Vancouver, ISO, and other styles

5

Bobek, Jiří, Jiří Šafka, Martin Seidl, and Jiří Habr. "Mechanical Properties of Metal-Plastic Composite with Internal Fractal Shape Reinforcing Structure." Defect and Diffusion Forum 368 (July 2016): 170–73. http://dx.doi.org/10.4028/www.scientific.net/ddf.368.170.

Full text

Abstract:

This paper deals with mechanical properties research of innovative polymer multiphase metal and polymer composite materials consisting of matrix and isotropic or anisotropic oriented deterministic fractal shapes made by 3D printing. By creating of reinforcing internal structure consisting of deterministic fractal connected shapes is possible to gain unlimited mechanical properties directing. These fractal shapes - placed in multiphase system matrix – are significantly influencing whole material system mechanical properties mainly in case of stress on the limit of strength, proportional elongat

APA, Harvard, Vancouver, ISO, and other styles

6

Montiel, M. Eugenia, Alberto S. Aguado, and Ed Zaluska. "Fourier Series Expansion of Irregular Curves." Fractals 05, no. 01 (1997): 105–19. http://dx.doi.org/10.1142/s0218348x97000115.

Full text

Abstract:

Fourier theory provides an important approach to shape analyses; many methods for the analysis and synthesis of shapes use a description based on the expansion of a curve in Fourier series. Most of these methods have centered on modeling regular shapes, although irregular shapes defined by fractal functions have also been considered by using spectral synthesis. In this paper we propose a novel representation of irregular shapes based on Fourier analysis. We formulate a parametric description of irregular curves by using a geometric composition defined via Fourier expansion. This description al

APA, Harvard, Vancouver, ISO, and other styles

7

Husain, Akhlaq, Manikyala Navaneeth Nanda, Movva Sitaram Chowdary, and Mohammad Sajid. "Fractals: An Eclectic Survey, Part II." Fractal and Fractional 6, no. 7 (2022): 379. http://dx.doi.org/10.3390/fractalfract6070379.

Full text

Abstract:

Fractals are geometric shapes and patterns that can describe the roughness (or irregularity) present in almost every object in nature. Many fractals may repeat their geometry at smaller or larger scales. This paper is the second (and last) part of a series of two papers dedicated to an eclectic survey of fractals describing the infinite complexity and amazing beauty of fractals from historical, theoretical, mathematical, aesthetical and technological aspects, including their diverse applications in various fields. In this article, our focus is on engineering, industrial, commercial and futuris

APA, Harvard, Vancouver, ISO, and other styles

8

Alghar, Muhammad Zia, Natasya Ziana Walidah, and Marhayati Marhayati. "Ethnomathematics: The exploration of fractal geometry in Tian Ti Pagoda using the Lindenmayer system." Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika 5, no. 1 (2023): 57–69. http://dx.doi.org/10.35316/alifmatika.2023.v5i1.57-69.

Full text

Abstract:

This study explores the concept of fractal geometry found in the Tian Ti Pagoda. Fractal geometry is a branch of mathematics describing the properties and shapes of various fractals. A qualitative method with an ethnographic approach is used in this study. Observation, field notes, interviews, documentation, and literature study obtained research data. The observation results were processed computationally using the Lindenmayer system method via the L-Studio application to view fractal shapes. The results show that the concept of fractal geometry is contained in the ornaments on the Tian Ti Pa

APA, Harvard, Vancouver, ISO, and other styles

9

Nadal Shareef, Ammar, Abbas Abdulhussein Mohammed, and Amer Basim Shaalan. "Multi-band hybrid fractal shape antenna for X and K band applications." International Journal of Engineering & Technology 7, no. 4.36 (2018): 193–96. http://dx.doi.org/10.14419/ijet.v7i4.36.23744.

Full text

Abstract:

Fractal shapes has unusual properties. These unique features will affect antenna parameters when designed in fractal shapes. Two fractal shapes combined together to generate new fractal shape dipole antenna. Seirpinski and modified Koch fractal shapes allow this antenna to operate at too far apart frequencies lies in X and K band. Fractal dimension of modified Koch is found to be 1.08 which led the antenna to be electrically small. This is explaining the resonant points at higher frequencies. Uniting X and K band in single antenna will make the possibility of combining the applications of thes

APA, Harvard, Vancouver, ISO, and other styles

10

Bobek, Jiří, Jiří Šafka, Jiří Habr, and Martin Seidl. "3D Printing of Fractal Deterministic Shapes into Polymer Matrix with Respect to Final Composite Mechanical Properties." Applied Mechanics and Materials 693 (December 2014): 207–12. http://dx.doi.org/10.4028/www.scientific.net/amm.693.207.

Full text

Abstract:

This paper deals with mechanical properties research of innovative polymer multiphase composite materials consisting of matrix and isotropic or anisotropic oriented deterministic fractal shapes made by 3D printing. Standard polymer composite materials consisting for example of polypropylene matrix and glass fibres have mechanical properties which depend mainly on matrix-fibre interface strength, fibre length, fibre strength and fibres orientation. [1] In case of under critical fibre length is fibres orientation stochastic in for example injection moulded composites. So is possible to say that

APA, Harvard, Vancouver, ISO, and other styles

11

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

12

PAVLOVITCH, BULAEV BORIS. "PHASE-PERIODIC STRUCTURES OF SELF-SIMILAR STAIRCASE FRACTALS." Fractals 08, no. 04 (2000): 323–35. http://dx.doi.org/10.1142/s0218348x00000378.

Full text

Abstract:

The possibilities of investigating the self-similar staircase fractals in a discrete coordinate system are clearly very promising. Surprisingly, such fractals are found to have holographic properties. Some geometric shapes e.g. a circle or a quadrate, are produced by a well-defined boundary through generating the staircase fractals in 2D discrete space. The obtained "luminous boundaries" are remembered outer boundaries of any geometric form, regardless of the size. Actually, this process is similar to the photographing of an exterior form. Thus there is destruction of a natural phase-periodica

APA, Harvard, Vancouver, ISO, and other styles

13

Bai, Runbo, Maosen Cao, Zhongqing Su, Wiesław Ostachowicz, and Hao Xu. "Fractal Dimension Analysis of Higher-Order Mode Shapes for Damage Identification of Beam Structures." Mathematical Problems in Engineering 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/454568.

Full text

Abstract:

Fractal dimension analysis is an emerging method for vibration-based structural damage identification. An unresolved problem in this method is its incapability of identifying damage by higher-order mode shapes. The natural inflexions of higher-order mode shapes may cause false peaks of high-magnitude estimates of fractal dimension, largely masking any signature of damage. In the situation of a scanning laser vibrometer (SLV) providing a chance to reliably acquire higher-order (around tenth-order) mode shapes, an improved fractal dimension method that is capable of treating higher-order mode sh

APA, Harvard, Vancouver, ISO, and other styles

14

Zair, C. E., and E. Tosan. "Fractal Geometric Modeling in Computer Graphics." Fractals 05, supp02 (1997): 45–61. http://dx.doi.org/10.1142/s0218348x97000826.

Full text

Abstract:

Free form techniques and fractals are complementary tools for modeling respectively man-made objects and complex irregular shapes. Fractal techniques, having the advantage of describing self-similar objects, suffer from the drawback of a lack of control of the fractal figures. In contrast, free form techniques provide a high flexibility with smooth figures. Our work focuses on the definition of an IFS-based model designed to inherit the advantages of fractals and free form techniques (control by a set of control points, convex hull) in order to manipulate fractal figures in the way as classica

APA, Harvard, Vancouver, ISO, and other styles

15

Tu, Cheng-Hao, Hong-You Chen, David Carlyn, and Wei-Lun Chao. "Learning Fractals by Gradient Descent." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 2 (2023): 2456–64. http://dx.doi.org/10.1609/aaai.v37i2.25342.

Full text

Abstract:

Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model pre-training. In this paper, we study the inverse problem --- given a target image (not necessarily a fractal), we aim to generate a fractal image that looks like it. We propose a novel approach that learns the parameters underlying a fractal image via gradient descent. We show that our approach can find fractal parameters of high visual quality and be compatible with

APA, Harvard, Vancouver, ISO, and other styles

16

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

17

Wright, Edward L. "Fractal Dust Grains." Symposium - International Astronomical Union 135 (1989): 337–42. http://dx.doi.org/10.1017/s0074180900125343.

Full text

Abstract:

Dust particles in the interstellar medium are almost certainly not spherical or any other shape which allows an analytical calculation of the extinction curve, even in the Rayleign limit. Particles in soot and interplanetary dust particles are aggregates formed by subclusters which stick together. This paper uses the discrete dipole approximation (DDA) to compute the absorption and extinction curves for fractal shapes generated by this clustering process. For fractals made from graphite the UV extinction curve shows a bump near the observed 220 nm feature, and a far infrared emission efficienc

APA, Harvard, Vancouver, ISO, and other styles

18

Terzic, A., V. V. Mitic, Lj Kocic, Z. Radojevic, and S. Pasalic. "Mechanical properties and microstructure fractal analysis of refractory bauxite concrete." Science of Sintering 47, no. 3 (2015): 331–46. http://dx.doi.org/10.2298/sos1503331t.

Full text

Abstract:

The surface topography analysis via fractals as a means of explanation of composite materials mechanical and microstructural characteristics has hardly been reported so far. This study proposes a method of fractal analysis and its application to refractory bauxite concrete surface tribological investigation. Fractal dimension, profilegrams and fast Fourier transform method are introduced and supported by the adequate software for analysing contours and surface roughness, depending on the observation scale and also numerically depending on horizontal lines intercepted by the investigated profil

APA, Harvard, Vancouver, ISO, and other styles

19

Zhang, Xiyin. "Analysis of the Principle and Applications of Fractal." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 337–42. http://dx.doi.org/10.54097/5fxx1704.

Full text

Abstract:

As a matter of fact, fractal is one of the mystery in math applications which attracts a large number of scholars even in recent years. With this in mind, a brief introductions for definition of fractals and a presentation of a brief history of fractal theory will be presented in this study. To be specific, this study will provide explanations on basic principles of fractal geometry like self-similarity and scaling. At the same time, this study will also give the idea of fractal dimensions and examples of fractal shapes. In detail, the essay will include two specific fractal applications in me

APA, Harvard, Vancouver, ISO, and other styles

20

Vlcek, J., and E. Cheung. "Fractal analysis of leaf shapes." Canadian Journal of Forest Research 16, no. 1 (1986): 124–27. http://dx.doi.org/10.1139/x86-020.

Full text

Abstract:

An application of fractal mathematics to the analysis of leaf shapes is presented. Six leaves randomly selected from nine tree species were used in the study. A video imaging method together with microcomputer-based image processing was used to generate leaf outlines. A fractal analysis program was written to calculate the fractal dimensions of the leaves. Recalling a leaf outline from a diskette and specifying both the starting position on it (e.g., the beginning of the petiole) and six step lengths (explained later), the program then generates the fractal dimension according to the theory de

APA, Harvard, Vancouver, ISO, and other styles

21

GENTIL, C., E. TOSAN, and M. NEVEU. "MIXED-ASPECT FRACTAL CURVES." Fractals 17, no. 04 (2009): 395–406. http://dx.doi.org/10.1142/s0218348x09004582.

Full text

Abstract:

The aim of our work is to elaborate a method to build parametric shapes (curves, surfaces, …) with a non uniform local aspect: every point is assigned a "geometric texture" that evolves continuously from a smooth aspect to a rough aspect. We rely on previous work that enables us to represent both smooth and fractal free form curves to propose a formalism based on finite families of iterated function systems that generalizes this previous approach. The principle is to blend shapes with uniform aspects to define a shape with a variable aspect.

APA, Harvard, Vancouver, ISO, and other styles

22

Gdawiec, Krzysztof, and Diana Domańska. "Partitioned iterated function systems with division and a fractal dependence graph in recognition of 2D shapes." International Journal of Applied Mathematics and Computer Science 21, no. 4 (2011): 757–67. http://dx.doi.org/10.2478/v10006-011-0060-8.

Full text

Abstract:

Partitioned iterated function systems with division and a fractal dependence graph in recognition of 2D shapesOne of the approaches in pattern recognition is the use of fractal geometry. The property of self-similarity of fractals has been used as a feature in several pattern recognition methods. All fractal recognition methods use global analysis of the shape. In this paper we present some drawbacks of these methods and propose fractal local analysis using partitioned iterated function systems with division. Moreover, we introduce a new fractal recognition method based on a dependence graph o

APA, Harvard, Vancouver, ISO, and other styles

23

Жихарев, Л., and L. Zhikharev. "Fractals In Three-Dimensional Space. I-Fractals." Geometry & Graphics 5, no. 3 (2017): 51–66. http://dx.doi.org/10.12737/article_59bfa55ec01b38.55497926.

Full text

Abstract:

It has long been known that there are fractals, which construction resolve into cutting out of elements from lines, curves or geometric shapes according to a certain law. If the fractal is completely self-similar, its dimensionality is reduced relative to the original object and usually becomes fractional. The whole fractal is often decomposing into a set of separate elements, organized in the space of corresponding dimension. German mathematician Georg Cantor was among the first to propose such fractal set in the late 19th century. Later in the early 20th century polish mathematician Vaclav S

APA, Harvard, Vancouver, ISO, and other styles

24

Roifah, Miftahur. "DESAIN MOZAIK PADA BINGKAI BELAH KETUPAT DENGAN MOTIF FRAKTAL DAN KONSTRUKSINYA PADA MATLAB." Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika 1, no. 1 (2019): 83–93. http://dx.doi.org/10.35316/alifmatika.2019.v1i1.83-93.

Full text

Abstract:

Mosaics are the artistic creations made from pieces of shape which are then arranged and affixed to a plane and designed using a tiling pattern with a basic pattern of geometric objects.. The progress of science and technology enables innovations especially after the invention of computers, one of which is fractals. Fractals are widely used in computer graphics to create amazing shapes. Mosaic designs can also be made with fractal concepts. The aims of this research are to get the procedure for mosaic design on circle and rhombus frames by hexagon and Pinwheel tiling with fractal motif. The re

APA, Harvard, Vancouver, ISO, and other styles

25

Aguirre-López, Mario A., José Ulises Márquez-Urbina, and Filiberto Hueyotl-Zahuantitla. "New Properties and Sets Derived from the 2-Ball Fractal Dust." Fractal and Fractional 7, no. 8 (2023): 612. http://dx.doi.org/10.3390/fractalfract7080612.

Full text

Abstract:

Due to their practicality and convenient parametrization, fractals derived from iterated function systems (IFSs) constitute powerful tools widely used to model natural and synthetic shapes. An IFS can generate sets other than fractals, extending its application field. Some of such sets arise from IFS fractals by adding minimal modifications to their defining rule. In this work, we propose two modifications to a fractal recently introduced by the authors: the so-called 2-ball fractal dust, which consists of a set of balls diminishing in size along an iterative process and delimited by an enclos

APA, Harvard, Vancouver, ISO, and other styles

26

Chen, Yanguang. "Two Sets of Simple Formulae to Estimating Fractal Dimension of Irregular Boundaries." Mathematical Problems in Engineering 2020 (February 26, 2020): 1–15. http://dx.doi.org/10.1155/2020/7528703.

Full text

Abstract:

Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of boundaries systematically when image data are limited. An approximation estimation formula of boundary dimension based on square is widely applied in urban and ecological studies. But the boundary dimension is sometimes overestimated. This paper is devoted to developing a series of practicable formulae for boundary dimension estimation using ideas from fractals.

APA, Harvard, Vancouver, ISO, and other styles

27

Alrammahi, Adil. "Condensation to Fractal Shapes Constructing." Journal of Kufa for Mathematics and Computer 6, no. 3 (2023): 1–7. http://dx.doi.org/10.31642/jokmc/2018/060300.

Full text

Abstract:

Two properties must be available in order to construct a fractal set. The first is the selfsimilarity of the elements. The second is the real fraction number dimension. In this paper,condensation principle is introduced to construct fractal sets. Condensation idea is represented in threetypes. The first is deduced from rotation –reflection linear transformation. The second is dealt withgroup action. The third is represented by graph function.

APA, Harvard, Vancouver, ISO, and other styles

28

JÁNOSI, IMRE M., and ANDRÁS CZIRÓK. "FRACTAL CLUSTERS AND SELF-ORGANIZED CRITICALITY." Fractals 02, no. 01 (1994): 153–68. http://dx.doi.org/10.1142/s0218348x94000156.

Full text

Abstract:

Self-organized criticality (SOC) and fractals have been shown to be related in various ways. On the one hand, the original idea of SOC suggests that the common explanation of the origin of fractal shapes in nature may be based on self-organized processes. Thus different models exhibiting SOC result in relaxation clusters or avalanches whose geometrical characteristics could be described by fractals. On the other hand, there exist several models for fractal growth phenomena, such as viscous fingering, invasion percolation, dielectric breakdown, etc., and it is possible that the concept of SOC m

APA, Harvard, Vancouver, ISO, and other styles

29

Vacc, Nancy Nesbitt. "Children's Descriptions of Fractal Shapes." Perceptual and Motor Skills 88, no. 2 (1999): 661–68. http://dx.doi.org/10.2466/pms.1999.88.2.661.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Alrammahi, Adil. "Condensation to Fractal Shapes Constructing." Journal of Kufa for Mathematics and Computer 6, no. 3 (2019): 1–7. http://dx.doi.org/10.31642/jokmc/2018/060301.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Herrmann, H. J., J. Kertész, and L. de Arcangelis. "Fractal Shapes of Deterministic Cracks." Europhysics Letters (EPL) 10, no. 2 (1989): 147–52. http://dx.doi.org/10.1209/0295-5075/10/2/010.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Ullah, A. M. M. Sharif, D. M. D’Addona, Khalifa H. Harib, and Than Lin. "Fractals and Additive Manufacturing." International Journal of Automation Technology 10, no. 2 (2016): 222–30. http://dx.doi.org/10.20965/ijat.2016.p0222.

Full text

Abstract:

Fractal geometry can create virtual models of complex shapes as CAD data, and from these additive manufacturing can directly create physical models. The virtual-model-building capacity of fractal geometry and the physical-model-building capacity of additive manufacturing can be integrated to deal with the design and manufacturing of complex shapes. This study deals with the manufacture of fractal shapes using commercially available additive manufacturing facilities and 3D CAD packages. Particular interest is paid to building physical models of an IFS-created fractal after remodeling it for man

APA, Harvard, Vancouver, ISO, and other styles

33

Mitic, Vojislav, Goran Lazovic, Jelena Manojlovic, et al. "Entropy and fractal nature." Thermal Science 24, no. 3 Part B (2020): 2203–12. http://dx.doi.org/10.2298/tsci191007451m.

Full text

Abstract:

Existing, the biunivocal correspondents between the fractal nature and the nature discovered by fractals is the source and meeting point from those two aspects which are similar to the thermodynamically philosophical point of view. Sometimes we can begin from the end. We are substantial part of such fractals space nature. The mathematics fractal structures world have been inspired from nature and Euclidian geometry imagined shapes, and now it is coming back to nature serving it. All our analysis are based on several experimental results. The substance of the question regarding entropy and frac

APA, Harvard, Vancouver, ISO, and other styles

34

Mitic, V. V., V. B. Pavlovic, L. Kocic, V. Paunovic, and L. Zivkovic. "Fractal Geometry and Properties of Doped BaTiO₃ Ceramics." Advances in Science and Technology 67 (October 2010): 42–48. http://dx.doi.org/10.4028/www.scientific.net/ast.67.42.

Full text

Abstract:

Taking into account that the complex grain structure is difficult to describe by using traditional analytical methods, in this study, in order to establish ceramic grain shapes of sintered BaTiO3, new approach on correlation between microstructure and properties of doped BaTiO3 ceramics based on fractal geometry has been developed. BaTiO3 ceramics doped with various dopants (MnCO3, Er2O3, Yb2O3) were prepared using conventional solid state procedure, and were sintered at 1350oC for four hours. The microstructure of sintered specimens was investigated by SEM-5300. Using method of fractal modeli

APA, Harvard, Vancouver, ISO, and other styles

35

TAKEHARA, TAKUMA, FUMIO OCHIAI, and NAOTO SUZUKI. "FRACTALS IN EMOTIONAL FACIAL EXPRESSION RECOGNITION." Fractals 10, no. 01 (2002): 47–52. http://dx.doi.org/10.1142/s0218348x02001087.

Full text

Abstract:

Following the Mandelbrot's theory of fractals, many shapes and phenomena in nature have been suggested to be fractal. Even animal behavior and human physiological responses can also be represented as fractal. Here, we show the evidence that it is possible to apply the concept of fractals even to the facial expression recognition, which is one of the most important parts of human recognition. Rating data derived from judging morphed facial images were represented in the two-dimensional psychological space by multidimensional scaling of four different scales. The resultant perimeter of the struc

APA, Harvard, Vancouver, ISO, and other styles

36

Wang, Xiao Jun, and Jian Qin. "Fractal Dependence Graph in 2D Shapes Recognition." Applied Mechanics and Materials 143-144 (December 2011): 715–20. http://dx.doi.org/10.4028/www.scientific.net/amm.143-144.715.

Full text

Abstract:

Fractal geometry is an useful approach in pattern recognition. Many fractal recognition methods use global analysis of the shape. In this paper we present a new fractal recognition method based on a dependence graph obtained from the PIFS. Moreover, this method uses local analysis of the shape which improves the recognition rate. The recognition algorithms have been tested to provide a feasible classification of the possible errors present in our similar object images datebase.

APA, Harvard, Vancouver, ISO, and other styles

37

Anitas, Eugen Mircea. "Structural Properties of Molecular Sierpiński Triangle Fractals." Nanomaterials 10, no. 5 (2020): 925. http://dx.doi.org/10.3390/nano10050925.

Full text

Abstract:

The structure of fractals at nano and micro scales is decisive for their physical properties. Generally, statistically self-similar (random) fractals occur in natural systems, and exactly self-similar (deterministic) fractals are artificially created. However, the existing fabrication methods of deterministic fractals are seldom defect-free. Here, are investigated the effects of deviations from an ideal deterministic structure, including small random displacements and different shapes and sizes of the basic units composing the fractal, on the structural properties of a common molecular fractal

APA, Harvard, Vancouver, ISO, and other styles

38

Özgür, Nihal, Swati Antal, and Anita Tomar. "Julia and Mandelbrot Sets of Transcendental Function via Fibonacci-Mann Iteration." Journal of Function Spaces 2022 (May 16, 2022): 1–13. http://dx.doi.org/10.1155/2022/2592573.

Full text

Abstract:

In this paper, utilizing the Fibonacci-Mann iteration process, we explore Julia and Mandelbrot sets by establishing the escape criteria of a transcendental function, sin z n + a z + c , n ≥ 2 ; here, z is a complex variable, and a and c are complex numbers. Also, we explore the effect of involved parameters on the deviance of color, appearance, and dynamics of generated fractals. It is well known that fractal geometry portrays the complexity of numerous complicated shapes in our surroundings. In fact, fractals can illustrate shapes and surfaces which cannot be described by the traditional Eucl

APA, Harvard, Vancouver, ISO, and other styles

39

ALTUN, SELIM, ALPER SEZER, and A. BURAK GOKTEPE. "EFFECT OF FRACTAL DIMENSION ON THE STRAIN BEHAVIOR OF PARTICULATE MEDIA." Fractals 24, no. 04 (2016): 1650047. http://dx.doi.org/10.1142/s0218348x1650047x.

Full text

Abstract:

In this study, the influence of several fractal identifiers of granular materials on dynamic behavior of a flexible pavement structure as a particulate stratum is considered. Using experimental results and numerical methods as well, 15 different grain-shaped sands obtained from 5 different sources were analyzed as pavement base course materials. Image analyses were carried out by use of a stereomicroscope on 15 different samples to obtain quantitative particle shape information. Furthermore, triaxial compression tests were conducted to determine stress–strain and shear strength parameters of s

APA, Harvard, Vancouver, ISO, and other styles

40

Wang, J., and S. Ogawa. "Fractal Analysis Of Colors And Shapes For Natural And Urbanscapes URBANSCAPES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-7/W3 (April 30, 2015): 1431–38. http://dx.doi.org/10.5194/isprsarchives-xl-7-w3-1431-2015.

Full text

Abstract:

Fractal analysis has been applied in many fields since it was proposed by Mandelbrot in 1967. Fractal dimension is a basic parameter of fractal analysis. According to the difference of fractal dimensions for images, natural landscapes and urbanscapes could be differentiated, which is of great significance. In this paper, two methods were used for two types of landscape images to discuss the difference between natural landscapes and urbanscapes. Traditionally, a box-counting method was adopted to evaluate the shape of grayscale images. On the other way, for the spatial distributions of RGB valu

APA, Harvard, Vancouver, ISO, and other styles

41

Bai, Run Bo, Zong Mei Xu, and Xiu Mei Qiu. "Damage Detection in Beam-Type Structures Using Fractal Dimension Trajectory of Rotated Higher Vibration Modes." Applied Mechanics and Materials 275-277 (January 2013): 1111–17. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.1111.

Full text

Abstract:

Damage-induced local response is probably easy to be captured by the higher modes of the structures, especially for the small defects. The aim of this paper is to overcome the inherent deficiency of fractal dimension to identify crack when implemented to higher mode shapes. The proposed approach reconstructs the higher mode shape through rotation transformation, and then the fractal dimension analysis is implemented on this new mode shape to yield a fractal dimension trajectory. The location of the crack can be determined by the sudden peaks at the fractal dimension trajectory. The applicabili

APA, Harvard, Vancouver, ISO, and other styles

42

A A, Sathakathulla. "Pinwheel tiling fractal graph- a notion to edge cordial and cordial labeling." International Journal of Applied Mathematical Research 5, no. 2 (2016): 84. http://dx.doi.org/10.14419/ijamr.v5i2.5700.

Full text

Abstract:

<p>A fractal is a complex geometric figure that continues to display self-similarity when viewed on all scales. Tile substitution is the process of repeatedly subdividing shapes according to certain rules. These rules are also sometimes referred to as inflation and deflation rule. One notable example of a substitution tiling is the so-called Pinwheel tiling of the plane. Many examples of self-similar tiling are made of fractiles: tiles with fractal boundaries. . The pinwheel tiling was the first example of this sort. There are many as such as family of tiling fractal curves, but for my s

APA, Harvard, Vancouver, ISO, and other styles

43

Shariff, Asma A., and M. Hadi Hafezi. "A Review on Fractals and Fracture, Part I: Calculating Fractal Dimensions by CAD Model." Applied Mechanics and Materials 148-149 (December 2011): 818–21. http://dx.doi.org/10.4028/www.scientific.net/amm.148-149.818.

Full text

Abstract:

The objective of this paper is to consider the use of fractal geometry as a tool for the study of non-smooth and discontinuous objects for which Euclidean coordinate is not able to fully describe their shapes. We categorized the methods for computing fractal dimension with a discussion into that. We guide readers up to the point they can dig into the literature, but with more advanced methods that researchers are developing. Considerations show that is necessary to understand the numerous theoretical and experimental results concerning searching of the conformality before evaluating the fracta

APA, Harvard, Vancouver, ISO, and other styles

44

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

45

Bai, Run Bo, Zong Mei Xu, and Xiu Mei Qiu. "Crack Identification in Plates Using Fractal Dimension Analysis." Applied Mechanics and Materials 405-408 (September 2013): 1051–55. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.1051.

Full text

Abstract:

Focusing on the damage detection using the fractal dimension analysis in plates, this study begins by giving a fractal dimension scanning method for beams. Then extend the algorithm to the plates by degrading the plate mode shape into transverse and longitudinal directions. With the affine transformation, the proposed method overcomes the incapability of identifying damage when using the higher-order mode shapes of the existing fractal dimension methods. Numerical results show that different types of cracks, crack locations and lengths can be detected using this method.

APA, Harvard, Vancouver, ISO, and other styles

46

SUZUKI, Michitaka, Yoshikane MUGURUMA, Mitsuaki HIROTA, and Toshio OSHIMA. "Fractal dimensions of particle projected shapes." Journal of the Society of Powder Technology, Japan 25, no. 5 (1988): 287–91. http://dx.doi.org/10.4164/sptj.25.287.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Suzuki, Michitaka, Yoshikane Muguruma, Mitsuaki Hirota, and Toshio Oshima. "Fractal dimensions of particle projected shapes." Advanced Powder Technology 1, no. 2 (1990): 115–23. http://dx.doi.org/10.1163/156855290x00126.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Taylor, Richard. "Personal reflections on Jackson Pollock's fractal paintings." História, Ciências, Saúde-Manguinhos 13, suppl (2006): 109–23. http://dx.doi.org/10.1590/s0104-59702006000500007.

Full text

Abstract:

The art world changed forever when Jackson Pollock picked up a can and poured paint onto a vast canvas rolled across the floor of his windswept barn. Fifty years on, art theorists recognize his patterns as being a revolutionary approach to aesthetics. A significant step forward in understanding Pollock's aesthetics occurred in 1999 when my scientific analysis showed that his paintings are fractal. Fractals consist of patterns that recur at finer and finer magnifications, building up shapes of immense complexity. Significantly, many natural patterns (for example, lightning, clouds, mountains, a

APA, Harvard, Vancouver, ISO, and other styles

49

Dunnavan, Edwin L., Zhiyuan Jiang, Jerry Y. Harrington, Johannes Verlinde, Kyle Fitch, and Timothy J. Garrett. "The Shape and Density Evolution of Snow Aggregates." Journal of the Atmospheric Sciences 76, no. 12 (2019): 3919–40. http://dx.doi.org/10.1175/jas-d-19-0066.1.

Full text

Abstract:

Abstract Snow aggregates evolve into a variety of observed shapes and densities. Despite this diversity, models and observational studies employ fractal or Euclidean geometric measures that are assumed universal for all aggregates. This work therefore seeks to improve understanding and representation of snow aggregate geometry and its evolution by characterizing distributions of both observed and Monte Carlo–generated aggregates. Two separate datasets of best-fit ellipsoid estimates derived from Multi-Angle Snowflake Camera (MASC) observations suggest the use of a bivariate beta distribution m

APA, Harvard, Vancouver, ISO, and other styles

50

Carlin, Mats. "Measuring the complexity of non-fractal shapes by a fractal method." Pattern Recognition Letters 21, no. 11 (2000): 1013–17. http://dx.doi.org/10.1016/s0167-8655(00)00061-1.

Full text

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!