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Relevant bibliographies by topics / Fractal shapes

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Academic literature on the topic 'Fractal shapes'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Fractal shapes"

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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.

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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

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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.

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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

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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.

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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

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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.

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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

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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.

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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

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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.

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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

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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.

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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

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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.

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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

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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.

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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

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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.

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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

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Dissertations / Theses on the topic "Fractal shapes"

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Neil, Geoffrey. "Shape recognition using fractal geometry." Thesis, University of Nottingham, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319951.

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Almutairi, Khaled S. M. KH. "Employing the Concept of Fractal Shape to Enhance Heat Transfer." Cleveland State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=csu1513093485786172.

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USUI, Shin'ichi, Masayuki TANIMOTO, Toshiaki FUJII, Tadahiko KIMOTO, and Hiroshi OHYAMA. "Fractal Image Coding Based on Classified Range Regions." Institute of Electronics, Information and Communication Engineers, 1998. http://hdl.handle.net/2237/14996.

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Heinson, William Raymond. "Simulation studies on shape and growth kinetics for fractal aggregates in aerosol and colloidal systems." Diss., Kansas State University, 2015. http://hdl.handle.net/2097/19714.

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Doctor of Philosophy<br>Physics<br>Amitabha Chakrabarti<br>The aim of this work is to explore, using computational techniques that simulate the motion and subsequent aggregation of particles in aerosol and colloidal systems, many common but not well studied systems that form fractal clusters. Primarily the focus is on cluster shape and growth kinetics. The structure of clusters made under diffusion limited cluster-cluster aggregation (DLCA) is looked at. More specifically, the shape anisotropy is found to have an inverse relationship on the scaling prefactor "k"_"0" and have no effect on the f

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Backes, Andre Ricardo. "Implementação e comparação de métodos de estimativa da dimensão fractal e sua aplicação à análise e processamento de imagens." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-06092006-152806/.

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A Dimensão Fractal pode ser utilizada para medir algumas características ligadas a complexidade da imagem, permitindo seu uso em análise de formas e texturas e reconhecimento de padrões. Neste trabalho é apresentado um estudo comparativo entre alguns dos principais métodos de estimativa da Dimensão Fractal. Foi realizada uma análise experimental e um estudo de casos para cada uma das técnicas, levando em consideração aspectos de implementação, precisão, variação de resultados segundo ajuste de parâmetros e tolerância a ruídos. Neste trabalho também foi desenvolvido um estudo sobre a Dimensão F

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Lottin, Delphine. "Dimensions fractales, morphologie et caractéristiques dimensionnelles 2D et 3D d'agrégats de nanoparticules de suie aéronautique : Etude par microscopie électronique en transmission et tomographie électronique." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4012/document.

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Les agrégats de suie émis par les processus de combustion dans les turbines aéronautiques contribuent à modifier le bilan radiatif de l'atmosphère et la qualité de l'air. La connaissance de leurs caractéristiques physiques et chimiques est indispensable pour évaluer leur rôle dans les processus physico-chimiques atmosphériques et leur impact sur l'environnement et la santé publique. Dans ce contexte, notre étude vise à déterminer la taille et la morphologie d'agrégats de suie aéronautique à partir de mesures expérimentales menées en microscopie électronique en transmission (MET) et en tomograp

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Frisch, Adam Arthur. "Development, test and application of a new method of particle shape analyses based on the concept of the fractal dimension." W&M ScholarWorks, 1988. https://scholarworks.wm.edu/etd/1539616650.

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Shape analysis methods based on the concept of the fractal dimension are emerging as a new method of quantifying complex particle shapes. The concept of the fractal dimension stems from the approximately linear relationship between the logarithm of the particle perimeter and the logarithm of the step length or unit of measure. as step length is shortened, the resulting particle perimeter is lengthened. The fractal dimension (D) is defined as 1 {dollar}-{dollar} b, where b is the slope of the log/log plot of perimeter against step length. Using two dimensional projected particle outlines measur

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Kharbachi, Chams. "Etude de la croissance électrochimique de dépôts ramifiés." Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30244.

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L'étude porte sur la croissance de branches métalliques ramifiées par électrolyse en mode galvanostatique, d'une solution aqueuse de sel métallique, stagnante, à l'intérieur d'une cellule de type Hele-Shaw. En l'absence d'électrolyte support, la contrainte d'électroneutralité pousse le dépôt à croitre, par des événements de nucléation/croissance successifs, sous forme de branches ramifiées constituées de nanocristaux. Le principal objectif consiste à comprendre et à élucider les mécanismes de formation des branches ramifiées électrocristallisées, ainsi que leur morphologie à l'échelle macrosco

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Neiva, Hugo Miguel Soares de Azevedo. "La Pedrera, Madrid." Master's thesis, Universidade de Lisboa, Faculdade de Arquitetura, 2019. http://hdl.handle.net/10400.5/18424.

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Dissertação de Mestrado Integrado em Arquitetura, com a especialização em Arquitetura apresentada na Faculdade de Arquitetura da Universidade de Lisboa para obtenção do grau de Mestre.<br>Madrid, tal como outras grandes cidades, não foi pensada e gerada como um todo. Pelo contrário, ela resulta de um conjunto de diferentes contextos e tecidos urbanos, a partir dos quais, se originam espaços de transição entre eles, e que, frequentemente, se reflectem em espaços fragmentados, com piores acessibilidades e descaracterizados, portanto, incapazes de gerar espaço urbano de qualidade e referência

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Backes, André Ricardo. "Estudos de métodos de análise de complexidade em imagens." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-02062010-112607/.

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A complexidade é uma característica de grande importância em processos de reconhecimento de padrões, especialmente naqueles que envolvem imagens biológicas. Este trabalho tem como objetivo estudar métodos que realizam a análise de imagens por meio da análise de sua complexidade. Os métodos a serem estudados foram selecionados com base na similaridade de seus algoritmos e metodologia: dimensão fractal, Caminhada Determinística do Turista e Redes Complexas. Estes métodos permitem realizar a análise e segmentação de formas ou texturas contidas em uma imagem com base na sua variação de complexidad

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Books on the topic "Fractal shapes"

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Stoyan, Dietrich. Fractals, random shapes, and point fields: Methods of geometrical statistics. Wiley, 1994.

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Fisher, Allen. Brixton fractals: Gravity as a consequence of shape. Aloes Books, 1985.

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J, Crilly A., Earnshaw Rae A. 1944-, and Jones H, eds. Applications of fractals and chaos: The shape of things. Springer-Verlag, 1993.

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Ann, David. Fractal Shapes Vividly Displaying the Structure of Nature. General Onologic Soft Corp., 2024.

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Todd, Angel. 100 Geometric Shapes and Patterns Adult Coloring Book: Stress Relief Mindfulness Art Activity Fractal Design Craft Relax Simple Fun Calming Create Mandala Magic Drawing Beautiful Symmetry Game Girls Action Adventure Universe Kid Logic Summer Therapy Happy. Independently Published, 2021.

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(Editor), H. Jones, A. J. Crilly (Editor), and Rae A. Earnshaw (Editor), eds. Applications of Fractals & Chaos: The Shape of Things. Not Avail, 1993.

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Crilly, A. J., and R. A. Earnshaw. Applications of Fractals and Chaos: The Shape of Things. Springer, 1993.

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Crilly, A. J., Rae Earnshaw, and Huw Jones. Applications of Fractals and Chaos: The Shape of Things. Springer London, Limited, 2013.

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Crilly, A. J., Rae Earnshaw, and Huw Jones. Applications of Fractals and Chaos: The Shape of Things. Springer Berlin / Heidelberg, 2014.

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Laney, Culbert B. Particle Dynamics with Aggregation and Fragmentation. Oxford University PressOxford, 2025. https://doi.org/10.1093/9780198920687.001.0001.

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Abstract This book concerns particle dynamics, where the term “particle” covers a wide range of shapes and sizes, from atoms to asteroids. While this book considers particles with fixed sizes, the main focus is on particles that grow and shrink over time, due to random or chaotic processes or events, such as inelastic or partially elastic collisions. Prior books on this subject typically focus on just one or a few applications in aerosol science, astrophysics, polymer science, and so forth. In this specialized literature, particle growth is referred to by terms such as aggregation, agglomerati

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Book chapters on the topic "Fractal shapes"

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Skarbek, Władysław, Krystian Ignasiak, and Miloud Ghuwar. "Fractal representation of planar shapes." In Discrete Geometry for Computer Imagery. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-62005-2_7.

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Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. "Irregular Shapes: Randomness in Fractal Constructions." In Chaos and Fractals. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-4740-9_10.

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Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. "Irregular Shapes: Randomness in Fractal Constructions." In Chaos and Fractals. Springer New York, 2004. http://dx.doi.org/10.1007/0-387-21823-8_10.

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Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. "Irregular Shapes: Randomness in Fractal Constructions." In Fractals for the Classroom. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-2172-0_7.

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Backes, André Ricardo, Danilo Medeiros Eler, Rosane Minghim, and Odemir Martinez Bruno. "Characterizing 3D Shapes Using Fractal Dimension." In Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16687-7_7.

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Mayatskaya, Irina, Aleksandr Ishchenko, Eduard Yanukyan, Polina Ivanova, and Svetlana Yazyeva. "Bionic and Fractal Shapes of Skyscrapers." In Lecture Notes in Civil Engineering. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-82938-3_48.

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Thollot, J., C. E. Zair, E. Tosan, and D. Vandorpe. "Modeling fractal shapes using generalisations of IFS techniques." In Fractals in Engineering. Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0995-2_6.

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Liu, Shu-Tang, Yu-Pin Wang, Zhi-Min Bi, and Yin Wang. "Mesoscale Eddies: Disk and Columnar Shapes." In Mathematical Principle and Fractal Analysis of Mesoscale Eddy. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-1839-0_8.

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Nonnenmacher, T. F. "Fractal Shapes of Cell Membranes and Pattern Formation by Dichotomous Branching Processes." In Thermodynamics and Pattern Formation in Biology, edited by Ingolf Lamprecht and A. I. Zotin. De Gruyter, 1988. http://dx.doi.org/10.1515/9783110848403-019.

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Chagroune, L., G. Maurice, V. A. Thomas, Ph Pigeat, and B. Weber. "Relations Between Fractal Models of Some Oxide Surface Shapes and Their Optical Properties." In Thermodynamic Modeling and Materials Data Engineering. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-72207-3_39.

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Conference papers on the topic "Fractal shapes"

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Neskorodov, Stanislav E., Denis P. Kondratyev, Grigory K. Uskov, and Artyom Yu Bolgov. "Analysis of Planar Fractal Radiators of Different Shapes." In 2024 IEEE 9th All-Russian Microwave Conference (RMC). IEEE, 2024. https://doi.org/10.1109/rmc62880.2024.10846841.

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Bindai, Sayani, Sapana Ranwa, and Rowdra Ghatak. "Comparing the Absorption Characteristics of Different Fractal Shapes as Unit Cells for THz Metasurface." In 2024 IEEE International Conference on Communication, Computing and Signal Processing (IICCCS). IEEE, 2024. http://dx.doi.org/10.1109/iicccs61609.2024.10763837.

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Yaziz, Nur Syahirah Mohd, Mohamad Kamal A. Rahim, Farid Zubir, Noor Asmawati Samsuri, Nabilah Ripin, and Taufiqqurrachman Taufiqqurrachman. "Reflective Metasurface on Different Position of Fractal Koch Shape." In 2024 International Symposium on Antennas and Propagation (ISAP). IEEE, 2024. https://doi.org/10.1109/isap62502.2024.10846118.

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Gdawiec, Krzysztof J. "Fractal recognition of shapes." In IEEE EUROCON 2009 (EUROCON). IEEE, 2009. http://dx.doi.org/10.1109/eurcon.2009.5167655.

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Kotarski, Wieslaw, and Agnieszka Lisowska. "Fractal Rendering of 3D Shapes." In IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics. IEEE, 2006. http://dx.doi.org/10.1109/iecon.2006.347289.

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Vieira Ferreira, Gustavo, Weliton Dal Pizzol Maria, and Adriano Rodrigues de Melo. "Introdução à Geometria Fractal no Ensino Médio Técnico: Uma Abordagem com Programação Python." In Computer on the Beach. Universidade do Vale do Itajaí, 2021. http://dx.doi.org/10.14210/cotb.v12.p543-546.

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This work is inserted in the context of technical high school andit aimed to analyze the integration between the branches of FractalGeometry, Analytical Geometry and Computer Programming.For this purpose, we carried out a bibliographic search about whatcharacterizes and distinguishes Fractal Geometry from EuclideanGeometry, we also seek in our readings to list the most famousfractals. Then, we developed (in python language) several fractalgeneration programs. It was possible to work with amazing andeasily programmable fractal shapes, such as the Cantor Set, theHilbert Curve and Sierpinski Tria

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Pickover, Clifford A. "The Fractal Simulation Of Biological Shapes." In Biostereometrics '88: Fifth Intl Mtg, edited by Juerg U. Baumann and Robin E. Herron. SPIE, 1989. http://dx.doi.org/10.1117/12.950472.

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Sayidmarie, Khalil H., and Yasser A. Fadhel. "UWB fractal monopoles of rectangular and triangular shapes." In 2011 IEEE 4th International Symposium on Microwave, Antenna, Propagation, and EMC Technologies for Wireless Communications (MAPE). IEEE, 2011. http://dx.doi.org/10.1109/mape.2011.6156214.

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Bhomia, Yogesh, Ashvini Chaturvedi, and Yogesh Kumar sharma. "Microstrip patch antenna combining crown and Sierpinski fractal-shapes." In the International Conference. ACM Press, 2012. http://dx.doi.org/10.1145/2345396.2345590.

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Shirazi, Mahmoud, and Xun Gong. "Singly-polarized reconfigurable slot-ring antenna/array with fractal shapes." In 2016 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. IEEE, 2016. http://dx.doi.org/10.1109/aps.2016.7696130.

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Reports on the topic "Fractal shapes"

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Rao, C. R., and S. R. Kumara. Shape and Image Analysis using Neural Networks Fractals and Wavelets. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada392772.

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