Relevant bibliographies by topics / Linear fractals

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Linear fractals'

Author: Grafiati
Published: 5 June 2025
Last updated: 11 July 2025

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Journal articles on the topic "Linear fractals"

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Maryenko, N. І., and O. Yu Stepanenko. "Fractal analysis of anatomical structures linear contours: modified Caliper method vs Box counting method." Reports of Morphology 28, no. 1 (2022): 17–26. http://dx.doi.org/10.31393/morphology-journal-2022-28(1)-03.

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Fractal analysis estimates the metric dimension and complexity of the spatial configuration of different anatomical structures. This allows the use of this mathematical method for morphometry in morphology and clinical medicine. Two methods of fractal analysis are most often used for fractal analysis of linear fractal objects: the Box counting method (Grid method) and the Caliper method (Richardson’s method, Perimeter stepping method, Ruler method, Divider dimension, Compass dimension, Yard stick method). The aim of the research is a comparative analysis of two methods of fractal analysis – Box counting method and author's modification of Caliper method for fractal analysis of linear contours of anatomical structures. A fractal analysis of three linear fractals was performed: an artificial fractal – a Koch snowflake and two natural fractals – the outer contours of the pial surface of the human cerebellar vermis cortex and the cortex of the cerebral hemispheres. Fractal analysis was performed using the Box counting method and the author's modification of the Caliper method. The values of the fractal dimension of the artificial linear fractal (Koch snowflakes) obtained by the Caliper method coincide with the true value of the fractal dimension of this fractal, but the values of the fractal dimension obtained by the Box counting method do not match the true value of the fractal dimension. Therefore, fractal analysis of linear fractals using the Caliper method allows you to get more accurate results than the Box counting method. The values of the fractal dimension of artificial and natural fractals, calculated using the Box counting method, decrease with increasing image size and resolution; when using the Caliper method, fractal dimension values do not depend on these image parameters. The values of the fractal dimension of linear fractals, calculated using the Box counting method, increase with increasing width of the linear contour; the values calculated using the Caliper method do not depend on the contour line width. Thus, for the fractal analysis of linear fractals, preference should be given to the Caliper method and its modifications.
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Pulinchery, Prasanth, Nishanth Pothyiodath, and Udayanandan Kandoth Murkoth. "Chaos to fractals." Momentum: Physics Education Journal 7, no. 1 (2023): 17–32. http://dx.doi.org/10.21067/mpej.v7i1.7502.

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In undergraduate classrooms, while teaching chaos and fractals, it is taught as if there is no relation between these two. By using some non linear oscillators we demonstrate that there is a connection between chaos and fractals. By plotting the phase space diagrams of four nonlinear oscillators and using box counting method of finding the fractal dimension we established the chaotic nature of the nonlinear oscillators. The awareness that all chaotic systems are good fractals will add more insights to the concept of chaotic systems.
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Logunov, Mikhail, Vladimir Neverov, Bari Mamin, Denis Skvortsov, and Roman Sidorov. "Study of Nanoscale Inhomogeneities in Silicon Carbide Crystals via Small-Angle X-Ray Scattering." Materials Science Forum 858 (May 2016): 349–52. http://dx.doi.org/10.4028/www.scientific.net/msf.858.349.

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The structure of 4H-SiC and 6H-SiC monocrystals’ nanoscale defects was studied by the small-angle X-ray scattering (SAXS) method. Analysis of dispersion indicatrices has shown the presence of inhomogeneities in the form of linear fractals in silicon carbide crystals of 6H and 4H polytypes, mass fractals in 6H polytype and inhomogeneities partition’s fractal surface in 4H polytype.
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SHALAEV, VLADIMIR, V. A. MARKEL, V. P. SAFONOV, and R. BOTET. "RESONANT OPTICS OF FRACTALS." Fractals 02, no. 02 (1994): 201–9. http://dx.doi.org/10.1142/s0218348x94000193.

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Fractal objects can sustain strongly localized optical modes with high quality-factor. Intense local fields associated with the dipolar eigenmodes in fractals ultimately result in significant enhancement of a number of optical effects. In particular, such basic optical processes as Rayleigh and Raman scattering, degenerate four-wave mixing and harmonic generation, two-photon absorption and non-linear photoemission can be enhanced by several orders of magnitude in small-particle fractal composites and self-affine films.
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Walsh, James A. "Fractals in Linear Algebra." College Mathematics Journal 27, no. 4 (1996): 298. http://dx.doi.org/10.2307/2687242.

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Walsh, James A. "Fractals in Linear Algebra." College Mathematics Journal 27, no. 4 (1996): 298–304. http://dx.doi.org/10.1080/07468342.1996.11973799.

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TATOM, FRANK B. "THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS." Fractals 03, no. 01 (1995): 217–29. http://dx.doi.org/10.1142/s0218348x95000175.

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The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation. Emphasis is placed on the proper application of fractional calculus to the function of the random fractal, as opposed to the trail. For fractional Brownian motion, the basic relations between the spectral decay exponent, Hurst exponent, fractal dimension of the function and the trail, and the order of the fractional integro-differentiation are developed. Based on an understanding of fractional calculus applied to random fractal functions, consideration is given to an analogous application to deterministic or nonrandom fractals. The concept of expressing each coordinate of a deterministic fractal curve as a “pseudo-time” series is investigated. Fractional integro-differentiation of such series is numerically carried out for the case of quadric Koch curves. The resulting time series produces self-similar patterns with fractal dimensions which are linear functions of the order of the fractional integro-differentiation. These curves are assigned the name, fractional Koch curves. The general conclusion is reached that fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates which can be expressed as functions of one independent variable, which is typically time (or pseudo-time).
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Anderson, AN, and AB Mcbratney. "Soil aggregates as mass fractals." Soil Research 33, no. 5 (1995): 757. http://dx.doi.org/10.1071/sr9950757.

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Soil aggregates have a fractal mass. That is, they are porous and, as they are studied in greater detail, more pores may be observed. Mass fractals have scale-dependent bulk density. Larger objects, or soil aggregates, have a smaller bulk density. Bulk density in soil studies is sometimes assumed to be constant. If this was the case, soil aggregates would not be mass fractals, and their porosity would not change with scale. The fact that soil aggregates are mass fractals places restrictions on the estimation of the fragmentation fractal dimension (Df) of soil. The mass fractal dimension of soil (Dm) may be calculated from bulk density-aggregate size data. Linear and nonlinear methods of estimating Dm were compared and were shown to give similar results. The Dm is shown to influence porosity and the saturated water content. Fractal theory, in particular Dm, has implications for the calculation of the pore-size distribution and the moisture characteristic. By equating Campbell's (1985) Version of the Brooks-Corey water retention function, � Proportional �(-1 / b)and an equivalent form to the Brooks-Corey relation given by Crawford (1994), � Proportional �(Dm - d) it is suggested that D-m = d - 1/b, where d is the embedding dimension.
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VOLTA, ANTONIO, MIRCEA GALICEANU, AUREL JURJIU, TOMMASO GALLO, and LUCIANO GUALANDRI. "DYNAMICS ON MULTILAYERED HYPERBRANCHED FRACTALS THROUGH CONTINUOUS TIME RANDOM WALKS." Modern Physics Letters B 26, no. 09 (2012): 1250055. http://dx.doi.org/10.1142/s0217984912500558.

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We introduce a new method to generate three-dimensional structures, with mixed topologies. We focus on Multilayered Regular Hyperbranched Fractals (MRHF), three-dimensional networks constructed as a set of identical generalized Vicsek fractals, known as Regular Hyperbranched Fractals (RHF), layered on top of each other. Every node of any layer is directly connected only to copies of itself from nearest-neighbor layers. We found out that also for MRHF the eigenvalue spectrum of the connectivity matrix is determined through a semi-analytical method, which gives the opportunity to analyze very large structures. This fact allows us to study in detail the crossover effects of two basic topologies: linear, corresponding to the way we connect the layers and fractal due to the layers' topology. From the wealth of applications which depends on the eigenvalue spectrum we choose the return-to-the-origin probability. The results show the expected short-time and long-time behaviors. In the intermediate time domain we obtained two different power-law exponents: the first one is given by the combination linear-RHF, while the second one is peculiar either of a single RHF or of a single linear chain.
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Alicia, Garcia-Falgueras. "Temporal Fractals in the Mammalian Hypothalamus and Music." Psychology & Psychological Research International Journal 9, no. 1 (2024): 1–11. http://dx.doi.org/10.23880/pprij-16000394.

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A fractal is a mathematical shape that is infinitely complex, while its pattern repeats endlessly. Regardless of how zoomed in or zoomed out the analysis is achieved, the segment to study looks very similar in every part of the fractal to the whole picture (in 3D fractals) or the whole composition (2D fractals). In mammalian metabolism, some fractals might be happening, since our inner rhythms and circadian cadences are following a natural sequence, grouped and organised. This series of waves and interconnected system enable the whole organism to have regulation and to monitor the biorhythms. Nature is written in fractal language and in its logarithmic or exponential formulas. Similarly also music is having fractals expressions, catenations, logic consecutive structures or waves in anchored oscillations. In this paper we will briefly study some visual linear and temporal fractals (2D) which might happen commonly for some hypothalamic functions and some parameters of music. Nevertheless for an accurate calculation of Hurst exponent many data and empirical records are required and in some cases this number is not achievable from biological samples or musical pieces with an end. However, statistical knowledge would be able to provide keys to subsane this lack. In those cases when it would be possible, finding temporal parameters, calculating the average and mathematical slope definition of the straight line might add more accurately knowledge for some human metabolic responses or anatomical structures in Neuroscience. Additionally musicians´ grandiose brains and how they were able to organised the music might be better acknowledged.
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Dissertations / Theses on the topic "Linear fractals"

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Custodio, Ricardo Felipe. "Análise não-linear no reconhecimento de padrões sonoros : estudo de caso para sons pulmonares." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 1999. http://hdl.handle.net/10183/17974.

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Nas últimas décadas uma considerável parcela das pesquisas nas áreas de Física e Matemática tem sido dedicada ao estudo de fenômenos não lineares. Uma possível explicação para isso foi o rápido desenvolvimento de sistemas computacionais, tanto em nível de hardware quanta em nível de software, algoritmos e técnicas de programação que propiciaram ao homem maiores facilidades no tratamento de sistemas não lineares, o que levou a um maior grau de entendimento de sua complexidade. Geralmente, aos sistemas não lineares esta associada uma geometria irregular, onde comum o aparecimento de regimes caóticos, com um conjunto atrator de órbitas cuja dimensão não é um inteiro positivo, mas sim um número real positivo. Por esta razão, tais atratores, são denominados estranhos e ditos possuírem uma geometria fractal. É possível, através de métodos cuidadosamente desenvolvidos, estimar-se as dimensões associadas à dinâmica de séries temporais. Uma das séries de maior dificuldade de análise através do computador, e de particular interesse na medicina, são as séries de sons pulmonares humanos. Desde quando o estetoscópio foi inventado até os dias de hoje não há uma ferramenta plenamente confiável para a análise destas séries. Recentemente, temos trabalhado com estas séries e verificamos que há uma geometria fractal. Esta tese propõe a utilização da análise não-linear para identificação de padrões sonoros. Além da geometria fractal, a análise por wavelets tem sido utilizada no estudo de sinais complexos, sobretudo naqueles que apresentam estruturas fractais. O conjunto de filtros construído através da translação, expansão ou compressão de uma função wavelet mãe tem uma estrutura auto-similar, mostrando-se particularmente apropriado para a verificação da auto similaridade dos sons. A técnica da estimativa dos expoentes de Lyapunov dependente do tempo, a qual e desenvolvida na tese, tem se mostrado bastante adequada para identificação de padrões sonoros de origem pulmonar.<br>It has been observed that in the last decades, considerable amount of the research in the areas of Physics and Mathematics have been dedicated to the study of nonlinear phenomena. A possible explanation for this fact is the fast development of computational systems occurring in the level of the hardware as in computer languages, algorithms and programming techniques. These developments propitiated to the researchers a broader contact with nonlinear systems, which led to a better understanding of their complexity. In general, for nonlinear systems an irregular geometry is associated, where the appearance of chaotic regimes has an associated attractor set of orbits whose dimension is not a positive integer number, but a real one. Such attractors are called strange and said to possess fractal geometry. It is possible, through carefully developed methods, to estimate the dimension associated to the dynamics of time series. One of the series with high difficulty to be analyzed through a computer and of particular interest in medicine, is the time series generated out of human pulmonary sounds. Since the creation of the stethoscope, there is not yet a fully trustworthy tool for the lung sound analysis. Recently, we have studied these series and verified that they have a fractal geometry nature. The purpose of this thesis is to investigate non-linear analysis as a tool for pattern recognition in lung sounds. In addition to fractal geometry, the wavelet analysis has been used in the study of complex signs, in particular for those presenting a fractal structure. The set of filters constructed through the translation, expansion or compression of a function wavelet mother has an auto-similar structure, being particularly useful for the verification of self similarity of pulmonary sounds. The largest time dependent Lyapunov exponent estimation technique that has been proposed in this thesis has shown a high degree of confidence for the identification of lung sound patterns.
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Huang, Jungang. "Spontaneous optical fractals in linear & nonlinear systems." Thesis, University of Salford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491053.

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This thesis concerns the generation and characterisation of optical fractals. Chapter 1 presents a brief introduction to fractals and fractal dimensions, and then a review of contexts where fractal concepts have arisen in optics. These contexts are classified in terms of whether the fractal-generating mechanisms at work are linear or nonlinear.
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Costa, Otto Augusto de Morais. "Superálgebras de Lie fractais de crescimento linear." reponame:Repositório Institucional da UnB, 2016. http://repositorio.unb.br/handle/10482/23245.

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Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2016.<br>Submitted by Raquel Viana (raquelviana@bce.unb.br) on 2017-04-12T21:52:26Z No. of bitstreams: 1 2016_OttoAugustodeMoraisCosta.pdf: 763428 bytes, checksum: 2ce046a02e4bd46358a4d5d3ee88ba15 (MD5)<br>Approved for entry into archive by Raquel Viana(raquelviana@bce.unb.br) on 2017-04-12T21:53:03Z (GMT) No. of bitstreams: 1 2016_OttoAugustodeMoraisCosta.pdf: 763428 bytes, checksum: 2ce046a02e4bd46358a4d5d3ee88ba15 (MD5)<br>Made available in DSpace on 2017-04-12T21:53:03Z (GMT). No. of bitstreams: 1 2016_OttoAugustodeMoraisCosta.pdf: 763428 bytes, checksum: 2ce046a02e4bd46358a4d5d3ee88ba15 (MD5)<br>Os grupos de Grigorchuk e Gupta-Sidkides empenham um papel fundamental na teoria de grupos moderna, pois são exemplos naturais de grupos periódicos finitamente gerados autos similares. Neste trabalho, construímos exemplos análogos aos grupos referidos no campo das super álgebras de Lie. Em 2006, Petrogradsky construiu exemplos análogos para álgebras de Lie restritas em característica 2.Shestakov e Zelmanov estenderam essa contrução para característica positiva arbitrária, dando um exemplo de algebra de Lie restrita finitamente gerada com p-aplicação nil. Martinez e Zelmanov provaram que, sobre um corpo de característica zero, não é possível construir exemplos de algebras de Lie análogas aos grupos de Grigorchuk. Neste trabalho, mostramos que a extensão desse resultado para super álgebras de Lie em característica zero não é válida. Em qualquer característica, construímos uma superálgebra de Lie R com as seguintes propriedades.R tem uma Z²- graduação apropriada tal que todo elemento homogêneo é ad-nilpotente. Além disso, R tem crescimento linear e sua envoltória associativa tem crescimento quadrático. Para uma característica positiva arbitrária p, construímos também exemplos de álgebras de Lie restritas fractais de crescimento linear cujas envoltórias associativas possuem crescimento quadrático.<br>The Grigorchuk and Gupta-Sidki groups play fundamental role in modern group theory because they are natural examples of self-similar finitely generated periodic groups. In this work we construct their analogue in the world of Lie superalgebras. In 2006, Petrogradsky made an analogous construction for restricted Lie algebras in characteristic 2. Next, Shestakov and Zelmanov extended this construction to an arbitrary positive characteristic, giving an example of finitely generated restricted Lie algebra with a nil p-mapping. Martinez and Zelmanov proved that similar examples do not exist for Lie algebras in characteristic zero. In this work we show that an extension of this result for Lie superalgebras in characteristic zero is not valid. Namely, we construct a Lie superalgebraR with the following properties. We prove thatR has a fine Z²-gradation and it is nil graded. Furthermore, R has linear growth and their associative hulls have quadratic growth. For an arbitrary positive characteristic p, we also construct examples of fractal restricted Lie algebras. These algebras have linear growth and its associative hull has quadratic growth.
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Fraideinberze, Antonio Canabrava. "Effective and unsupervised fractal-based feature selection for very large datasets: removing linear and non-linear attribute correlations." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-17112017-154451/.

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Given a very large dataset of moderate-to-high dimensionality, how to mine useful patterns from it? In such cases, dimensionality reduction is essential to overcome the well-known curse of dimensionality. Although there exist algorithms to reduce the dimensionality of Big Data, unfortunately, they all fail to identify/eliminate non-linear correlations that may occur between the attributes. This MSc work tackles the problem by exploring concepts of the Fractal Theory and massive parallel processing to present Curl-Remover, a novel dimensionality reduction technique for very large datasets. Our contributions are: (a) Curl-Remover eliminates linear and non-linear attribute correlations as well as irrelevant attributes; (b) it is unsupervised and suits for analytical tasks in general not only classification; (c) it presents linear scale-up on both the data size and the number of machines used; (d) it does not require the user to guess the number of attributes to be removed, and; (e) it preserves the attributes semantics by performing feature selection, not feature extraction. We executed experiments on synthetic and real data spanning up to 1.1 billion points, and report that our proposed Curl-Remover outperformed two PCA-based algorithms from the state-of-the-art, being in average up to 8% more accurate.<br>Dada uma grande base de dados de dimensionalidade moderada a alta, como identificar padrões úteis nos objetos de dados? Nesses casos, a redução de dimensionalidade é essencial para superar um fenômeno conhecido na literatura como a maldição da alta dimensionalidade. Embora existam algoritmos capazes de reduzir a dimensionalidade de conjuntos de dados na escala de Terabytes, infelizmente, todos falham em relação à identificação/eliminação de correlações não lineares entre os atributos. Este trabalho de Mestrado trata o problema explorando conceitos da Teoria de Fractais e processamento paralelo em massa para apresentar Curl-Remover, uma nova técnica de redução de dimensionalidade bem adequada ao pré-processamento de Big Data. Suas principais contribuições são: (a) Curl-Remover elimina correlações lineares e não lineares entre atributos, bem como atributos irrelevantes; (b) não depende de supervisão do usuário e é útil para tarefas analíticas em geral não apenas para a classificação; (c) apresenta escalabilidade linear tanto em relação ao número de objetos de dados quanto ao número de máquinas utilizadas; (d) não requer que o usuário sugira um número de atributos para serem removidos, e; (e) mantêm a semântica dos atributos por ser uma técnica de seleção de atributos, não de extração de atributos. Experimentos foram executados em conjuntos de dados sintéticos e reais contendo até 1,1 bilhões de pontos, e a nova técnica Curl-Remover apresentou desempenho superior comparada a dois algoritmos do estado da arte baseados em PCA, obtendo em média até 8% a mais em acurácia de resultados.
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Vera, Epiphany. "Fractal modelling of residual in linear predictive coding of speech." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0006/MQ41642.pdf.

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Panyella, i. Roses Magí. "Aspectes caòtics i fractals en el comportament organitzacional: Caos, organitzacions i management." Doctoral thesis, Universitat de Barcelona, 2002. http://hdl.handle.net/10803/2661.

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Aquest treball tracta, en primer lloc, sobre les possibilitats d'aplicació de la teoria del caos a l'estudi de les organitzacions i el canvi organitzatiu, a la seva comprensió i gestió des d'una nova perspectiva. <br/><br/>La part teòrica és una introducció als principals conceptes implicats en el què es coneix com a teoria de la complexitat, centrant-se principalment en el concepte de caos determinista i el d'autoorganització sense oblidar, però, la seva relació amb altres conceptes importants com els de règim dinàmic, no linealitat i fractals i la seva aplicacio a les ciències socials i a la teoria de l'organització en particular.<br/><br/>La part empírica és el resultat d'un estudi fet en organitzacions reals utilitzant metodologia quantitativa i qualitativa. Quantitativament prenent la grandària com a variable important en l'evolució de les organitzacions i, aplicant un model de creixement no lineal (equació de Verhulst) clàssic en el tractament de dades des de la teoria del caos. Qualitativament, utilitzant l'entrevista per a la identificació d'indicadors en organitzacions immerses en règims dinàmics diferents pel que fa a la variable grandària. Les estratègies de recerca utilitzades són doncs, l'estudi i comparació de casos i la "Grounded Theory Methodology". <br/><br/>En segon lloc, aquest treball pretén ajudar a construir què signifiquen conceptes com caos, autoorganització, fractals, atractors... quan els apliquem a la vida i evolució de les organitzacions, mitjançant la interrelació entre teoria i resultats obtinguts. Hi ha doncs, un intent de desenvolupament teòric, en un marc paradigmàtic emergent en la teoria de l'organització.
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Machado, Bruno Brandoli. "Texture analysis using complex system models: fractal dimension, swarm systems and non-linear diffusion." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-24112016-113253/.

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Texture is one of the primary visual attributes used to describe patterns found in nature. Several texture analysis methods have been used as powerful tools for real applications involving analysis and computer vision. However, existing methods do not successfully discriminate the complexity of texture patterns. Such methods disregard the possibility of describing image structures by means of measures such as the fractal dimension. Fractality-based measures allow a non-integer geometric interpretation with applications in areas such as mathematics, physics, and biology. With this gap in mind, the central hypothesis of this thesis is that textures can be described as irregular fractal surfaces due to their complex geometry; such geometry can be exploited for image analysis and computer vision. By exploring such possibilities, pushing the limits of the state-of-the-art, this thesis starts with an analysis of texture features achieved by means of agents on image surfaces. To do so, we used the Bouligand-Minkowski fractal dimension, swarm-system Artificial Crawlers, and non-linear diffusion of Perona-Malik, techniques that led to methodologies with efficacy and efficiency comparable to the state-of-the-art. Our first method combines fractal dimension with random walks on the surface of images. In a second approach, non-linear diffusion is used to represent texture images at different scales, which are described via their fractal dimension for image classification purposes. In a third proposal, we employ fractal dimension concepts over multiple scales derived from the same image for a richer texture description. One of the purposes is the automatic detection of diseases in soybean leaves. Finally, texture characteristics were exploited in a method based on complex networks used to analyze the agglomeration of particles in nanotechnology images. The results achieved in the four methodologies described in this thesis demonstrated the potential of using texture features in tasks of classification and pattern recognition. The contributions of this work shall support significant advances in materials engineering, computer vision, and agriculture.<br>A textura é um dos principais atributos visuais para a descrição de padrões encontrados na natureza. Diversos métodos de análise de textura têm sido usados como uma poderosa ferramenta para aplicações reais que envolvem análise de imagens e visão computacional. Entretanto, os métodos existentes não conseguem discriminar com sucesso a complexidade dos padrões de textura. Tais métodos desconsideram a possibilidade de se descrever estruturas de imagens por meio de medidas como a dimensão fractal. Medidas baseadas em fractalidade permitem uma interpretação geométrica não-inteira que possui aplicações encontradas em áreas como matemática, física, e biologia. Sobre esta lacuna metodológica, a hipótese central desta tese é que texturas presentes na natureza podem ser medidas como superfícies fractais irregulares devido à sua geometria complexa, o que pode ser explorado para fins de análise de imagens e visão computacional. Para superar tais limitações, avançando o estado da arte, esta tese se inicia com uma análise das características de texturas baseada em caminhadas aleatórias de agentes sobre superfícies de imagens. Esta primeira análise leva a um método que combina dimensão fractal com caminhadas de agentes sobre a superfície de imagens. Em uma segunda abordagem, usa-se a difusão não-linear para representar imagens de texturas em diferentes escalas, as quais são descritas via dimensão fractal para fins de classificação de imagens. Em uma terceira proposta, emprega-se a dimensão fractal sobre múltiplas escalas derivadas de uma mesma imagem com o propósito de se realizar a descrição multi-escala de texturas. Um dos propósitos específicos foi a detecção automática de doenças em folhas de soja. Por último, as características de textura foram exploradas segundo uma metodologia baseada em redes complexas para análise de aglomeração de partículas em imagens de nanotecnologia. Os resultados alcançados nesta tese demonstraram o potencial do uso de características de textura. Para tanto foram usadas técnicas de dimensão fractal de Bouligand-Minkowski, multiagentes Artificial Crawlerse difusão não-linear de Perona-Malik, os quais alcançaram eficácia e eficiência comparáveis ao do estado da arte. As contribuições obtidas devem suportar avanços significativos nas áreas de engenharia de materiais, visão computacional, e agricultura.
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Rabay, Yara Silvia Freire. "Estudo e aplicações da geometria fractal." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7651.

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Submitted by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-27T11:58:14Z No. of bitstreams: 1 arquivototal.pdf: 8972192 bytes, checksum: e0a82ad433e62b83d048d78778d60dd2 (MD5)<br>Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-11-30T10:51:37Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 8972192 bytes, checksum: e0a82ad433e62b83d048d78778d60dd2 (MD5)<br>Made available in DSpace on 2015-11-30T10:51:37Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 8972192 bytes, checksum: e0a82ad433e62b83d048d78778d60dd2 (MD5) Previous issue date: 2013-04-12<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>Here we present a research about fractals, its history, mathematical concepts and applications. Some constructions were developed using some basic concepts of the Theory of Numbers, Trigonometry and Linear Algebra that can be applied in High School. We presented some activities that can be applied in High School’s classes in order to develop mathematical concepts such as geometric transformations, Geometry, Trigonometry, Logarithm, notions of limit among other topics. Keywords: Fractal Geometry, Geometric Transformation, Logarithm, Pascal Triangle, Arrays, Linear Algebra, High School.<br>Este trabalho apresenta uma pesquisa sobre os fractais, sua história, conceitos matemáticos utilizados e aplicações. Foram desenvolvidas algumas construções de fractais utilizando-se alguns conceitos básicos de Teoria dos Números, Trigonometria e Álgebra Linear que podem ser explorados no Ensino Médio. Foram apresentadas algumas atividades que podem ser aplicadas em sala de aula do Ensino Médio no desenvolvimento de conceitos matemáticos como Progressão Geométrica, Geometria, Trigonometria, Logaritmo e noções de limite entre outros temas.
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Sant'Ana, Antonio Carlos [UNESP]. "Aplicações médicas das abordagens complexas não lineares: a geometria fractal do EEG." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/131883.

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Made available in DSpace on 2015-12-10T14:22:23Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-01-03. Added 1 bitstream(s) on 2015-12-10T14:28:29Z : No. of bitstreams: 1 000854378.pdf: 6674616 bytes, checksum: d5106f3df91d25255a99661658612b89 (MD5)<br>O uso de técnicas não lineares (sistemas complexos, geometria fractal e física quântica), com enfoques mais amparados pelos princípios do caos, é uma tendência crescente no estudo das ciências naturais, e estão sendo progressivamente apresentadas como opções válidas às suas correspondentes medidas em sistemas lineares (estruturas simples, geometria euclidiana e física clássica newtoniana), com seus enfoques mais cartesianos. Neste sentido, a neurobiologia e a acupuntura podem ajudar a lançar alguma luz nesta busca. Para se avaliar o alcance do uso de técnicas não lineares - mais especificamente a dimensão fractal - foi realizado estudo piloto experimental em humanos para avaliar a sensibilidade do eletroencefalograma na identificação de alterações provocadas por pontos auriculares de acupuntura, conforme critérios clínicos, neurofisiológicos e de geometria fractal. Pacientes de ambos os sexos, tendo cefaléia como queixa comum, mas não exclusiva, foram submetidos a exames eletroencefalográficos, antes e após a estimulação de pontos de acupuntura auricular, ou após ciclos de tratamento ambulatorial por acupuntura auricular e sistêmica. As dimensões fractais pelo 'método da contagem de caixas', foram obtidas com o auxílio do sofware ImageJ, a partir de imagens tratadas dos traçados digitalizados do eletroencefalograma, e os resultados apresentados como estudos de caso. Mediante análise das variações das dimensões fractais efetuada por estudo descritivo e quantitativo, foram observados os comportamentos evolutivos da condição clínica ou sintomática do paciente, e sua relação com os conceitos de desenvolvimento caótico dos sistemas complexos dinâmicos e adaptativos<br>The use of nonlinear techniques (complex systems, fractal geometry and quantum physics), with approaches more related with the principles of chaos theory, is a growing tendency in the study of the natural sciences, and are being progressively presented as valid options to their correspondent measures in linear systems (simple structures, Euclidean geometry and newtonian classical physics), with their more Cartesian approaches. In this sense, neurobiology and acupuncture may help to shed some light upon this search. Aiming to evaluate the reach of the use of nonlinear techniques - more specifically the fractal dimension - a pilot experimental essay was taken in human beings in order to evaluate the sensibility of eletroencefalography in the identification of alterations resulting from the stimulation of auricular acupuncture points, according to clinical, neurophysiologic and fractal geometry criteria. Both male and female patients, having headache as a common but not exclusive complaint, were subject to eletroencefalographic examinations, before and after the stimulation of auricular acupuncture points, or after cycles of both auricular and systemic acupuncture follow up in an outpatient basis. The fractal dimensions calculated by the 'box counting method' were obtained with the aid of ImageJ software, using digitalized images from the eletroencefalographic examinations, and the results are presented as case reports. By analysing the variations in the fractal dimensions both by descriptive and quantitative approaches, observations were made on the evolutive behaviours either from the clinical or from the symptomatic condition of the patient, and their relationship with the concepts of chaotic development of the complex dynamic adaptative systems
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Sant'Ana, Antonio Carlos. "Aplicações médicas das abordagens complexas não lineares : a geometria fractal do EEG /." Botucatu, 2015. http://hdl.handle.net/11449/131883.

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Orientador: Karina Pavão Patrício<br>Banca: Moacir Fernandes de Godoy<br>Banca: Niura Aparecida Padula<br>Resumo: O uso de técnicas não lineares (sistemas complexos, geometria fractal e física quântica), com enfoques mais amparados pelos princípios do caos, é uma tendência crescente no estudo das ciências naturais, e estão sendo progressivamente apresentadas como opções válidas às suas correspondentes medidas em sistemas lineares (estruturas simples, geometria euclidiana e física clássica newtoniana), com seus enfoques mais cartesianos. Neste sentido, a neurobiologia e a acupuntura podem ajudar a lançar alguma luz nesta busca. Para se avaliar o alcance do uso de técnicas não lineares - mais especificamente a dimensão fractal - foi realizado estudo piloto experimental em humanos para avaliar a sensibilidade do eletroencefalograma na identificação de alterações provocadas por pontos auriculares de acupuntura, conforme critérios clínicos, neurofisiológicos e de geometria fractal. Pacientes de ambos os sexos, tendo cefaléia como queixa comum, mas não exclusiva, foram submetidos a exames eletroencefalográficos, antes e após a estimulação de pontos de acupuntura auricular, ou após ciclos de tratamento ambulatorial por acupuntura auricular e sistêmica. As dimensões fractais pelo 'método da contagem de caixas', foram obtidas com o auxílio do sofware ImageJ, a partir de imagens tratadas dos traçados digitalizados do eletroencefalograma, e os resultados apresentados como estudos de caso. Mediante análise das variações das dimensões fractais efetuada por estudo descritivo e quantitativo, foram observados os comportamentos evolutivos da condição clínica ou sintomática do paciente, e sua relação com os conceitos de desenvolvimento caótico dos sistemas complexos dinâmicos e adaptativos<br>Abstract: The use of nonlinear techniques (complex systems, fractal geometry and quantum physics), with approaches more related with the principles of chaos theory, is a growing tendency in the study of the natural sciences, and are being progressively presented as valid options to their correspondent measures in linear systems (simple structures, Euclidean geometry and newtonian classical physics), with their more Cartesian approaches. In this sense, neurobiology and acupuncture may help to shed some light upon this search. Aiming to evaluate the reach of the use of nonlinear techniques - more specifically the fractal dimension - a pilot experimental essay was taken in human beings in order to evaluate the sensibility of eletroencefalography in the identification of alterations resulting from the stimulation of auricular acupuncture points, according to clinical, neurophysiologic and fractal geometry criteria. Both male and female patients, having headache as a common but not exclusive complaint, were subject to eletroencefalographic examinations, before and after the stimulation of auricular acupuncture points, or after cycles of both auricular and systemic acupuncture follow up in an outpatient basis. The fractal dimensions calculated by the 'box counting method' were obtained with the aid of ImageJ software, using digitalized images from the eletroencefalographic examinations, and the results are presented as case reports. By analysing the variations in the fractal dimensions both by descriptive and quantitative approaches, observations were made on the evolutive behaviours either from the clinical or from the symptomatic condition of the patient, and their relationship with the concepts of chaotic development of the complex dynamic adaptative systems<br>Mestre
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Books on the topic "Linear fractals"

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D, Schertzer, and Lovejoy S. 1956-, eds. Non-linear variability in geophysics: Scaling and fractals. Kluwer Academic Publishers, 1991.

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1959-, Castillo Oscar, ed. Modelling, simulation and control of non-linear dynamical systems: An intelligent approach using soft computing and fractal theory. Taylor & Francis, 2002.

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1944-, Morozov Albert D., ed. Invariant sets for Windows. World Scientific, 1999.

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Gaponov-Grekhov, A. V. Nonlinearities in action: Oscillations, chaos, order, fractals. Springer-Verlag, 1992.

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Moon, Francis C. Chaotic vibrations: Anintroduction for applied scientists and engineers. Wiley, 1987.

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Miller, Richard K., and Terri C. Walker. Chaos fractals & non-linear dynamic systems. Future Technology Surveys, 1989.

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Non-Linear Variability in Geophysics: Scaling and Fractals. Springer, 2012.

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(Editor), D. Schertzer, and S. Lovejoy (Editor), eds. Non-Linear Variability in Geophysics: Scaling and Fractals. Springer, 1990.

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Schertzer, D., and S. Lovejoy. Non-Linear Variability in Geophysics: Scaling and Fractals. Springer London, Limited, 2012.

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Schertzer, D., and S. Lovejoy. Non-Linear Variability in Geophysics: Scaling and Fractals. Springer, 2012.

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Book chapters on the topic "Linear fractals"

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Dichter, Mitchal. "Fractals." In Student Solutions Manual for Non Linear Dynamics and Chaos, 3rd ed. CRC Press, 2024. http://dx.doi.org/10.1201/9780429293979-10.

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Malinverno, Alberto. "Testing Linear Models of Sea-Floor Topography." In Fractals in Geophysics. Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-6389-6_8.

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Akhmet, Marat, Mehmet Onur Fen, and Ejaily Milad Alejaily. "Unpredictable Solutions of Hyperbolic Linear Equations." In Dynamics with Chaos and Fractals. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35854-9_6.

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Chatziafratis, A., L. Grafakos, S. Kamvissis, and I. G. Stratis. "Instabilities of Linear Evolution PDEs via the Fokas Method." In Chaos, Fractals and Complexity. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-37404-3_20.

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Jacob-Da Col, Marie-Andrée, and Pierre Tellier. "Quasi-Linear Transformations, Numeration Systems and Fractals." In Discrete Geometry for Computer Imagery. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19867-0_16.

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Mandelbrot, Benoit B. "The map z → λ (z+1/z) and roughening of chaos, from linear to planar (computer-assisted homage to K. Hokusai)." In Fractals and Chaos. Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4017-2_13.

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Meissner, Rolf. "Non-Linear Processes in Earthquake Prediction Research, a Review." In Fractals and Dynamic Systems in Geoscience. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-662-07304-9_12.

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Chen, Joe P., Michael Hinz, and Alexander Teplyaev. "From Non-symmetric Particle Systems to Non-linear PDEs on Fractals." In Stochastic Partial Differential Equations and Related Fields. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74929-7_34.

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Luor, Dah-Chin, and Chiao-Wen Liu. "A Comparison of Linear Fractal Interpolants in Data Fitting Problems." In Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-58641-5_1.

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Rihan, Fathalla A., and Ola Mohamed. "Chebyshev Collocation Method for Pantograph Delay Differential Equations with Linear Functional Arguments." In Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-58641-5_16.

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Conference papers on the topic "Linear fractals"

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Mishra, Jibitesh. "Classification of Linear Fractals through L-System." In 2008 First International Conference on Emerging Trends in Engineering and Technology. IEEE, 2008. http://dx.doi.org/10.1109/icetet.2008.116.

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Hart, John C., and Thomas A. DeFanti. "Efficient antialiased rendering of 3-D linear fractals." In the 18th annual conference. ACM Press, 1991. http://dx.doi.org/10.1145/122718.122728.

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Sibilia, C. "Optical properties of quasiperiodic (fractals) one-dimensional structures." In International school of quantum electronics: Nanoscale linear and nonlinear optics. AIP, 2001. http://dx.doi.org/10.1063/1.1372727.

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De Castro, M. R., B. G. M. Robert, and C. Goeldel. "Experimental chaos and fractals in a linear switched reluctance motor." In 2010 14th International Power Electronics and Motion Control Conference (EPE/PEMC 2010). IEEE, 2010. http://dx.doi.org/10.1109/epepemc.2010.5606648.

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Wang, Li-Ming, and Xiao-Jian Li. "Chaos Synchronization of Coupled Ring and Linear Arrays System Using Adaptive Control." In 2011 Fourth International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2011. http://dx.doi.org/10.1109/iwcfta.2011.70.

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Oertel, Carsten, and Peter Bock. "General Shape Generation by Contouring Fractals and Applying Linear Boundary Regression." In 2007 36th IEEE Applied Imagery Pattern Recognition Workshop (AIPR 2007). IEEE, 2007. http://dx.doi.org/10.1109/aipr.2007.23.

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Kolesnikov, Andrey Vitalievich. "Nonlinear images as art objects." In 6th International Conference “Futurity designing. Digital reality problems”. Keldysh Institute of Applied Mathematics, 2023. http://dx.doi.org/10.20948/future-2023-15.

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Thanks to a powerful calculating tool - a computer, as well as the development of mathematical modeling methods, synergetics for the first time in the history of science began to describe and reproduce the processes of self-organization and development. On this path, magnificent, previously unseen images began to appear - strange attractors, fractals, cellular automata, which to a large extent contributed to the popularity of synergetics in the scientific and philosophical community. The article is devoted to images that arise in models, experiments and computational experiments developed and conducted by the author. Continual cellular automata with non-linear transition rules, cycles, fractal structures and chaos in non-linear mappings that describe social processes give rise to images that make you think, awaken aesthetic sensations and allow you to better understand, visualize how it all (surrounding world, the Universe) was created, organized and works. And this is the function of Science Art.
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Gui, Yongxin, and Zhiming Zhou. "Hausdorff Dimension of a Class of Self-affine Fractals Generated by Linear Fibre Coding." In 2008 9th International Conference for Young Computer Scientists (ICYCS). IEEE, 2008. http://dx.doi.org/10.1109/icycs.2008.196.

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Rocha, Fernando Silveira, Saulo Brivaldo Mendonça da Silva, Vitória Maria de Araujo Oliveira, Emyliana Cristine da Paz de Santana, and Thiago de Salazar e. Fernandes. "CITOGENÉTICA HUMANA – UMA VISÃO FRACTAL." In XXVII Semana de Biomedicina Inovação e Ciência. Editora IME, 2021. http://dx.doi.org/10.51161/9786588884119/18.

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Introdução: Atualmente, existe um esforço crescente da comunidade científica em compreender a organização e funcionamento do genoma (i.e., nucleoma), com base no pressuposto de que a sua forma está relacionada às suas funções, e não com base apenas no sequenciamento linear do DNA(2). Um método atual e promissor é a geometria fractal, conceito do matemático francês Benoît Mandelbrot na década de 1970, que estuda as propriedades e comportamentos de objetos complexos que não seguem uma geometria euclidiana. Formas irregulares não euclidianas foram chamadas de “fractais”, por parecerem com estruturas “fraturadas”, com repetibilidade de padrões de forma, inclusive em diferentes escalas. Os fractais ocorrem por toda a natureza, desde ramificações das árvores à rede vascular e pulmonar, e têm sido aplicados em diferentes campos da biologia, a exemplo da mais recente elucidação da estrutura do glóbulo fractal da cromatina e dos territórios cromossômicos(3). Objetivos: Este resumo tem como objetivo discutir a possibilidade da utilização da dimensão fractal (DF) como método de investigação do dano à cromatina. Métodos: As buscas foram realizadas nas bases de dados do Google Acadêmico e do PubMed. Os artigos científicos foram encontrados por meio dos descritores: “fractal dimension”, “fractal analysis” e “fractal analysis and genetics”. Foram encontrados um total de 266 artigos que usaram a análise fractal, dos quais foram selecionados 4 artigos mais relacionados ao tema. Resultados: Observa-se que o uso dos métodos fractais na citogenética se mostrou capaz de distinguir, por exemplo, mudanças da cromatina quando as células foram irradiadas, evidenciando que danos induzidos radioinduzidos ao DNA já podem ser observados na cromatina interfásica. É possível que mutações radioinduzidas alterem a complexidade topológica física global da cromatina, e isso pode ser mensurável por ferramentas computacionais, como a dimensão fractal. O método também mostra ser de grande aplicabilidade para o diagnóstico e prognóstico de diversos tipos de câncer(3). Conclusões: A análise fractal da cromatina indica ser um promissor biomarcador morfométrico de exposições humanas às radiações ionizantes, radiações não-ionizantes e para o diagnóstico e prognóstico de diversos tipos de câncer, pois se baseia na análise da textura cromatina, como um sinal geral de que houve alterações estruturais na organização fractal do genoma humano. Este método pode vir a ser útil em triagens de pacientes ou de indivíduos expostos às radiações, bem como poderá melhor elucidar o processo de organização da cromatina.
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Altayeb, Mohammad, Paul W. J. Glover, Piroska Lorinczi, and Steve Cuddy. "Fractal Dimension Measurement Using Wireline-Derived Saturation Height Function." In International Petroleum Technology Conference. IPTC, 2024. http://dx.doi.org/10.2523/iptc-24118-ms.

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Abstract Fractal geometry represents a self-similar object or behavior over different scales. Fractals occur in many aspects of nature including reservoir pore geometry. Fractal dimension is a key parameter that represents how complexity changes with scale. This study attempts to measure the fractal dimension using a power law-based saturation height function that is derived from wireline data. The approach involves estimating the saturation height function (SwH) using Cuddy's method with wire-line data. This method plots water bulk volume (BVW) against height above the free water level (H). Major steps to estimate SwH include identification of the free water level, the presence of shale volume and calculating porosity, water resistivity and water saturation. Cuddy's method often reveals that SwH follows a power law behavior, which is expressed linearly when logarithmic scales are used. Consequently, SwH can be estimated by fitting a line to the data and obtaining two parameters a and b representing the intercept and gradient, respectively. The SwH of 13 wells were derived using Cuddy's method and showed acceptable fit to the power-law assumption. The parameter b, which represents the gradient of the best fit line, has been hypothesized to be related to the fractal dimension. Therefore, the estimated SwH may provide a measurement of fractal dimension of the pore geometry. The fractal dimension is related to the pore geometry heterogeneity, where higher fractal dimension implies higher heterogeneity. Fractal dimension applications include heterogeneity evaluation of pore geometry, reservoir modelling and performance simulation.
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