Relevant bibliographies by topics / Variable dimension fractal

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

Academic literature on the topic 'Variable dimension fractal'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Variable dimension fractal"

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Zhihui, Ni, Wu Lichun, Wang Ming-hui, Yi Jing, and Zeng Qiang. "The Fractal Dimension of River Length Based on the Observed Data." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/327297.

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Although the phenomenon that strictly meets the constant dimension fractal form in the nature does not exist, fractal theory provides a new way and means for the study of complex natural phenomena. Therefore, we use some variable dimension fractal analysis methods to study river flow discharge. On the basis of the flood flow corresponding to the waterline length, the river of the overall and partial dimensions are calculated and the relationships between the overall and partial dimensions are discussed. The law of the length in section of Chongqing city of Yangtze River is calibrated by using
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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-dif
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PRASAD, SRIJANANI ANURAG, and G. P. KAPOOR. "FRACTAL DIMENSION OF COALESCENCE HIDDEN-VARIABLE FRACTAL INTERPOLATION SURFACE." Fractals 19, no. 02 (2011): 195–201. http://dx.doi.org/10.1142/s0218348x11005336.

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In the present paper, the bounds on fractal dimension of Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) in ℝ3 on a equispaced mesh are found. These bounds determine the conditions on the free parameters for fractal dimension of the constructed CHFIS to become close to 3. The results derived here are tested on a tsunami wave surface by computing the lower and upper bounds of the fractal dimension of its CHFIS simulation.
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JÄRVENPÄÄ, ESA, MAARIT JÄRVENPÄÄ, ANTTI KÄENMÄKI, HENNA KOIVUSALO, ÖRJAN STENFLO, and VILLE SUOMALA. "Dimensions of random affine code tree fractals." Ergodic Theory and Dynamical Systems 34, no. 3 (2013): 854–75. http://dx.doi.org/10.1017/etds.2012.168.

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AbstractWe study the dimension of code tree fractals, a class of fractals generated by a set of iterated function systems. We first consider deterministic affine code tree fractals, extending to the code tree fractal setting the classical result of Falconer and Solomyak on the Hausdorff dimension of self-affine fractals generated by a single iterated function system. We then calculate the almost sure Hausdorff, packing and box counting dimensions of a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in
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Tunas, I. Gede, Nadjadji Anwar, and Umboro Lasminto. "Fractal Characteristic Analysis of Watershed as Variable of Synthetic Unit Hydrograph Model." Open Civil Engineering Journal 10, no. 1 (2016): 706–18. http://dx.doi.org/10.2174/1874149501610010706.

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Fractal characteristic of watershed is an important parameter which influences the formation of synthetic unit hydrograph. Based on a previous study, hydrology response of watershed expressed in hydrograph form could be well presented by hydrology network characteristic as a form of fractal characteristic of watershed [1]. Fractal characteristic of watershed was stated as fractal dimension which was presented in three parametersi.e.river branch ratio (RB), river length ratio (RL) and watershed river area ratio (RA). The purpose of this research was to analyze fractal characteristic and to veri
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Fan, Youping, Dai Zhang, and Jingjiao Li. "Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture." Advances in Materials Science and Engineering 2018 (November 1, 2018): 1–10. http://dx.doi.org/10.1155/2018/6019269.

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The paper aims to understand how the fractal dimension and growth time of electrical trees change with temperature and moisture. The fractal dimension of final electrical trees was estimated using 2-D box-counting method. Four groups of electrical trees were grown at variable moisture and temperature. The relation between growth time and fractal dimension of electrical trees were summarized. The results indicate the final electrical trees can have similar fractal dimensions via similar tree growth time at different combinations of moisture level and temperature conditions.
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Sinclair, Scott E., Steve McKinney, Robb W. Glenny, Susan L. Bernard, and Michael P. Hlastala. "Exercise alters fractal dimension and spatial correlation of pulmonary blood flow in the horse." Journal of Applied Physiology 88, no. 6 (2000): 2269–78. http://dx.doi.org/10.1152/jappl.2000.88.6.2269.

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We determined the changes in fractal dimensions and spatial correlations of regional pulmonary blood flow with increasing exercise in race horses ( n= 4) by using 15-μm fluorescent microspheres. Fluorescence was measured to quantitate regional blood to 1.3-cm3 samples ( n = 1,621–2,503). Perfusion distributions were characterized with fractal dimensions (a measure of spatial variability) and spatial correlations. On average, the fractal dimension decreased with exercise (trot 1.216 to gallop 1.173; P < 0.05) despite a variable fractal dimension at rest. Spatial correlation of flow to neighb
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Cherny, A. Yu, E. M. Anitas, A. I. Kuklin, M. Balasoiu, and V. A. Osipov. "Scattering from generalized Cantor fractals." Journal of Applied Crystallography 43, no. 4 (2010): 790–97. http://dx.doi.org/10.1107/s0021889810014184.

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A fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set, is considered. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from zero to one in one dimension and from zero to three in three dimensions. The intensity profile of small-angle scattering from the generalized Cantor fractal in three dimensions is calculated. The system is generated by a set of iterative rules, each iteration corresponding to a certain fractal generation. Small-angle scattering is considered from monodisper
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Wen, Hua. "Quantitative Identification of Reservoir Fracture with the Variable Scale Fractal Technique in Su53 Gas Field, Ordos Basin." Advanced Materials Research 1010-1012 (August 2014): 1723–26. http://dx.doi.org/10.4028/www.scientific.net/amr.1010-1012.1723.

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Typical tight gas reservoirs in the Su53 Gas Field, Ordos Basin, are the demonstration region for deploying horizontal wells. In order to provide foundation for evaluating the volume fracturing adaptability of horizontal wells, through using the amplitude difference data between deep investigate double lateral resistivity (Rd) and shallow investigate double lateral resistivity (Rs), and other conventional logging data, in combination with the response characteristics of fracture in the logging curve, reservoir fracture was quantitatively identified with the variable scale fractal technique, th
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Tian, Shi Min, Xiao Hui Su, Wei Hong Wang, and Rui Xun Lai. "Application of Fractal Theory in the River Regime in the Lower Yellow River." Applied Mechanics and Materials 190-191 (July 2012): 1238–43. http://dx.doi.org/10.4028/www.scientific.net/amm.190-191.1238.

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From 1960 to 1999, the river regime in the Lower Yellow River had been the wandering. After the operation of Xiaolangdi Reservoir, the river regime in the Lower Yellow River has experienced some changes because of the reduced discharge and sediment loads. According to the river regime maps, the wandering features of the Lower Yellow River are inhibited and the river channel is becoming stable. In addition, the fractal dimension method is introduced to discriminate the river regime. The river fractal features are able to reflect the features of river system and the fractal dimension is an impor
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Dissertations / Theses on the topic "Variable dimension fractal"

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Dubarry, Blandine. "Comportement asymptotique des systèmes de fonctions itérées et applications aux chaines de Markov d'ordre variable." Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S114/document.

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L'objet de cette thèse est l'étude du comportement asymptotique des systèmes de fonctions itérées (IFS). Dans un premier chapitre, nous présenterons les notions liées à l'étude de tels systèmes et nous rappellerons différentes applications possibles des IFS telles que les marches aléatoires sur des graphes ou des pavages apériodiques, les systèmes dynamiques aléatoires, la classification de protéines ou encore les mesures quantiques répétées. Nous nous attarderons sur deux autres applications : les chaînes de Markov d'ordre infini et d'ordre variable. Nous donnerons aussi les principaux résult
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Kaiser, Tashniba. "Node Localization using Fractal Signal Preprocessing and Artificial Neural Network." WorldComp, International Conference on Security and Management, 2012, 2012. http://hdl.handle.net/1993/22730.

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This thesis proposes an integrated artificial neural network based approach to classify the position of a wireless device in an indoor protected area. Our experiments are conducted in two different types of interference affected indoor locations. We found that the environment greatly influences the received signal strength. We realized the need of incorporating a complexity measure of the Wi-Fi signal as additional information in our localization algorithm. The inputs to the integrated artificial neural network were comprised of an integer dimension representation and a fractional dimension r
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Thouy, Romain. "Structures et propriétés d'agrégats de dimension fractale variable : simulations numériques." Montpellier 2, 1997. http://www.theses.fr/1997MON20094.

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Dans ce travail, nous presentons un modele d'agregation amas-amas, capable de construire des agregats fractals de dimension fractale variable, avec ou sans support de reseau, pour plusieurs dimensions euclidiennes. Nous avons ensuite systematiquement etudie, en fonction de cette dimension fractale, certaines de leurs proprietes physiques. Nous avons analyse les projections d'agregats 3d par deux methodes, l'une propre au modele, et l'autre plus proche des methodes experimentales (box-counting), pour en tester la faisabilite. Nous avons determine le facteur de structure (a partir des fonctions
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Grieder, Warren S. "Variance fractal dimension for signal feature enhancement and segmentation from noise." 1996. http://hdl.handle.net/1993/19180.

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Books on the topic "Variable dimension fractal"

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Fractals and universal spaces in dimension theory. Springer, 2009.

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Book chapters on the topic "Variable dimension fractal"

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Tricot, Claude. "The Constant-Deviation Variable-Step Algorithm." In Curves and Fractal Dimension. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4170-6_15.

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Atangana, Abdon, and Anum Shafiq. "Volterra Equation with Constant Fractional Order and Variable Order Fractal Dimension." In Advances in Mathematical Modelling, Applied Analysis and Computation. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0179-9_17.

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Freiberg, Uta Renata. "Some Remarks on the Hausdorff and Spectral Dimension of V-Variable Nested Fractals." In Recent Developments in Fractals and Related Fields. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4888-6_17.

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Kaiser, Samilat, and Ken Ferens. "Variance Fractal Dimension Feature Selection for Detection of Cyber Security Attacks." In Transactions on Computational Science and Computational Intelligence. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-70296-0_82.

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Lv, Dongbin, Honggang Zhang, Lihao Zeng, and Jiechao Lei. "Study on High Temperature Performance of Asphalt Mixture and Correlation of Its Evaluation Indexes." In Lecture Notes in Civil Engineering. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-2532-2_4.

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AbstractIn order to better evaluate the high-temperature performance of asphalt mixture, based on the conventional rutting test and Hamburg rutting test, this paper further studies the influence of temperature, grading and asphalt type on the high-temperature shear resistance of asphalt mixture by using uniaxial penetration test and uniaxial compression test. Based on Mohr Coulomb theory, the cohesive force and internal friction angle of mixture were calculated. Based on the analysis of variance, the significance of the influence of temperature and gradation on the high-temperature shear chara
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Zhang Fei, Zhou Haidong, and Zhao Yunxia. "3D Reconstruction of Rock Cracks CT Image Fractal Damage Study." In Information Technology in Geo-Engineering. IOS Press, 2010. https://doi.org/10.3233/978-1-60750-617-1-157.

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Based on the CT image of rock, we come up with a new method of CT image analysis and make the best use of information of CT images. Accomplish reinforcement of CT image of rock according to regulating contrast of CT image. The real microstructure, cranny and hole could be extracted through the technique of image segmentation. On the basis stated above, Marching Cube algorithm is applied to conduct a 3D reconstruction of successive CT tomographic images, visualization is implemented on rock cracks distribution during different damage stages, In this way we can get not only the directly visual c
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Suárez-Meaney, Tonatiuh, Héctor Daniel Reséndiz López, Jair Arriaga Carbajal, and Luis Chías Becerril. "La medición de la dimensión fractal en las ciudades, una aproximación para conocer su eficiencia en movilidad." In La interdisciplina en el estudio de la forma urbana. Universidad Autónoma Metropolitana. Unidad Azcapotzalco. División de Ciencias y Artes para el Diseño., 2022. http://dx.doi.org/10.24275/uama.9205.9210.

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The description of the shape of cities requires the analysis of complex geometries in two ways, 1) the shape of city contour, and 2) the inner shape of street network. Quantify contour characteristics it is important because its intrinsic relation with urban construction process, which is related to urban mobility. Fractal geometry can be applied for this purpose: in this paper the fractal dimension of Mexican cities with more than 200 thousand inhabitants has been calculated and then the relationship of this result with the mobility variables of the Mexican Institute of Competition (IMCO) has
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Sprott, Julien Clinton. "Fractals." In Chaos and Time-Series Analysis. Oxford University PressOxford, 2003. http://dx.doi.org/10.1093/oso/9780198508397.003.0011.

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Abstract Identifying chaos in experimental data usually includes searching for a strange attractor in the state-space dynamics, identified by its fractal structure. Having found such an attractor, you can try to estimate its dimension, which is a measure of the number of active variables and hence the complexity of the equations required to model the dynamics.
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Imre, Emőke, and Vijay Pal Singh. "The Finite Fractal Distributions as Mean Grain Size Distributions of Granular Matter." In Fractal Analysis - Applications and Updates [Working Title]. IntechOpen, 2024. http://dx.doi.org/10.5772/intechopen.1003760.

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The grading entropy is the statistical entropy of the finite discrete grain size distribution on N uniform statistical cells in terms of the N sieve cells, consisting of two terms, the base entropy and the entropy increment (depending on N), which have normalized forms as well (basically independent of N). Being the most adequate statistical variables, both physical phenomena and physical model parameters can be best described by their use. Among others, the normalized base entropy A can be used to measure internal stability, being related to erosion, piping and liquefaction phenomena. Its val
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Dobrescu, Radu, and Dan Popescu. "Image Processing Applications Based on Texture and Fractal Analysis." In Applied Signal and Image Processing. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-60960-477-6.ch014.

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Texture analysis research attempts to solve two important kinds of problems: texture segmentation and texture classification. In some applications, textured image segmentation can be solved by classification of small regions obtained from image partition. Two classes of features are proposed in the decision theoretic recognition problem for textured image classification. The first class derives from the mean co-occurrence matrices: contrast, energy, entropy, homogeneity, and variance. The second class is based on fractal dimension and is derived from a box-counting algorithm. For the purpose o
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Conference papers on the topic "Variable dimension fractal"

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Zhihai, Qin, and Qin Peng. "Using improved variable dimension fractal to model seawall settlement." In 2010 2nd IEEE International Conference on Information Management and Engineering. IEEE, 2010. http://dx.doi.org/10.1109/icime.2010.5478048.

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Liou, Jen Luen, and Jen Fin Lin. "A Microcontact Model Developed for Asperity Heights With a Variable Profile Fractal Dimension, a Surface Fractal Dimension, Topothesy, and Non-Gaussian Distribution." In STLE/ASME 2008 International Joint Tribology Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/ijtc2008-71086.

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The cross sections formed by the contact asperities of two rough surfaces at an interference are island-shaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, the relationship between D and Ds was given as D = Ds+1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to be varying
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Koshovy, Andrew G., George I. Koshovy, and Yuryi F. Logvinov. "Novel Planar Self-Similar Fractal Sets with a Variable Hausdorf Dimension." In 2022 IEEE 2nd Ukrainian Microwave Week (UkrMW). IEEE, 2022. http://dx.doi.org/10.1109/ukrmw58013.2022.10037022.

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Wang, Shao, and Wai Kin Chan. "Experimental Observation of Fractal-Regular Surfaces and a Transformation Scheme for Extracting Fractal Parameters." In World Tribology Congress III. ASMEDC, 2005. http://dx.doi.org/10.1115/wtc2005-63585.

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To account for the effects of asperity contacts at various length scales, it is appropriate to characterize an engineering surface as a fractal-regular surface. In spite of significant theoretical advancement, there is a desperate need for experimental verification of the theory of fractal-regular surfaces and a consistent scheme of obtaining the fractal parameters. In the present study, the existence of a fractal region and a regular-shape region in the power spectral density function for fractal-regular surfaces was confirmed experimentally, for the first time, with data obtained from magnet
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Wang, Zhi-Wang, Xiao Han, and Suo-Ying Mao. "Research on the Characteristics of the Spatial Distribution of Landslides Based on Variable Dimension Fractal." In 2nd International Forum on Management, Education and Information Technology Application (IFMEITA 2017). Atlantis Press, 2018. http://dx.doi.org/10.2991/ifmeita-17.2018.79.

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Ni, Zhihui, and Zhiyao Song. "Study on the Two Patters of Vertical Velocity Profile of Tidal Current and Their Law in Estuary and Coastal Waters." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79685.

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Many scholars at home and abroad have studied tidal velocity profile in estuarine and coastal waters. The results show that velocity profile of tidal current often deviated obviously from the traditional logarithmic profile, due to the flow including wind-driven current, wave-driven current, salinity and so on. In estuarine waters, runoff should be included as a component. In this paper, two patters of vertical velocity profile of tidal current are firstly divided, that are monotone increasing I-velocity profile (during flood tide and ebb tide stage) and non-monotone increasing II -velocity pr
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Craciunescu, Oana I., Shiva K. Das, Terrence Z. Wong, and Thaddeus V. Samulski. "Fractal Reconstruction of Breast Perfusion Before and After Hyperthermia Treatments." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33692.

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Thermal modeling for hyperthermia breast patients can provide relevant information to better understand the temperatures achieved during treatment. However, human breast is much perfused, making knowledge of the perfusion crucial to the accuracy of the temperature computations. It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index (RPI) determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI). It was also concluded that the 3D reconstruction of tumor perfusion can be performed using fractal interpolation functi
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Stark, G. A., and K. S. Moon. "Modeling Texture of Peripheral-Milled Surfaces Using a Neural Network and Fractal Method With Evidence of Chaos." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-1088.

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Abstract Modeling texture of milled surfaces using analytic methods requires explicit knowledge of a large number of variables some of which change during machining. These include dynamically changing tool runout, deflection, work-piece material properties, displacement of the workpiece within its fixture and others. Due to the complexity of all factors combined, an alternative approach is presented utilizing the ability of neural networks and fractals to implicitly account for these combined conditions. In the initial model, predicted surface points are first connected using splines to recons
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Grieder and Kinsner. "Speech segmentation by variance fractal dimension." In Proceedings of Canadian Conference on Electrical and Computer Engineering CCECE-94. IEEE, 1994. http://dx.doi.org/10.1109/ccece.1994.405793.

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Kumar, Tribhawan, Peng Zhou, and D. A. Glaser. "Discrimination of the fractal dimension for luminance and spatial displacement of 1-D patterns." In OSA Annual Meeting. Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.wv4.

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Observers were shown images that had luminance variations in the vertical direction (y) and constant luminance in the horizontal direction (x). Variance of the difference of the luminance at any two ys was proportional to the differences in the ys to some fractional power. The fractional power is related to the fractal dimension. Discrimination thresholds were measured using the second alternative six-level forced choice paradigm. Thresholds were found to be insensitive to changes in the fractal dimension, viewing time, change in width of the image beyond 8 arcmin, and to noise flanking the ve
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Reports on the topic "Variable dimension fractal"

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Russo, David, Daniel M. Tartakovsky, and Shlomo P. Neuman. Development of Predictive Tools for Contaminant Transport through Variably-Saturated Heterogeneous Composite Porous Formations. United States Department of Agriculture, 2012. http://dx.doi.org/10.32747/2012.7592658.bard.

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The vadose (unsaturated) zone forms a major hydrologic link between the ground surface and underlying aquifers. To understand properly its role in protecting groundwater from near surface sources of contamination, one must be able to analyze quantitatively water flow and contaminant transport in variably saturated subsurface environments that are highly heterogeneous, often consisting of multiple geologic units and/or high and/or low permeability inclusions. The specific objectives of this research were: (i) to develop efficient and accurate tools for probabilistic delineation of dominant geol
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