Relevant bibliographies by topics / Fractal modelling

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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 'Fractal modelling'

Author: Grafiati
Published: 4 June 2021
Last updated: 2 November 2024

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Journal articles on the topic "Fractal modelling"

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Bolshakov, V. I., V. M. Volchuk, M. A. Kotov, and D. P. Fisunenko. "Aspects of fractal modelling application." Physical Metallurgy and Heat Treatment of Metals 2, no. 2 (97) (July 26, 2022): 7–18. http://dx.doi.org/10.30838/j.pmhtm.2413.050722.7.858.

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Purpose of research. More than 40 years ago, the theory of fractals applied to model of materials structure and properties firstly. During this time in many publications, the connection between the fractal (fractional) dimension of various materials structural elements and their physical and mechanical properties have confirmed. But unified approach to the organisation of fractal modelling not defined. This article analyses some steps of fractal modelling in order to assess their application to specific cases of predicting quality criteria for metals and concretes. Results. One of the fractal modelling algorithms used in materials science is considered. The algorithm consist of: calculation of the fractal dimension D for the research object according to F. Hausdorff's formula; definition of object self-similarity (invariance with reference to the representation scale); model investigation for compliance with the conditions corresponding to the sensitivity index; choice of a objective function (quality criterion), variables (fractal dimensions of structural elements) and reference points; formalization of the obtained results (selection of an adequate model describing the connection between the fractal structure of the material and its properties); estimation of the fractal object heterogeneity degree according to Rainier's formula for belonging to multifractals; interpretation of the obtained results. Examples of implementation for each step of the fractal modelling algorithm are given. The expediency of supplementing the considered algorithm due to the possibility of applying fractal formalism in the quality criteria ranking by the metal and concrete example is considered. The application of such a systematic approach in fractal modelling allows to improve the investigated material properties prediction based on the analysis of their structure and macrostructure. In turn, this leads to the finding of new structure-property regularities. Conclusions. Variants for supplementing the algorithm for fractal modelling of the structure and properties for metals (steel and cast iron) and concretes are proposed. The application of these algorithms allow the correlation and sensitivity estimation between the fractal dimension of the structure and the properties, as well as the ranking of the quality criteria for the materials based on the analysis of the working range of their values.
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Chen, Yanguang. "Characterizing Growth and Form of Fractal Cities with Allometric Scaling Exponents." Discrete Dynamics in Nature and Society 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/194715.

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Fractal growth is a kind of allometric growth, and the allometric scaling exponents can be employed to describe growing fractal phenomena such as cities. The spatial features of the regular fractals can be characterized by fractal dimension. However, for the real systems with statistical fractality, it is incomplete to measure the structure of scaling invariance only by fractal dimension. Sometimes, we need to know the ratio of different dimensions rather than the fractal dimensions themselves. A fractal-dimension ratio can make an allometric scaling exponent (ASE). As compared with fractal dimension, ASEs have three advantages. First, the values of ASEs are easy to be estimated in practice; second, ASEs can reflect the dynamical characters of system's evolution; third, the analysis of ASEs can be made through prefractal structure with limited scale. Therefore, the ASEs based on fractal dimensions are more functional than fractal dimensions for real fractal systems. In this paper, the definition and calculation method of ASEs are illustrated by starting from mathematical fractals, and, then, China's cities are taken as examples to show how to apply ASEs to depiction of growth and form of fractal cities.
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LAI, PENG-JEN. "HOW TO MAKE FRACTAL TILINGS AND FRACTAL REPTILES." Fractals 17, no. 04 (December 2009): 493–504. http://dx.doi.org/10.1142/s0218348x09004533.

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Intensive research on fractals began around 1980 and many new discoveries have been made. However, the connection between fractals, tilings and reptiles has not been thoroughly explored. This paper shows that a method, similar to that used to construct irregular tilings in ℜ2 can be employed to construct fractal tilings. Five main methods, including methods in Escher style paintings and the Conway criterion are used to create the fractal tilings. Also an algorithm is presented to generate fractal reptiles. These methods provide a more geometric way to understand fractal tilings and fractal reptiles and complements iteration methods.
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LAPIDUS, MICHEL L. "FRACTALS AND VIBRATIONS: CAN YOU HEAR THE SHAPE OF A FRACTAL DRUM?" Fractals 03, no. 04 (December 1995): 725–36. http://dx.doi.org/10.1142/s0218348x95000643.

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We study various aspects of the question “Can one hear the shape of a fractal drum?”, both for “drums with fractal boundary” (or “surface fractals”) and for “drums with fractal membrane” (or “mass fractals”).
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CHEN, YAN-GUANG. "FRACTAL TEXTURE AND STRUCTURE OF CENTRAL PLACE SYSTEMS." Fractals 28, no. 01 (February 2020): 2050008. http://dx.doi.org/10.1142/s0218348x20500085.

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The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. However, the fractal texture cannot be verified by empirical analyses based on observed data. On the other hand, fractal structure of central place systems in the real world can be empirically confirmed by positive studies, but there are no corresponding models. The spatial structure of classic central place models bears Euclidean dimension [Formula: see text] rather than fractal dimensions [Formula: see text]. This paper is devoted to deriving structural fractals of central place models from the textural fractals. The method is theoretical deduction based on the dimension rules of fractal sets. The main results and findings are as follows. First, the central place fractals were formulated by the [Formula: see text] numbers and [Formula: see text] numbers. Second, three structural fractal models were constructed for central place systems according to the corresponding fractal dimensions. Third, the classic central place models proved to comprise Koch snowflake curve, Sierpinski space filling curve, and Gosper snowflake curve. Moreover, the traffic principle plays a leading role in urban and rural settlements evolution. A conclusion was reached that the textural fractal dimensions of central place models can be converted into the structural fractal dimensions and vice versa, and the structural dimensions can be directly used to appraise human settlement distributions in reality. Thus, the textural fractals can be indirectly employed to characterize the systems of human settlements.
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SUZUKI, MASUO. "FRACTAL FORM ANALYSIS." Fractals 04, no. 03 (September 1996): 237–39. http://dx.doi.org/10.1142/s0218348x96000327.

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Gospodinova, Evgeniya. "Methods and Algorithms for Simulation Modelling of Fractal Processes." Innovative STEM Education 1, no. 1 (August 29, 2019): 48–58. http://dx.doi.org/10.55630/stem.2019.0107.

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The report presents methods and algorithms for simulation modelling of fractal processes. Fractal processes based on fractal Brownian motion, fractal Gaussian noise and, fractal Gaussian noise-wavelet transformation are simulated. Based on the performed comparative analysis of the algorithms for simulation modelling of fractal processes with respect to the accuracy parameter, it follows that the algorithms based on the models of fractal Gaussian noise and fractal Gaussian noise-wavelet transformation have the smallest relative error with respect to the Hurst parameter. The value of the Hurst parameter is one of the most important characteristics determining the degree of self-similarity of fractal processes. The considered algorithms based on these two models can be applied for modelling of physiological data, including cardiological data, because they have fractal properties.
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Avery, I., F. R. Hall, and C. E. N. Sturgess. "Fractal modelling of materials." Journal of Materials Processing Technology 80-81 (August 1998): 565–71. http://dx.doi.org/10.1016/s0924-0136(98)00124-1.

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Semkow, Thomas M. "Neighborhood Volume for Bounded, Locally Self-Similar Fractals." Fractals 05, no. 01 (March 1997): 23–33. http://dx.doi.org/10.1142/s0218348x97000048.

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We derive the formulas for neighborhood volume (Minkowski volume in d-dimensions) for fractals which have a curvature bias and are thus bounded. Both local surface fractal dimension and local mass fractal dimension are included as well as a radius of the neighborhood volume comparable with the size of the fractal. We consider two types of the neighborhood volumes: simplified and generalized, as well as the volumes below and above the fractal boundary. The formulas derived are generalizations of the equations for isotropic unbounded fractals. Based on the simplified-volume concept, we establish the procedure for calculating a distribution of physical quantities on bounded fractals and apply it to the distribution of trace elements in soil particles. Using the concept of the generalized volume, we show how an expectation value of a physical process can be calculated on bounded fractals, and apply it to the radon emanation from solid particles.
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Coppens, Marc-Olivier, and Gilbert F. Froment. "The Effectiveness of Mass Fractal Catalysts." Fractals 05, no. 03 (September 1997): 493–505. http://dx.doi.org/10.1142/s0218348x97000395.

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Many porous catalysts have a fractal surface, but only rarely do they have a fractal volume, the main exceptions being extremely porous aerogels. It has been suggested that a fractal shape of their volume would be ideal, because it has an infinite area per unit mass that is easily accessible by the reactants. This paper investigates the efficiency of mass fractals by comparing them with nonfractal catalysts. It is found that the specific surface areas of comparable nonfractal catalysts are of the same order of magnitude, if not higher than those of mass fractals. Despite the high effectiveness factor of mass fractals due to the exceptionally easy accessibility of their active sites, production in a nonfractal catalyst is often higher than in a mass fractal, because of the high porosity of the latter. For some strongly diffusion limited reactions, especially in mesoporous catalysts, an added mass fractal macroporosity, with a finite scaling regime, would increase the yields beyond what is possible with a nonfractal catalyst. Nonetheless, when transport through viscous flow in macropores is very rapid the effective reaction rates in classical bimodal catalysts are higher than in fractal catalysts with their high macroporosity.
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Dissertations / Theses on the topic "Fractal modelling"

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Sharma, A. "Modelling biological systems: a fractal approach." Thesis(Ph.D.), CSIR-National Chemical Laboratory, Pune, 1991. http://dspace.ncl.res.in:8080/xmlui/handle/20.500.12252/3009.

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Gregotski, Mark Edward. "Fractal stochastic modelling of airborne magnetic data." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74300.

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Airborne magnetic field data exhibit downward continued power spectra of the form $1/f sp beta$ (where f is the spatial frequency and $ beta$ is a non-negative real number). This form of spectrum is observed for magnetic data recorded over a range of sampling scales from various areas of the Canadian Shield. Two scaling regimes have been discovered. The first has a $ beta$ value near 3 for wavelengths $ sbsp{ sim}{$25 km. These results suggest a "variable fractal" description of the distribution of near-surface magnetic sources.
From a data modelling viewpoint, the magnetic measurements are derived from a linear superposition of a deterministic system function and a stochastic excitation process. A symmetric operator corresponds to the system function, and the near-surface magnetic source distribution represents the excitation process. The deconvolution procedure assumes an autoregressive (AR) system function and proceeds iteratively using bi-directional AR (BDAR) filtering in one dimension, which is extended to four-pass AR filtering in two dimensions. The traditional assumption of a spectrally white innovation is used in the deconvolution procedure. The data are modified prior to deconvolution by a Fourier domain prewhitening technique, to account for the long wavelength content of the fractal innovation. Deconvolution of the modified data produces the system function, which is removed from the original data to produce the near-surface magnetic source distribution. This distribution serves as a susceptibility map which can be used for enhancing magnetic field anomalies and geological mapping. Thus, the statistical descriptions of near-surface magnetic sources are useful for modelling airborne magnetic data in "shield-type" geologic environments.
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Nilsen, Christopher. "Fractal modelling of turbulent flows : Subgrid modelling for the Burgers equation." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for energi- og prosessteknikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-13916.

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The stochastically forced Burgers equation shares some of the same characteristics as the three-dimensional Navier-Stokes equations. Because of this it is sometimes used as a model equation for turbulence. Simulating the stochastically forced Burgers equation with low resolution can be considered as a one dimensional model of a three-dimensional large eddy simulation, and can be used to evaluate subgrid models. Modified versions of subgrid models using the fractal interpolation technique are presented here and tested in low resolution simulations of the stochastically forced Burgers equations. The results are compared with high resolution simulations, then low resolution simulations first using the dynamic Smagorinsky model and then using no subgrid model other than the numerical dissipation of the convective flux discretisation scheme. The fractal models perform reasonably well and most of the large scale features from the high resolution simulations are reproduced by corresponding simulations with low resolution. The performance of the fractal models is not, however, better than the performance of the dynamic Smagorinsky model. Therefore one might say that although the fractal models give promising results, it is not obvious that they are in any way superior to the traditional models. Also the low resolution simulation with the dissipative convective scheme performs well, suggesting that numerical dissipation can be sufficient as a subgrid model in one dimension.The solutions to the stochastically forced Burgers equation follow a k^(-5/3) energy spectrum, but high order statistics are not similar to real turbulence, due to the complete domination of shocks. Thus the stochastically forced Burgers equation might not be a suitable model for turbulence. It is not likely that the complexity of three-dimensional subgrid modelling is sufficiently represented by the one-dimensional case either.
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Lauren, Michael Kyle. "The fractal modelling of turbulent surface-layer winds." Thesis, University of Auckland, 1999. http://hdl.handle.net/2292/1106.

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Multiscaling analysis and cascade simulation techniques, which form part of the more general field of fractals, are introduced as a method for characterising and simulating surface-layer winds, particularly for time scales associated with the energy-containing range. This type of analysis consists of determining the power-law parameter of the spectrum of the data, and the scaling of the statistical moments. These techniques were applied to determine how the statistics depended on the duration (or scale) of the fluctuations in wind speed, the atmospheric conditions, and the topography of the site. It was found that the parameterisations produced using multiscaling analysis characterised differences in the statistics for each of these cases. Furthermore, the fractal cascade simulation techniques used provided simple methods for reproducing these statistics. This analysis is followed by an investigation into the robustness of some of these results. In particular, the data is examined for the existence of self-similar distributions of the cascade weighting factor, W. Such self-similar analysis allows the direct simulation of the data via a cascade. Cascade models have the virtue of being able to reproduce statistical properties such as intermittency, and in particular, the nesting of intermittency from different wavenumber bands in the same region of space. The existence of these properties in both the experimental and simulated data is investigated, with consideration given to the consequence of the results for simulation techniques. One notable discovery is the failure of these methods to reproduce the bias in the distribution of the gradients in the wind velocity field. This result has important implications for all workers dealing with simulation of geophysical data by fractal cascades. Finally, a brief numerical experiment is carried out to both demonstrate how this bias may be exploited to construct a model, and to test some of the analysis techniques presented on non-cascade based data. While not a particularly convincing simulator of turbulence, the model nevertheless displays some interesting turbulence-like characteristics.
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Kentwell, D. J. "Fractal relationships and spatial distribution of ore body modelling." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 1997. https://ro.ecu.edu.au/theses/882.

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The nature of spatial distributions of geological variables such as ore grades is of primary concern when modelling ore bodies and mineral resources. The aim of any mineral resource evaluation process is to determine the location, extent, volume and average grade of that resource by a trade off between maximum confidence in the results and minimum sampling effort. The principal aim of almost every geostatistical modelling process is to predict the spatial variation of one or more geological variables in order to estimate values of those variables at locations that have not been sampled. From the spatial analysis of these variables, in conjunction with the physical geology of the region of interest, the location, extent and volume, or series of discrete volumes, whose average ore grade exceeds a specific ore grade cut off value determined' by economic parameters can be determined, Of interest are not only the volume and average grade of the material but also the degree of uncertainty associated with each of these. Geostatistics currently provides many methods of assessing spatial variability. Fractal dimensions also give us a measure of spatial variability and have been found to model many natural phenomenon successfully (Mandelbrot 1983, Burrough 1981), but until now fractal modelling techniques have not been able to match the versatility and accuracy of geostatistical methods. Fractal ideas and use of the fractal dimension may in certain cases provide a better understanding of the way in which spatial variability manifests itself in geostatistical situations. This research will propose and investigate a new application of fractal simulation methods to spatial variability and spatial interpolation techniques as they relate to ore body modelling. The results show some advantages over existing techniques of geostatistical simulation.
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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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Arfeen, Muhammad Asad. "Contributions to modelling of internet traffic by fractal renewal processes." Thesis, University of Canterbury. Department of Computer Science & Software Engineering, 2014. http://hdl.handle.net/10092/10194.

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The principle of parsimonious modelling of Internet traffic states that a minimal number of descriptors should be used for its characterization. Until early 1990s, the conventional Markovian models for voice traffic had been considered suitable and parsimonious for data traffic as well. Later with the discovery of strong correlations and increased burstiness in Internet traffic, various self-similar count models have been proposed. But, in fact, such models are strictly mono-fractal and applicable at coarse time scales, whereas Internet traffic modelling is about modelling traffic at fine and coarse time scales; modelling traffic which can be mono and multi-fractal; modelling traffic at interarrival time and count levels; modelling traffic at access and core tiers; and modelling all the three structural components of Internet traffic, that is, packets, flows and sessions. The philosophy of this thesis can be described as: “the renewal of renewal theory in Internet traffic modelling”. Renewal theory has a great potential in modelling statistical characteristics of Internet traffic belonging to individual users, access and core networks. In this thesis, we develop an Internet traffic modelling framework based on fractal renewal processes, that is, renewal processes with underlying distribution of interarrival times being heavy-tailed. The proposed renewal framework covers packets, flows and sessions as structural components of Internet traffic and is applicable for modelling the traffic at fine and coarse time scales. The properties of superposition of renewal processes can be used to model traffic in higher tiers of the Internet hierarchy. As the framework is based on renewal processes, therefore, Internet traffic can be modelled at both interarrival times and count levels.
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Yasrebi, Amir Bijan. "Determination of an ultimate pit limit utilising fractal modelling to optimise NPV." Thesis, University of Exeter, 2014. http://hdl.handle.net/10871/18449.

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The speed and complexity of globalisation and reduction of natural resources on the one hand, and interests of large multinational corporations on the other, necessitates proper management of mineral resources and consumption. The need for scientific research and application of new methodologies and approaches to maximise Net Present Value (NPV) within mining operations is essential. In some cases, drill core logging in the field may result in an inadequate level of information and subsequent poor diagnosis of geological phenomenon which may undermine the delineation or separation of mineralised zones. This is because the interpretation of individual loggers is subjective. However, modelling based on logging data is absolutely essential to determine the architecture of an orebody including ore distribution and geomechanical features. For instance, ore grades, density and RQD values are not included in conventional geological models whilst variations in a mineral deposit are an obvious and salient feature. Given the problems mentioned above, a series of new mathematical methods have been developed, based on fractal modelling, which provide a more objective approach. These have been established and tested in a case study of the Kahang Cu-Mo porphyry deposit, central Iran. Recognition of different types of mineralised zone in an ore deposit is important for mine planning. As a result, it is felt that the most important outcome of this thesis is the development of an innovative approach to the delineation of major mineralised (supergene and hypogene) zones from ‘barren’ host rock. This is based on subsurface data and the utilisation of the Concentration-Volume (C-V) fractal model, proposed by Afzal et al. (2011), to optimise a Cu-Mo block model for better determination of an ultimate pit limit. Drawing on this, new approaches, referred to Density–Volume (D–V) and RQD-Volume (RQD-V) fractal modelling, have been developed and used to delineate rock characteristics in terms of density and RQD within the Kahang deposit (Yasrebi et al., 2013b; Yasrebi et al., 2014). From the results of this modelling, the density and RQD populations of rock types from the studied deposit showed a relationship between density and rock quality based on RQD values, which can be used to predict final pit slope. Finally, the study introduces a Present Value-Volume (PV-V) fractal model in order to identify an accurate excavation orientation with respect to economic principals and ore grades of all determined voxels within the obtained ultimate pit limit in order to achieve an earlier pay-back period.
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Bonsu, Kofi. "Urban hierarchy and the analysis of spatial patterns : towards explicit fractal modelling." Electronic Thesis or Diss., Université Gustave Eiffel, 2024. http://www.theses.fr/2024UEFL2021.

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La thèse vise à explorer le potentiel des résultats empiriques dans l'identification des centres et sous-centres urbains en utilisant des données accumulées extraites d'images de télédétection et d'analyses fractales disponibles gratuitement. Il répond au défi de l’indisponibilité des données dans ce contexte. Bien que diverses méthodes aient été utilisées dans la littérature, telles que le seuil minimum, les méthodes statistiques spatiales et la méthode des prix hédoniques, celles-ci sont principalement basées sur le contexte local des pays développés, avec des études limitées axées sur les pays en développement en raison de la rareté des données. Cette recherche cherche à combler cette lacune en étudiant l'efficacité de la géométrie fractale pour identifier explicitement les centres et sous-centres urbains, caractériser leur organisation spatiale pour l'analyse de la croissance urbaine et délimiter les modèles de croissance urbaine basés sur la disposition spatiale des centres urbains, des sous-centres et des transports primaires. réseaux. Comprendre ces dynamiques est crucial pour des décisions éclairées en matière d’urbanisme et d’infrastructure. En utilisant la zone métropolitaine du Grand Accra (GAMA) comme étude de cas, des images satellite disponibles gratuitement couvrant la période 1991 à 2022 ont été téléchargées et classées à l'aide de diverses techniques, notamment la forêt aléatoire, la machine à vecteurs de support et le cluster itératif linéaire simple (SLIC) avec K-Means. pour extraire des modèles construits. Une analyse longitudinale a été menée pour évaluer l'impact de la croissance urbaine sur la biodiversité, révélant des changements dans la composition de la couverture terrestre, les zones bâties dominant de plus en plus la végétation, conduisant à une fragmentation de l'habitat. La couverture terrestre et les modèles de paysage pour 2030 ont été prédits avec succès, soulignant l'importance de la connectivité du paysage et de la fragmentation de l'habitat dans l'évaluation des processus écologiques et des impacts du développement urbain. En outre, l'analyse fractale multiradiale et la morphologie mathématique ont été utilisées pour identifier les centres et sous-centres urbains à partir de données de télédétection, sur la base des dimensions fractales et de l'organisation spatiale. Un modèle conceptuel de croissance urbaine a été développé pour visualiser les modèles d'expansion urbaine attendus. Ces résultats contribuent de manière significative à l’identification et à l’organisation spatiale des centres et sous-centres urbains, en particulier dans les villes manquant de données statistiques ou géospatiales adéquates, en particulier dans les pays en développement. La reproduction de cette méthodologie pourrait contribuer à une base de données mondiale plus complète sur les villes
The thesis aims to explore the potential of empirical results in identifying urban centers and subcenters by utilizing built-up data extracted from freely-available remote sensing images and fractal analyses. It addresses the challenge of data unavailability in this context. While various methods have been employed in literature, such as minimum cut-off point, spatial statistical methods, and hedonic price method, these are predominantly based on the local context of developed nations, with limited studies focused on developing nations due to data scarcity. This research seeks to fill this gap by investigating the effectiveness of fractal geometry in explicitly identifying urban centers and subcenters, characterizing their spatial organization for urban growth analysis, and delineating urban growth patterns based on the spatial arrangement of urban centers, subcenters, and primary transportation networks. Understanding these dynamics is crucial for informed urban planning and infrastructure decisions. Using the Greater Accra Metropolitan Area (GAMA) as a case study, freely available satellite images spanning from 1991 to 2022 were downloaded and classified using various techniques including random forest, support vector machine, and simple linear iterative cluster (SLIC) with K-Means to extract built-up patterns. A longitudinal analysis was conducted to assess the impact of urban growth on biodiversity, revealing shifts in land cover composition with built-up areas increasingly dominating over vegetation, leading to habitat fragmentation. Land cover and landscape patterns for 2030 were successfully predicted, emphasizing the importance of landscape connectivity and habitat fragmentation in evaluating ecological processes and urban development impacts. Furthermore, multi-radial fractal analysis and mathematical morphology were employed to identify urban centers and subcenters from remote sensing data, based on fractal dimensions and spatial organization. A conceptual urban growth model was developed to visualize expected urban expansion patterns. These findings contribute significantly to the identification and spatial organization of urban centers and subcenters, particularly in cities lacking adequate statistical or geospatial data, especially in developing countries. Replicating this methodology could contribute to a more comprehensive global database on cities
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Wohlberg, Brendt. "Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective." Doctoral thesis, University of Cape Town, 1996. http://hdl.handle.net/11427/9475.

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Bibliography: p. 208-225.
Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques.
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Books on the topic "Fractal modelling"

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Kaandorp, Jaap A. Fractal Modelling. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6.

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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. London: Taylor & Francis, 2002.

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Kaandorp, Jaap A. Modelling growth forms of biological objects using fractals. Meppel, the Netherlands: Printed by Krips Repro, 1992.

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Arulprakash, Gowrisankar, Kishore Bingi, and Cristina Serpa, eds. Mathematical Modelling of Complex Patterns Through Fractals and Dynamical Systems. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-2343-0.

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Kaandorp, Jaap A. Fractal Modelling. Island Press, 1994.

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Kaandorp, Jaap A. Fractal Modelling: Growth and Form in Biology. Springer, 2012.

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Prusinkiewicz, P., and Jaap A. Kaandorp. Fractal Modelling: Growth and Form in Biology. Springer London, Limited, 2012.

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Fractal modelling: Growth and form in biology. Berlin: Springer-Verlag, 1994.

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Modelling of Flow and Transport in Fractal Porous Media. Elsevier, 2021. http://dx.doi.org/10.1016/c2018-0-02631-6.

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Wei, Wei, Liehui Zhang, and Jianchao Cai. Modelling of Flow and Transport in Fractal Porous Media. Elsevier, 2020.

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Book chapters on the topic "Fractal modelling"

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Kaandorp, Jaap A. "Introduction." In Fractal Modelling, 1–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_1.

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Kaandorp, Jaap A. "Methods for Modelling Biological Objects." In Fractal Modelling, 7–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_2.

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Kaandorp, Jaap A. "2D Models of Growth Forms." In Fractal Modelling, 55–101. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_3.

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Kaandorp, Jaap A. "A Comparison of Forms." In Fractal Modelling, 103–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_4.

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Kaandorp, Jaap A. "3D Models of Growth Forms." In Fractal Modelling, 129–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_5.

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Kaandorp, Jaap A. "Final Conclusions." In Fractal Modelling, 189–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_6.

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Appleby, S. "Fractal Populations." In Modelling Future Telecommunications Systems, 22–44. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4615-2049-8_3.

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Walters, Glenn D. "The Fractal Nature of Lifestyles." In Modelling the Criminal Lifestyle, 53–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57771-5_3.

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Pardo-Igúzquiza, Eulogio, Juan José Durán, Pedro Robledo, Carolina Guardiola, Juan Antonio Luque, and Sergio Martos. "Fractal Modelling of Karst Conduits." In Lecture Notes in Earth System Sciences, 217–20. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-32408-6_50.

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Trethewey, K. R., and P. R. Roberge. "Towards Improved Quantitative Characterization of Corroding Surfaces Using Fractal Models." In Modelling Aqueous Corrosion, 443–63. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1176-8_21.

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Conference papers on the topic "Fractal modelling"

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Coloşi, Tiberiu, and Steliana Codreanu. "A new method of modelling and numerical simulation of nonlinear dynamical systems." In Chaotic, fractal, and nonlinear signal processing. AIP, 1996. http://dx.doi.org/10.1063/1.51011.

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Burkovets, D. M., O. P. Maksimyak, and K. I. Nestina. "Modelling of light scattering by fractal clusters." In SPIE Proceedings, edited by Malgorzata Kujawinska and Oleg V. Angelsky. SPIE, 2008. http://dx.doi.org/10.1117/12.797011.

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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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Yun, Chen, and Gao Ruidong. "A New Fractal Hyperspectral Image Compression Algorithm." In 2nd International Conference on Modelling, Identification and Control. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/mic-15.2015.32.

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Tafti, Pouya Dehghani, Ricard Delgado-Gonzalo, Aurelien F. Stalder, and Michael Unser. "Fractal modelling and analysis of flow-field images." In 2010 7th IEEE International Symposium on Biomedical Imaging: From Nano to Macro. IEEE, 2010. http://dx.doi.org/10.1109/isbi.2010.5490416.

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Potapov, A. A., E. N. Matveev, V. A. Potapov, and A. V. Laktyunkin. "Mathematical and physics modelling of fractal antennas and fractal frequency selective surfaces and volumes for the fractal radio systems." In 2nd European Conference on Antennas and Propagation (EuCAP 2007). Institution of Engineering and Technology, 2007. http://dx.doi.org/10.1049/ic.2007.1192.

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Bagmanov, Valeriy H., Sergey V. Dyblenko, Klaus Janschek, Anton E. Kiselev, Albert H. Sultanov, and Valeriy V. Tchernykh. "Fractal approach to mathematical modelling of space observation data." In SPIE Proceedings, edited by Vladimir A. Andreev, Vladimir A. Burdin, Oleg G. Morozov, and Albert H. Sultanov. SPIE, 2008. http://dx.doi.org/10.1117/12.801495.

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"EEG/SEEG SIGNAL MODELLING USING FREQUENCY AND FRACTAL ANALYSIS." In International Conference on Bio-inspired Systems and Signal Processing. SciTePress - Science and and Technology Publications, 2012. http://dx.doi.org/10.5220/0003780302490253.

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Cao, Xiaobin, Zhongmei Li, Zude Lu, Ruifang Li, and Haiman Wang. "Controllable fractal modelling method based on soil statistical parameters." In 2024 IEEE 7th International Electrical and Energy Conference (CIEEC）. IEEE, 2024. http://dx.doi.org/10.1109/cieec60922.2024.10583295.

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Kinsner, Witold, and Epiphany Vera. "Fractal modelling of residues in linear predictive coding of speech." In 2009 8th IEEE International Conference on Cognitive Informatics (ICCI). IEEE, 2009. http://dx.doi.org/10.1109/coginf.2009.5250762.

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Reports on the topic "Fractal modelling"

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Nechaev, V., Володимир Миколайович Соловйов, and A. Nagibas. Complex economic systems structural organization modelling. Politecnico di Torino, 2006. http://dx.doi.org/10.31812/0564/1118.

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One of the well-known results of the theory of management is the fact, that multi-stage hierarchical organization of management is unstable. Hence, the ideas expressed in a number of works by Don Tapscott on advantages of network organization of businesses over vertically integrated ones is clear. While studying the basic tendencies of business organization in the conditions of globalization, computerization and internetization of the society and the results of the financial activities of the well-known companies, the authors arrive at the conclusion, that such companies, as IBM, Boeing, Mercedes-Benz and some others companies have not been engaged in their traditional business for a long time. Their partner networks performs this function instead of them. The companies themselves perform the function of system integrators. The Tapscott’s idea finds its confirmation within the framework of a new powerful direction of the development of the modern interdisciplinary science – the theory of the complex networks (CN) [2]. CN-s are multifractal objects, the loss of multifractality being the indicator of the system transition from more complex state into more simple state. We tested the multifractal properties of the data using the wavelet transform modulus maxima approach in order to analyze scaling properties of our company. Comparative analysis of the singularity spectrumf(®), namely, the difference between maximum and minimum values of ® (∆ = ®max ¡ ®min) shows that IBM company is considerably more fractal in comparison with Apple Computer. Really, for it the value of ∆ is equal to 0.3, while for the vertically integrated company Apple it only makes 0.06 – 5 times less. The comparison of other companies shows that this dependence is of general character. Taking into consideration the fact that network organization of business has become dominant in the last 5-10 years, we carried out research for the selected companies in the earliest possible period of time which was determined by the availability of data in the Internet, or by historically later beginning of stock trade of computer companies. A singularity spectrum of the first group of companies turned out to be considerably narrower, or shifted toward the smaller values of ® in the pre-network period. The latter means that dynamic series were antipersistant. That is, these companies‘ management was rigidly controlled while the impact of market mechanisms was minimized. In the second group of companies if even the situation did changed it did not change for the better. In addition, we discuss applications to the construction of portfolios of stock that have a stable ratio of risk to return.
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