Journal articles: 'Fractal computing'

1

Semenov, A. S. "Fractal feedback control for Elastic computing based on the Container–Component model." Journal of Physics: Conference Series 2308, no. 1 (July 1, 2022): 012009. http://dx.doi.org/10.1088/1742-6596/2308/1/012009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Abstract One of the most significant characteristics of cloud computing is elasticity, which refers to the autoscaling control of resources based on the demands of the application or service. The problem of setting parameters of elastic autoscaling is not trivial and its solution depends on the control model. The Container-Component model that exploits the properties of fractals is investigated for this purpose. The fractal dimension is proposed to characterize the auto-scalability of distributed computing, independent of the implementation. The control of the fractal complexity by means of fractal feedback is considered.

2

Zhao, Yongwei, Yunji Chen, and Zhiwei Xu. "Fractal Parallel Computing." Intelligent Computing 2022 (September 5, 2022): 1–10. http://dx.doi.org/10.34133/2022/9797623.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

As machine learning (ML) becomes the prominent technology for many emerging problems, dedicated ML computers are being developed at a variety of scales, from clouds to edge devices. However, the heterogeneous, parallel, and multilayer characteristics of conventional ML computers concentrate the cost of development on the software stack, namely, ML frameworks, compute libraries, and compilers, which limits the productivity of new ML computers. Fractal von Neumann architecture (FvNA) is proposed to address the programming productivity issue for ML computers. FvNA is scale-invariant to program, thus making the development of a family of scaled ML computers as easy as a single node. In this study, we generalize FvNA to the field of general-purpose parallel computing. We model FvNA as an abstract parallel computer, referred to as the fractal parallel machine (FPM), to demonstrate several representative general-purpose tasks that are efficiently programmable. FPM limits the entropy of programming by applying constraints on the control pattern of the parallel computing systems. However, FPM is still general-purpose and cost-optimal. We settle some preliminary results showing that FPM is as powerful as many fundamental parallel computing models such as BSP and alternating Turing machine. Therefore, FvNA is also generally applicable to various fields other than ML.

3

Naylor, Michael. "Exploring Fractals in the Classroom." Mathematics Teacher 92, no. 4 (April 1999): 360–66. http://dx.doi.org/10.5951/mt.92.4.0360.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

This article introduces students to fractals, allows them to study the properties of some famous fractals, and encourages them to create their own fractal artwork. Students will learn about iterative processes, exponential functions, limits, writing general formulas, creating and following algorithms, and computing areas and perimeters of increasingly complex figures.

4

Jahanmiri, Fatemeh, and Dawn Cassandra Parker. "An Overview of Fractal Geometry Applied to Urban Planning." Land 11, no. 4 (March 25, 2022): 475. http://dx.doi.org/10.3390/land11040475.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Since computing advances in the last 30 years have allowed automated calculation of fractal dimensions, fractals have been established as ubiquitous signatures of urban form and socioeconomic function. Yet, applications of fractal concepts in urban planning have lagged the evolution of technical analysis methods. Through a narrative literature review around a series of “big questions” and automated bibliometric analysis, we offer a primer on fractal applications in urban planning, targeted to urban scholars and participatory planners. We find that developing evidence demonstrates linkages between urban history, planning context, and urban form and between “ideal” fractal dimension values and urban aesthetics. However, we identify gaps in the literature around findings that directly link planning regulations to fractal patterns, from both positive and normative lenses. We also find an increasing trend of most literature on fractals in planning being published outside of planning. We hypothesize that this trend results from communication gaps between technical analysts and applied planners, and hope that our overview will help to bridge that gap.

5

LIU, SHUAI. "EDITORIAL." Fractals 25, no. 04 (July 25, 2017): 1702001. http://dx.doi.org/10.1142/s0218348x17020017.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Fractal represents a special feature of nature and functional objects. However, fractal based computing can be applied to many research domains because of its fixed property resisted deformation, variable parameters and many unpredictable changes. Theoretical research and practical application of fractal based computing have been hotspots for 30 years and will be continued. There are many pending issues awaiting solutions in this domain, thus this thematic issue containing 14 papers publishes the state-of-the-art developments in theorem and application of fractal based computing, including mathematical analysis and novel engineering applications. The topics contain fractal and multifractal features in application and solution of nonlinear odes and equation.

6

Craus, Mitică, Vlad-Sergiu Bîrlescu, and Maricel Agop. "Fractal Aspects in Classical Parallel Computing." Computers 5, no. 3 (September 12, 2016): 19. http://dx.doi.org/10.3390/computers5030019.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

SUGINO, Toshiki, Taisuke KOBAYASHI, and Kenji SUGIMOTO. "Continuous Learning using Fractal Reservoir Computing." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2018 (2018): 1A1—D13. http://dx.doi.org/10.1299/jsmermd.2018.1a1-d13.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Liu, Si Ping. "Research on Cloud Computing Strategy Based on Security Model." Applied Mechanics and Materials 644-650 (September 2014): 1835–39. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.1835.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Based on the threats of cloud computing security, combined with the principle of private cloud computing, this paper introduces the variable dimension fractal theory into the cloud computing and security policy model, and puts forwards multidimensional data model C2MDSM of the cloud computation. The model can protect 2D and 3D protection of user information in a private cloud space. Through the 3D fractal it greatly improves the user use of cloud resources, and improves the security of information, which realizes the true sense of the reasonable distribution for cloud resources. In order to verify the validity of the mathematical model and the algorithm designed in this paper, we use the MATLAB software to draw 2D and 3D fractal, and obtain the number of cloud users, security level and calculation residual results. It provides the technical reference for the research on cloud computing.

9

Levin, I. I., and M. D. Chekina. "THE PARALLEL-PIPELINED IMPLEMENTATION OF THE FRACTAL IMAGE COMPRESSION FOR RECONFIGURABLE COMPUTING SYSTEMS." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 202 (April 2021): 37–44. http://dx.doi.org/10.14489/vkit.2021.04.pp.037-044.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

The developed fractal image compression method, implemented for reconfigurable computing systems is described. The main idea parallel fractal image compression based on parallel execution pairwise comparison of domain and rank blocks. Achievement high performance occurs at the expense of simultaneously comparing maximum number of pairs. Implementation fractal image compression for reconfigurable computing systems has two critical resources, as number of input channels and FPGA Look-up Table (LUT). The main critical resource for fractal image compression is data channels, and implementation this task for reconfigurable computing systems requires parallel-pipeline computations organization replace parallel, preliminarily produced performance reduction parallel computational structure. The main critical resource for fractal image compression is data channels, and implementation this task for reconfigurable computing systems requires parallel-pipeline computations organization replace parallel computations organiation. For using parallel-pipeline computations organization, preliminarily have produce performance reduction parallel computational structure. Each operator has routed to computational structure sequentially (bit by bit) to save computational resources and reduces equipment downtime. Storing iterated functions system coefficients for image encoding has been introduced in data structure, which correlates between corresponding parameters the numbers of rank and domain blocks. Applying this approach for parallel-pipeline programs allows scaling computing structure to plurality programmable logic arrays (FPGAs). Task implementation on the reconfigurable computer system Tertius-2 containing eight FPGAs 15 000 times provides performed acceleration relatively with universal multi-core processor, and 18 – 25 times whit to existing solutions for FPGAs.

10

PRASAD, SRIJANANI ANURAG, and G. P. KAPOOR. "FRACTAL DIMENSION OF COALESCENCE HIDDEN-VARIABLE FRACTAL INTERPOLATION SURFACE." Fractals 19, no. 02 (June 2011): 195–201. http://dx.doi.org/10.1142/s0218348x11005336.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

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.

11

Khudhair, Muslim Mohsin, Adil AL-Rammahi, and Furkan Rabee. "An innovativefractal architecture model for implementing MapReduce in an open multiprocessing parallel environment." Indonesian Journal of Electrical Engineering and Computer Science 30, no. 2 (May 1, 2023): 1059. http://dx.doi.org/10.11591/ijeecs.v30.i2.pp1059-1067.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

One of the infrastructure applications that cloud computing offers as a service is parallel data processing. MapReduce is a type of parallel processing used more and more by data-intensive applications in cloud computing environments. MapReduce is based on a strategy called "divide and conquer," which uses regular computers, also called "nodes," to do processing in parallel. This paper looks at how open multiprocessing (OpenMP), the best shared-memory parallel programming model for high-performance computing, can be used with the proposed fractal network model in the MapReduce application. A well-known model, the cube, is used to compare the fractal network model and its work. Where experiments demonstrated that the fractal model is preferable to the cube model. The fractal model achieved an average speedup of 2.7 and an efficiency rate of 67.7%. In contrast, the cube model could only reach an average speedup of 2.5 and an efficiency rate of 60.4%.

12

Shams, Mudassir, Naila Rafiq, Bruno Carpentieri, and Nazir Ahmad Mir. "A New Approach to Multiroot Vectorial Problems: Highly Efficient Parallel Computing Schemes." Fractal and Fractional 8, no. 3 (March 12, 2024): 162. http://dx.doi.org/10.3390/fractalfract8030162.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

In this article, we construct an efficient family of simultaneous methods for finding all the distinct as well as multiple roots of polynomial equations. Convergence analysis proves that the order of convergence of newly constructed family of simultaneous methods is seventeen. Fractal-based simultaneous iterative algorithms are thoroughly examined. Using self-similar features, fractal-based simultaneous schemes can converge to solutions faster, saving computational time and resources necessary for solving nonlinear equations. Fractals analysis illustrates the newly developed method’s global convergence behavior when compared to single root-finding procedures for solving fractional order polynomials that arise in complex engineering applications. Some real problems from various branches of engineering along with some higher degree polynomials are considered as test examples to show the global convergence property of simultaneous methods, performance and efficiency of the proposed family of methods. Further computational efficiencies, CPU time and residual graphs are also drawn to validate the efficiency, robustness of the newly introduced family of methods as compared to the existing methods in the literature.

13

Jiang, Fan, Wei Ping Chen, and Zhong Wei Liang. "Bidirectional Fractal Test of Dust Particle." Advanced Materials Research 108-111 (May 2010): 954–59. http://dx.doi.org/10.4028/www.scientific.net/amr.108-111.954.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

To describe surface shape of the dust particle comprehensively, uses the bidirectional CCD to shoot picture of dust particle, through recognizing the bidirectional particle picture, matching the particle, computing the fractal results of identical particle in two pictures, and integrating two fractal results, obtains the dust particle bidirectional fractal. The results indicated that three fractal dimensions of spherical particle are quite closed, but the three fractal dimensions of flat type particle are significantly different.

14

Khudhair, Muslim Mohsin, Furkan Rabee, and Adil AL_Rammahi. "New efficient fractal models for MapReduce in OpenMP parallel environment." Bulletin of Electrical Engineering and Informatics 12, no. 4 (August 1, 2023): 2313–27. http://dx.doi.org/10.11591/beei.v12i4.4977.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Parallel data processing is one of the specific infrastructure applications categorized as a service provided by cloud computing. In cloud computing environments, data-intensive applications increasingly use the parallel processing paradigm known as MapReduce. MapReduce is based on a strategy called "divide and conquer," which uses ordinary computers, also called "nodes," to do processing in parallel. This paper looks at how open multiprocessing (OpenMP), the best shared-memory parallel programming model for high-performance computing, can be used in the MapReduce application using proposed fractal network models. Two fractal network models are offered, and their work is compared with a well-known network model, the hypercube. The first fractal network model achieved an average speedup of 3.239 times while an efficiency ranged from 73-95%. In the second model of the network, the speedup got to 3.236 times while keeping an efficiency of 70-92%. Furthermore, the path-finding algorithm employed in the recommended fractal network models remarkably identified all paths and calculated the shortest and longest routes.

15

Khudhair, Muslim Mohsin, Furkan Rabee, and Adil AL_Rammahi. "New efficient fractal models for MapReduce in OpenMP parallel environment." Bulletin of Electrical Engineering and Informatics 12, no. 4 (August 1, 2023): 2313–27. http://dx.doi.org/10.11591/eei.v12i4.4977.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Parallel data processing is one of the specific infrastructure applications categorized as a service provided by cloud computing. In cloud computing environments, data-intensive applications increasingly use the parallel processing paradigm known as MapReduce. MapReduce is based on a strategy called "divide and conquer," which uses ordinary computers, also called "nodes," to do processing in parallel. This paper looks at how open multiprocessing (OpenMP), the best shared-memory parallel programming model for high-performance computing, can be used in the MapReduce application using proposed fractal network models. Two fractal network models are offered, and their work is compared with a well-known network model, the hypercube. The first fractal network model achieved an average speedup of 3.239 times while an efficiency ranged from 73-95%. In the second model of the network, the speedup got to 3.236 times while keeping an efficiency of 70-92%. Furthermore, the path-finding algorithm employed in the recommended fractal network models remarkably identified all paths and calculated the shortest and longest routes.

16

CHEN, Rong-xin, Wei-bin CHEN, and Hu-sheng LIAO. "Fractal computing parallelization and implementation in TBB." Journal of Computer Applications 31, no. 3 (May 18, 2011): 839–42. http://dx.doi.org/10.3724/sp.j.1087.2011.00839.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Willson, Stephen J. "Computing fractal dimensions for additive cellular automata." Physica D: Nonlinear Phenomena 24, no. 1-3 (January 1987): 190–206. http://dx.doi.org/10.1016/0167-2789(87)90074-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Słomczyński, Wojciech, Jarosław Kwapień, and Karol Życzkowski. "Entropy computing via integration over fractal measures." Chaos: An Interdisciplinary Journal of Nonlinear Science 10, no. 1 (March 2000): 180–88. http://dx.doi.org/10.1063/1.166492.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Jia, Li. "Unified Login Authentication Method Based on Cloud Computing." Advanced Materials Research 926-930 (May 2014): 2245–48. http://dx.doi.org/10.4028/www.scientific.net/amr.926-930.2245.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

According to the single sign-on authentication mode, cloud computing unified login authentication method was put forward, and point set topology changing method was used for generating fractal random key, improved login authentication safety grade. Firstly, analyzed cloud computing login authentication system structure, and then used network public databases of fingerprint image as an example do fractal changes ring operation, generated a pseudo-random sequence, then the sequence encrypted and sent to the server for authentication through UDP. Lastly, made a simulation example.

20

LAIZET, S., and J. C. VASSILICOS. "MULTISCALE GENERATION OF TURBULENCE." Journal of Multiscale Modelling 01, no. 01 (January 2009): 177–96. http://dx.doi.org/10.1142/s1756973709000098.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

This paper presents a brief but general introduction to the physics and engineering of fractals, followed by a brief introduction to fluid turbulence generated by multiscale flow actuation. Numerical computations of such turbulent flows are now beginning to be possible because of the immersed boundary method (IBM) and terascale parallel high performance computing capabilities. The first-ever direct numerical simulation (DNS) results of turbulence generated by fractal grids are detailed and compared with recent wind tunnel measurements.

21

Popa, Bogdan, Dan Selișteanu, and Alexandra Elisabeta Lorincz. "Possibilities of Use for Fractal Techniques as Parameters of Graphic Analysis." Fractal and Fractional 6, no. 11 (November 19, 2022): 686. http://dx.doi.org/10.3390/fractalfract6110686.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Image processing remains an area that has impact on the software industry and is a field that is permanently developing in both IT and industrial contexts. Nowadays, the demand for fast computing times is becoming increasingly difficult to fulfill in the case of massive computing systems. This article proposes a particular case of efficiency for a specifically developed model for fractal generations. From the point of view of graphic analysis, the application can generate a series of fractal images. This process is analyzed and compared in this study from a programming perspective in terms of both the results at the processor level and the graphical generation possibilities. This paper presents the structure of the software and its implementation for generating fractal images using the Mandelbrot set. Starting from the complex mathematical set, the component iterations of the Mandelbrot algorithm lead to optimization variants for the calculation. The article consists of a presentation of an optimization variant based on applying parallel calculations for fractal generation. The method used in the study assumes a high grade of accuracy regarding the selected mathematical model for fractal generation and does not characterize a method specially built for a certain kind of image. A series of scenarios are analyzed, and details related to differences in terms of calculation times, starting from the more efficient proposed variant, are presented. The developed software implementation is parallelization-based and is optimized for generating a wide variety of fractal images while also providing a test package for the generated environment. The influence of parallel programming is highlighted in terms of its difference to sequential programming to, in turn, highlight recent methods of speeding up computing times. The purpose of the article is to combine the complexity of the mathematical calculation behind the fractal sets with programming techniques to provides an analysis of the graphic results from the point of view of the use of computing resources and working time.

22

House, Garvey, and Paul F. Zelhart. "Agreement between Two Methods of Computing the Fractal Dimensions of Complex Figures." Perceptual and Motor Skills 80, no. 2 (April 1995): 377–78. http://dx.doi.org/10.2466/pms.1995.80.2.377.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Agreement between two methods of computing the fractal dimensions of complex figures was examined. 16 complex figures were scanned and the fractal dimensions were computed under two conditions. There was no significant difference between the two methods.

23

Ayari, Mohamed, and Saleh Altowaijri. "The Efficiency of Surface Impedance Technique in the Transverse Wave Approach for the EM-Modeling of Fractal-Like Tree Structure used in 5G Applications." Engineering, Technology & Applied Science Research 14, no. 2 (April 2, 2024): 13216–21. http://dx.doi.org/10.48084/etasr.6744.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Fractal antenna technology is a promising approach for 5G applications because its complex nature offers optimization potential in terms of time and space trade-offs. However, the computational effort required to analyze such antennas is significant. This paper investigates the Advanced Transverse Wave Approach (ATWA), which utilizes the surface impedance technique to improve simulation efficiency. This study introduces and analyzes a fractal-like 5G tree structure, displaying improved computational accuracy and efficacy, as well as peak memory utilization compared to current works. The proposed approach demonstrates significant effectiveness in enhancing the performance of complex fractal antennas for 5G technology and shows promise for integration with cloud, fog, and edge computing environments. This integration could potentially optimize data processing and network efficiency in these advanced computing landscapes.

24

Dobrescu, Gianina, Florica Papa, Daniela Culita, Ioan Balint, and Niculae I. Ionescu. "Cerofolini’s Model and the Fractal Adsorption Isotherms." Fractal and Fractional 7, no. 3 (March 14, 2023): 262. http://dx.doi.org/10.3390/fractalfract7030262.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

The close link between the roughness of a surface and its adsorptive properties in Cerofolini’s model yields, with an adequate choice of adsorption energy, the well-known Dubinin-Radushkevich or Freundlich adsorption isotherms. Assuming fractal behavior concerning both energetic and geometric surface heterogeneities described by the power-law expressions and fractal dimensions, the paper will develop some fractal adsorption isotherms. Using our theoretical approach, fractal isotherms will provide insights not only into the fractal behavior of the surface geometry but also into the fractal energetic heterogeneities, implying that a sorbent does not need to be porous to apply a fractal isotherm: adsorption on “flat” surfaces can also be described by fractal isotherms and fractal dimensions related to energetic disorders. For example, the theory will be applied to computing the energetic fractal dimensions of some nanoparticle catalysts, Rh/Al2O3, Rh/TiO2, and Rh/WO3.

25

Гулаков, Василий, Vasiliy Gulakov, Сергей Клепинин, and Sergey Klepinin. "Performance improving of fractal encoding based on perceptual hash functions." Bulletin of Bryansk state technical university 2014, no. 4 (December 5, 2014): 141–45. http://dx.doi.org/10.12737/23050.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

The application of fractal encodingfor image recognition is considered, system requirements to computing resources of classic fractal encoding system implementation is analyzed. The proposal for improving performance characteristics is suggested and implemented, obtained results and comparison of two implementations are provided in the last part of article.

26

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

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

The objective of this paper is to consider the use of fractal geometry as a tool for the study of non-smooth and discontinuous objects for which Euclidean coordinate is not able to fully describe their shapes. We categorized the methods for computing fractal dimension with a discussion into that. We guide readers up to the point they can dig into the literature, but with more advanced methods that researchers are developing. Considerations show that is necessary to understand the numerous theoretical and experimental results concerning searching of the conformality before evaluating the fractal dimension to our own objects. We suggested examining a cloud of points of growth of fracture surface at laboratory using CATIA - Digitized Shape Editor software in order to reconstruct the surface (CAD model). Then, the author carried out measurement/calculation of more accurate fractal dimension which are introduced by [1] in the other paper as Part II.

27

Yoon, Moon Chul, and Do Hun Chin. "Roundness Modeling Using Fractal Interpolation." Key Engineering Materials 329 (January 2007): 521–26. http://dx.doi.org/10.4028/www.scientific.net/kem.329.521.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

There are many modelling methods using theoretical and experimental data. Recently, fractal interpolation methods have been widely used to estimate and analyse various data. Due to the chaotic nature of dynamic roundness profile data in roundness, some desirable method must be used for the analysis of data which is natural to sequential data. Fractal analysis used in this paper is within the scope of the fractal interpolation and fractal dimension. Also, two methods for computing the fractal dimension have been introduced, which can calculate the fractal dimension of typical dynamic roundness profile data according to the number of data points in which the fixed data are generally lower than 120 data points. This fractal analysis shows a possible prediction and analysis of roundness profile that has some different roundness profile in round shape operation such as cylindrical grinding, turning, drilling and boring.

28

Xu, Shan Hua, Bin Shi, and Xin Long Yang. "The Research of Corroded Stell-Structured Surface Characteristic." Advanced Materials Research 368-373 (October 2011): 1477–81. http://dx.doi.org/10.4028/www.scientific.net/amr.368-373.1477.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Parameter method and fractal theory are carried out for appraising corroded the stell-structured surface of the atmospheric acid corroded the environment. Provided three dimensional parameter definitions. reference datum and computing method of fractal dimension, adopted non-contact-type infiniteFocus full-automatic zooming 3-D superficial measuring apparatus and MATLAB software to deal with the resulting data of the experiment, the results show that parameters method and fractal theory to comprehensive evaluation of corrosion surface of steel structure is more reliability.

29

Remo, Lynn M., Jerome N. Ramirez, and Leonora G. Evangelista. "A Fractal Analysis on the Population Distribution of Bukidnon." Asia Pacific Journal of Social and Behavioral Sciences 10 (July 18, 2017): 10. http://dx.doi.org/10.57200/apjsbs.v10i0.65.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

This paper described and analyzed the population distribution of Bukidnon. A fractal analysis was used by computing the fractal dimensions of the population distribution of the province. Data are based on the population of 20 municipalities and two (2) cities in 16 years, from 1995 to 2010. The results showed that there is a slight decrease of fractal dimensions which implies that there is an approximately equal population in the municipalities over a period. Various conditions account for the decrease of variability in the population distribution. It may be attributed to their economic situations and cultural practices.Keywords: Fractal analysis, population distribution, Bukidnon, municipalities, cities

30

EPITROPAKIS, MICHAEL G., and MICHAEL N. VRAHATIS. "STUDYING THE BASIN OF CONVERGENCE OF METHODS FOR COMPUTING PERIODIC ORBITS." International Journal of Bifurcation and Chaos 21, no. 08 (August 2011): 2079–106. http://dx.doi.org/10.1142/s0218127411029653.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Starting from the well-known Newton's fractal which is formed by the basin of convergence of Newton's method applied to a cubic equation in one variable in the field ℂ, we were able to find methods for which the corresponding basins of convergence do not exhibit a fractal-like structure. Using this approach we are able to distinguish reliable and robust methods for tackling a specific problem. Also, our approach is illustrated here for methods for computing periodic orbits of nonlinear mappings as well as for fixed points of the Poincaré map on a surface of section.

31

WEI, WEI, JIANCHAO CAI, XIANGYUN HU, PING FAN, QI HAN, JINGE LU, CHU-LIN CHENG, and FENG ZHOU. "A NUMERICAL STUDY ON FRACTAL DIMENSIONS OF CURRENT STREAMLINES IN TWO-DIMENSIONAL AND THREE-DIMENSIONAL PORE FRACTAL MODELS OF POROUS MEDIA." Fractals 23, no. 01 (March 2015): 1540012. http://dx.doi.org/10.1142/s0218348x15400125.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

The fractal dimension of random walker (FDRW) is an important parameter for description of electrical conductivity in porous media. However, it is somewhat empirical in nature to calculate FDRW. In this paper, a simple relation between FDRW and tortuosity fractal dimension (TFD) of current streamlines is derived, and a novel method of computing TFD for different generations of two-dimensional Sierpinski carpet and three-dimensional Sierpinski sponge models is presented through the finite element method, then the FDRW can be accordingly predicted; the proposed relation clearly shows that there exists a linear relation between pore fractal dimension (PFD) and TFD, which may have great potential in analysis of transport properties in fractal porous media.

32

Paramanathan, P., and R. Uthayakumar. "An algorithm for computing the fractal dimension of waveforms." Applied Mathematics and Computation 195, no. 2 (February 2008): 598–603. http://dx.doi.org/10.1016/j.amc.2007.05.011.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Khorsheed, Murad B., Qasim M. Zainel, Oday A. Hassen, and Saad M. Darwish. "The Application of Fractal Transform and Entropy for Improving Fault Tolerance and Load Balancing in Grid Computing Environments." Entropy 22, no. 12 (December 15, 2020): 1410. http://dx.doi.org/10.3390/e22121410.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effective and reliable. A fractal dimension of a cloud of points gives an estimate of the intrinsic dimensionality of the data in that space. The main drawback of this technique is the long computing time. The main contribution of the suggested work is to investigate the effect of fractal transform by adding R-tree index structure-based entropy to existing grid computing models to obtain a balanced infrastructure with minimal fault. In this regard, the presented work is going to extend the commonly scheduling algorithms that are built based on the physical grid structure to a reduced logical network. The objective of this logical network is to reduce the searching in the grid paths according to arrival time rate and path’s bandwidth with respect to load balance and fault tolerance, respectively. Furthermore, an optimization searching technique is utilized to enhance the grid performance by investigating the optimum number of nodes extracted from the logical grid. The experimental results indicated that the proposed model has better execution time, throughput, makespan, latency, load balancing, and success rate.

34

PHINYOMARK, ANGKOON, PORNCHAI PHUKPATTARANONT, and CHUSAK LIMSAKUL. "APPLICATIONS OF VARIANCE FRACTAL DIMENSION: A SURVEY." Fractals 22, no. 01n02 (March 2014): 1450003. http://dx.doi.org/10.1142/s0218348x14500030.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Chaotic dynamical systems are pervasive in nature and can be shown to be deterministic through fractal analysis. There are numerous methods that can be used to estimate the fractal dimension. Among the usual fractal estimation methods, variance fractal dimension (VFD) is one of the most significant fractal analysis methods that can be implemented for real-time systems. The basic concept and theory of VFD are presented. Recent research and the development of several applications based on VFD are reviewed and explained in detail, such as biomedical signal processing and pattern recognition, speech communication, geophysical signal analysis, power systems and communication systems. The important parameters that need to be considered in computing the VFD are discussed, including the window size and the window increment of the feature, and the step size of the VFD. Directions for future research of VFD are also briefly outlined.

35

Li, Jie, Shi Liu, Yao Song Huang, and Jing Lei. "Analysis of Multi-Scale and Multi-Fractal Characteristic of Flame Optical Radiation Signal." Applied Mechanics and Materials 48-49 (February 2011): 219–23. http://dx.doi.org/10.4028/www.scientific.net/amm.48-49.219.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

In this paper, we take flame optical radiation signal in low-frequency on a gas combustion test-bed as research objects, multi-fractal spectrum can analyze the micro structures and characteristic of flame optical radiation time series is corroborated through computing. We research the trend of the sharps and key parameters of the multi-fractal spectrum under different scales. Result shows that as one of the most important parameters of multi-fractal spectrum, the width of the multi-fractal spectrum has the significant correlation with variance, which reflects the status of the combustion stability, and the accuracy of the combustion stability judgement is increased further through multi-scale and multi-fractal analysis. As a developmental assisted analysis method, the multi-scale and multi-fractal analysis method can effectively reveal the dynamic process of the flame radiation, which provides to the operation staff with multi-angle supplementary method in judging the combustion stability.

36

Paluch, Michał, and Lidia Jackowska-Strumiłło. "Hybrid Models Combining Technical and Fractal Analysis with ANN for Short-Term Prediction of Close Values on the Warsaw Stock Exchange." Applied Sciences 8, no. 12 (December 3, 2018): 2473. http://dx.doi.org/10.3390/app8122473.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

This paper presents new methods and models for forecasting stock prices and computing hybrid models, combining analytical and neural approaches. First, technical and fractal analyses are conducted and selected stock market indices calculated, such as moving averages and oscillators. Next, on the basis of these indices, an artificial neural network (ANN) provides predictions one day ahead of the closing prices of the assets. New technical analysis indicators using fractal modeling are also proposed. Three kinds of hybrid model with different degrees of fractal analysis were considered. The new hybrid modeling approach was compared to previous ANN-based prediction methods. The results showed that the hybrid model with fractal analysis outperforms other models and is more robust over longer periods of time.

37

B, Shadaksharappa. "High Availability and Fault Tolerance in AWS." International Journal of Innovative Research in Information Security 09, no. 03 (June 23, 2023): 66–72. http://dx.doi.org/10.26562/ijiris.2023.v0903.03.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

With the increasing adoption of cloud computing, ensuring high availability and fault tolerance has become paramount for organizations. Amazon Web Services (AWS) offers a robust infrastructure for hosting applications, but it requires careful architectural design and implementation to achieve desired levels of availability and fault tolerance. This research paper explores two innovative concepts, namely Cloud Fractal and Decentralized Replication and Orchestration, and their application in achieving high availability and fault tolerance in AWS. We present a comprehensive analysis of these concepts and provide practical guidelines for their implementation in real-world scenarios. Our findings demonstrate the effectiveness of Cloud Fractal and Decentralized Replication and Orchestration in enhancing the reliability and resilience of AWS deployments. Keywords: Fault Isolation, High Availability, Load Balancing, Auto-scaling, Disaster Recovery, Data Replication, Backup and Restore, Fault Tolerance, Cloud Computing, Amazon Elastic Compute Cloud (EC2), Amazon Relational Database Service (RDS), Amazon Simple Storage Service (S3), AWS Elastic Load Balancer (ELB), Complexity, Operational Management, Cloud Fractal, AWS Lambda, Amazon SQS, Decentralized Replication and Orchestration (DOI).

38

ZHU, JIALI, LI TIAN, JIAQI FAN, and LIFENG XI. "TWO-POINT RESISTANCES IN SAILBOAT FRACTAL NETWORKS." Fractals 28, no. 02 (March 2020): 2050027. http://dx.doi.org/10.1142/s0218348x20500279.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

The two-point resistance of fractal network has been studied extensively by mathematicians and physicists. In this paper, for a class of self-similar networks named sailboat networks, we obtain a recursive algorithm for computing resistance between any two nodes, using elimination principle, substitution principle and local sum rules on effective resistance.

39

Du, Jianwei, Zhengguang Xu, Zhichun Mu, Yuan Yan Tang, Limin Cui, and Tianxuan Duan. "EMD fractal feature extraction technique in fingerprint of medicinal herbs." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 04 (July 2015): 1550022. http://dx.doi.org/10.1142/s0219691315500228.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

This paper proposes the fractal features for glycyrrhiza fingerprint of medicinal herbs, to obtain the intrinsic mode functions (IMFs) from high to low frequency by using empirical mode decomposition (EMD). The EMD fractal features are extracted through computing the fractal dimensions of each IMF. The novel approach is applied to the recognition of the three types of glycyrrhiza fingerprints. Experiments show that EMD fractal features have better recognition rate than that of the traditional ones in the case of concentration-change, i.e. the number of peak and peak drift of sample which has slight changes. An existing method to extract the fractal features for fingerprint of medicinal herbs based on wavelet transform, which is called fractal-wavelet features, was presented. This method has anti-jamming property against the change of samples concentration. However, the recognition rate based on fractal-wavelet features is not satisfactory when fingerprint of medicinal herbs has some slight concentrations changes, the number of peak and peak drift of samples are processed in the special situation.

40

Feldman, A., G. Provan, and A. Van Gemund. "A Model-Based Active Testing Approach to Sequential Diagnosis." Journal of Artificial Intelligence Research 39 (September 29, 2010): 301–34. http://dx.doi.org/10.1613/jair.3031.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Model-based diagnostic reasoning often leads to a large number of diagnostic hypotheses. The set of diagnoses can be reduced by taking into account extra observations (passive monitoring), measuring additional variables (probing) or executing additional tests (sequential diagnosis/test sequencing). In this paper we combine the above approaches with techniques from Automated Test Pattern Generation (ATPG) and Model-Based Diagnosis (MBD) into a framework called FRACTAL (FRamework for ACtive Testing ALgorithms). Apart from the inputs and outputs that connect a system to its environment, in active testing we consider additional input variables to which a sequence of test vectors can be supplied. We address the computationally hard problem of computing optimal control assignments (as defined in FRACTAL) in terms of a greedy approximation algorithm called FRACTAL-G. We compare the decrease in the number of remaining minimal cardinality diagnoses of FRACTAL-G to that of two more FRACTAL algorithms: FRACTAL-ATPG and FRACTAL-P. FRACTAL-ATPG is based on ATPG and sequential diagnosis while FRACTAL-P is based on probing and, although not an active testing algorithm, provides a baseline for comparing the lower bound on the number of reachable diagnoses for the FRACTAL algorithms. We empirically evaluate the trade-offs of the three FRACTAL algorithms by performing extensive experimentation on the ISCAS85/74XXX benchmark of combinational circuits.

41

Zhao, Hui, Jian Liu, and Hong Jun Wang. "Recognition of Working Condition in Cement Rotary Kiln Based on Generalized Dimensions." Applied Mechanics and Materials 740 (March 2015): 676–79. http://dx.doi.org/10.4028/www.scientific.net/amm.740.676.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

There has been a tight correlation between the change of the cement rotary kiln carrent and operation conditions, such as the kiln thermal condition, the thickness of the crust, the kiln tyre collapse and so on. Considering the different fractal characteristics that cement rotary kiln current signal exhibit in different conditions, this paper has study on the generalized fractal dimension of kiln current signal under different working conditions as the characteristic parameter. The levels and trends of rotary kiln current and working condition will be identified by computing the maximum correlation coefficient according to the generalized fractal dimension of detected signal and of cement rotary kiln current under different working condition.

42

Bembir, P. "African fractals as a tool for transformative education in Africa." Contemporary Journal of African Studies 6, no. 1 (May 31, 2019): 1–26. http://dx.doi.org/10.4314/contjas.v6i1.1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Nature is replete with repetitive patterns in diminishing scales. Similarly, cultures produce recursive patterns that characterize their specific social, cultural, economic and political organisation. These self-similar, variously scaled and mostly infinitive patterns are called fractals. The uniqueness of African fractals emanates from the culture of the African peoples. Particular elements of these fractals have contributed immensely in mathematical learning especially in modern computing. This paper contends that the inclusion of African fractal education in curricula at all levels in Africa have the potential to contribute to better understanding of African identity, and promote African centred education that forestalls the alienation of the African from their environment. The paper argues that the teaching of African fractals in Africa is a needed project to facilitate understanding of the intricacies between nature and humans. It should deepen understanding about the concept of embedded humanity expressed in ideas of Ubuntu; and help awaken African consciousness about possibilities beyond empiricism. Recommendations are made on ways to include African fractals in the syllabus in Africa using the Ghana’s pre-tertiary level (Senior High School) as an example.

43

Fuss, Franz Konstantin. "A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications." Computational and Mathematical Methods in Medicine 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/178476.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal’s time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.

44

Mohammed, Arkan. "Performance evolution of a fractal dimension estimated by an escape time algorithm." Boletim da Sociedade Paranaense de Matemática 38, no. 7 (October 14, 2019): 109–24. http://dx.doi.org/10.5269/bspm.v38i7.44496.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

The non-geometric and irregular objects are considered as complex patterns. The geometric complexity is measured as space lling capacity by a factor known as a fractal dimension. Dierent techniques are proposed to nd this complexity measure according to the properties of the pattern. This paper is aimed to introduce a method for counting the dimension of the lled Julia fractal set generated by the Escape Time Algorithm using the method of spreading the points inside the proposed window. The resulted dimension is called Escape Time dimension. A new method to compute a correlation dimension of the Filled Julia fractal set is also proposed based on the Grassberger-Procaccia algorithm by computing the correlation function. A log-log graph of the correlation function versus the distances between every pair of points in the lled Julia fractal set is an approximation of the correlation dimension. Finally, a comparison between these two fractal dimensions of the led Julia fractal set which is generated by the Escape Time Algorithm is presented to show the efficiency of the proposed method.

45

Huang, Penghe, Dongyan Li, and Huimin Zhao. "An Improved Robust Fractal Image Compression Based on M-Estimator." Applied Sciences 12, no. 15 (July 27, 2022): 7533. http://dx.doi.org/10.3390/app12157533.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

In this paper, a robust fractal image compression method based on M-estimator is presented. The proposed method applies the M-estimator to the parameter estimation in the fractal encoding procedure using Huber and Tukey’s robust statistics. The M-estimation reduces the influence of the outliers and makes the fractal encoding algorithm robust to the noisy image. Meanwhile, the quadtree partitioning approach has been used in the proposed methods to improve the efficiency of the encoding algorithm, and some unnecessary computations are eliminated in the parameter estimation procedures. The experimental results demonstrate that the proposed method is insensitive to the outliers in the noisy corrupted image. The comparative data shows that the proposed method is superior in both the encoding time and the quality of retrieved images over other robust fractal compression algorithms. The proposed algorithm is useful for multimedia and image archiving, low-cost consumption applications and progressive image transmission of live images, and in reducing computing time for fractal image compression.

46

Shankar Beriha, Siba. "Computer Aided Diagnosis System To Distinguish Adhd From Similar Behavioral Disorders." Biomedical and Pharmacology Journal 11, no. 2 (June 12, 2018): 1135–41. http://dx.doi.org/10.13005/bpj/1474.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

ADHD is one of the most prevalent psychiatric disorder of childhood, characterized by inattention and distractibility, with or without accompanying hyperactivity. The main aim of this research work is to develop a Computer Aided Diagnosis (CAD) technique with minimal steps that can differentiate the ADHD children from the other similar children behavioral disorders such as anxiety, depression and conduct disorder based on the Electroencephalogram (EEG) signal features and symptoms. The proposed technique is based on soft computing and bio inspired computing algorithms. Four non-linear features are extracted from the EEG such as Higuchi fractal dimension, Katz fractal dimension, Sevick fractal dimension and Lyapunov exponent and 14 symptoms which are most important in differentiation are extracted by experts in the field of psychiatry. Particle Swarm Optimization (PSO) tuned Back Propagation Neural Network (BPNN) and PSO tuned Radial Basis Function (RBF) employed as a classifier. By investigating these integrated features, we obtained good classification accuracy. Simulation results suggest that the proposed technique offer high potential in the diagnosis of ADHD and may be a good preliminary assistant for psychiatrists in diagnosing high risk behavioral disorders of children.

47

Ghazwani, Haleemah, Muhammad Faisal Nadeem, Faiza Ishfaq, and Ali N. A. Koam. "On Entropy of Some Fractal Structures." Fractal and Fractional 7, no. 5 (April 30, 2023): 378. http://dx.doi.org/10.3390/fractalfract7050378.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Abstract:

Shannon entropy, also known as information entropy or entropy, measures the uncertainty or randomness of probability distribution. Entropy is measured in bits, quantifying the average amount of information required to identify an event from the distribution. Shannon’s entropy theory initiates graph entropies and develops information-theoretic magnitudes for structural computational evidence of organic graphs and complex networks. Graph entropy measurements are valuable in several scientific fields, such as computing, chemistry, biology, and discrete mathematics. In this study, we investigate the entropy of fractal-type networks by considering cycle, complete, and star networks as base graphs using degree-based topological indices.

48

Eglash, Ron, Mukkai Krishnamoorthy, Jason Sanchez, and Andrew Woodbridge. "Fractal Simulations of African Design in Pre-College Computing Education." ACM Transactions on Computing Education 11, no. 3 (October 2011): 1–14. http://dx.doi.org/10.1145/2037276.2037281.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Uthayakumar, R., and P. Paramanathan. "An algorithm for computing fractal dimension of rectifiable irregular graphs." Applied Mathematics and Computation 190, no. 1 (July 2007): 305–8. http://dx.doi.org/10.1016/j.amc.2007.01.048.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Breban, R., and H. E. Nusse. "Computing fractal dimension in supertransient systems directly, rapidly and reliably." Europhysics Letters (EPL) 76, no. 6 (December 2006): 1036–42. http://dx.doi.org/10.1209/epl/i2006-10407-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Fractal computing'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles