Log in

Relevant bibliographies by topics / Box counting fractal dimension / Journal articles

To see the other types of publications on this topic, follow the link: Box counting fractal dimension.

Journal articles on the topic 'Box counting fractal dimension'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Box counting fractal dimension.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

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

Full text

Abstract:

Fractal analysis estimates the metric dimension and complexity of the spatial configuration of different anatomical structures. This allows the use of this mathematical method for morphometry in morphology and clinical medicine. Two methods of fractal analysis are most often used for fractal analysis of linear fractal objects: the Box counting method (Grid method) and the Caliper method (Richardson’s method, Perimeter stepping method, Ruler method, Divider dimension, Compass dimension, Yard stick method). The aim of the research is a comparative analysis of two methods of fractal analysis – Bo

APA, Harvard, Vancouver, ISO, and other styles

2

Chen, Xiang, Jingchao Li, Hui Han, and Yulong Ying. "Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors." Royal Society Open Science 5, no. 5 (2018): 180087. http://dx.doi.org/10.1098/rsos.180087.

Full text

Abstract:

Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the H

APA, Harvard, Vancouver, ISO, and other styles

3

CHEN, WEN-SHIUNG, and SHANG-YUAN YUAN. "SOME FRACTAL DIMENSION ESTIMATE ALGORITHMS AND THEIR APPLICATIONS TO ONE-DIMENSIONAL BIOMEDICAL SIGNALS." Biomedical Engineering: Applications, Basis and Communications 14, no. 03 (2002): 100–108. http://dx.doi.org/10.4015/s1016237202000152.

Full text

Abstract:

Fractals can model many classes of time-series data. The fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales. The covering methods are a class of efficient approaches, e.g., box-counting (BC) method, to estimate the fractal dimension. In this paper, the differential box-counting (DBC) approach, originally for 2-D applications, is modified and applied to 1-D case. In addition, two algorithms, called 1-D shifting-DBC (SDBC-1D) and 1-D scanning-BC (SBC-1D), are also proposed for 1-D signal analysis. The fracta

APA, Harvard, Vancouver, ISO, and other styles

4

Meng, Xianmeng, Pengju Zhang, Jing Li, Chuanming Ma, and Dengfeng Liu. "The linkage between box-counting and geomorphic fractal dimensions in the fractal structure of river networks: the junction angle." Hydrology Research 51, no. 6 (2020): 1397–408. http://dx.doi.org/10.2166/nh.2020.082.

Full text

Abstract:

Abstract In the past, a great deal of research has been conducted to determine the fractal properties of river networks, and there are many kinds of methods calculating their fractal dimensions. In this paper, we compare two most common methods: one is geomorphic fractal dimension obtained from the bifurcation ratio and the stream length ratio, and the other is box-counting method. Firstly, synthetic fractal trees are used to explain the role of the junction angle on the relation between two kinds of fractal dimensions. The obtained relationship curves indicate that box-counting dimension is d

APA, Harvard, Vancouver, ISO, and other styles

5

Jiang, Shiguo, and Desheng Liu. "Box-Counting Dimension of Fractal Urban Form." International Journal of Artificial Life Research 3, no. 3 (2012): 41–63. http://dx.doi.org/10.4018/jalr.2012070104.

Full text

Abstract:

The difficulty to obtain a stable estimate of fractal dimension for stochastic fractal (e.g., urban form) is an unsolved issue in fractal analysis. The widely used box-counting method has three main issues: 1) ambiguities in setting up a proper box cover of the object of interest; 2) problems of limited data points for box sizes; 3) difficulty in determining the scaling range. These issues lead to unreliable estimates of fractal dimensions for urban forms, and thus cast doubt on further analysis. This paper presents a detailed discussion of these issues in the case of Beijing City. The authors

APA, Harvard, Vancouver, ISO, and other styles

6

FATHALLAH-SHAYKH, HASSAN M. "FRACTAL DIMENSION OF THE DROSOPHILA CIRCADIAN CLOCK." Fractals 19, no. 04 (2011): 423–30. http://dx.doi.org/10.1142/s0218348x11005476.

Full text

Abstract:

Fractal geometry can adequately represent many complex and irregular objects in nature. The fractal dimension is typically computed by the box-counting procedure. Here I compute the box-counting and the Kaplan-Yorke dimensions of the 14-dimensional models of the Drosophila circadian clock. Clockwork Orange (CWO) is transcriptional repressor of direct target genes that appears to play a key role in controlling the dynamics of the clock. The findings identify these models as strange attractors and highlight the complexity of the time-keeping actions of CWO in light-day cycles. These fractals are

APA, Harvard, Vancouver, ISO, and other styles

7

PERFECT, E., and B. DONNELLY. "BI-PHASE BOX COUNTING: AN IMPROVED METHOD FOR FRACTAL ANALYSIS OF BINARY IMAGES." Fractals 23, no. 01 (2015): 1540010. http://dx.doi.org/10.1142/s0218348x15400101.

Full text

Abstract:

Many natural systems are irregular and/or fragmented, and have been interpreted to be fractal. An important parameter needed for modeling such systems is the fractal dimension, D. This parameter is often estimated from binary images using the box-counting method. However, it is not always apparent which fractal model is the most appropriate. This has led some researchers to report different D values for different phases of an analyzed image, which is mathematically untenable. This paper introduces a new method for discriminating between mass fractal, pore fractal, and Euclidean scaling in imag

APA, Harvard, Vancouver, ISO, and other styles

8

Górski, A. Z., M. Stróż, P. Oświȩcimka, and J. Skrzat. "Accuracy of the box-counting algorithm for noisy fractals." International Journal of Modern Physics C 27, no. 10 (2016): 1650112. http://dx.doi.org/10.1142/s0129183116501126.

Full text

Abstract:

The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude [Formula: see text]. The accuracy of calculated numerical values of the fractal dimensions is analyzed as a function of [Formula: see text] for different sizes of the data sample. In particular, it has been found that even in case of pure fractals ([Formula: see text]) as well as for tiny noise ([Formula: see text]) one has considerable error for the calculated exponents of order 0.01. For larger noise the error is growing up to 0.1 an

APA, Harvard, Vancouver, ISO, and other styles

9

MASTERS, BARRY R. "FRACTAL ANALYSIS OF NORMAL HUMAN RETINAL BLOOD VESSELS." Fractals 02, no. 01 (1994): 103–10. http://dx.doi.org/10.1142/s0218348x94000090.

Full text

Abstract:

The fractal dimension of the pattern of retinal blood vessels in the normal human eye was calculated. Photomontages were constructed from 10 red-free retinal photographs. Manual tracings of the vessels were made. Digital images of the tracings were analyzed on a computer using the box-counting method to determine the fractal dimension. The mean value and standard deviation of the fractal dimension (box-counting dimension), computed as described in the Methods section, is 1.70 ± 0.02 (N = 10). The use of standard methods for both data acquisition and computer assisted box-counting to determine

APA, Harvard, Vancouver, ISO, and other styles

10

Yang, Zon-Yee, and Jian-Liang Juo. "Interpretation of sieve analysis data using the box-counting method for gravelly cobbles." Canadian Geotechnical Journal 38, no. 6 (2001): 1201–12. http://dx.doi.org/10.1139/t01-052.

Full text

Abstract:

In fractal theory, the fractal dimension (D) is a measure of the complexity of particle distribution in nature. It can provide a description of how much space a particle set fills. The box-counting method uses squared grids of various sizes to cover the particles to obtain a box dimension. This sequential counting concept is analogous to the sieve analysis test using stacked sieves. In this paper the box-counting method is applied to describe the particle-size distribution of gravelly cobbles. Three approaches to obtain the fractal dimension are presented. In the first approach the data obtain

APA, Harvard, Vancouver, ISO, and other styles

11

KYRIACOS, S., S. BUCZKOWSKI, F. NEKKA, and L. CARTILIER. "A MODIFIED BOX-COUNTING METHOD." Fractals 02, no. 02 (1994): 321–24. http://dx.doi.org/10.1142/s0218348x94000417.

Full text

Abstract:

Fractal geometry has been widely used to characterize irregular structures. Our interest in applying this concept in biomedical research leads us to the conclusion that there are no standard methods. In order to objectively set parameters involved in the estimation of fractal dimension, a significantly more accurate and efficient box-counting method based on a new algorithm was developed. Measurements of mathematical objects with known fractal dimension was performed using the traditional method and the proposed modification. The latter always yields results with less than 1% difference from t

APA, Harvard, Vancouver, ISO, and other styles

12

Pothiyodath, Nishanth, and Udayanandan Kandoth Murkoth. "Fractals and music." Momentum: Physics Education Journal 6, no. 2 (2022): 119–28. http://dx.doi.org/10.21067/mpej.v6i2.6796.

Full text

Abstract:

Many natural phenomena we find in our surroundings, are fractals. Studying and learning about fractals in classrooms is always a challenge for both teachers and students. We here show that the sound of musical instruments can be used as a good resource in the laboratory to study fractals. Measurement of fractal dimension which indicates how much fractal content is there, is always uncomfortable, because of the size of the objects like coastlines and mountains. A simple fractal source is always desirable in laboratories. Music serves to be a very simple and effective source for fractal dimensio

APA, Harvard, Vancouver, ISO, and other styles

13

Al-Janabi, Israa Mohsin Kadhim, Zahraa Ahmed AL-Mammori, Sabah Mohammed Abd Mosehab, et al. "An Effective Method for Compute the Roughness of Fractal Facades Based on Box-Counting Dimension (D_b)." BIO Web of Conferences 97 (2024): 00037. http://dx.doi.org/10.1051/bioconf/20249700037.

Full text

Abstract:

Benoit Mandelbrot coined the word “fractal” in the late 1970s, but an object is now defined as fractals in form known to artists and mathematicians for centuries. A fractal object is self-similar in that the subsections of the object are somewhat similar to the whole object. No matter how small the subdivision is, the subsection contains no less detail than the whole. Atypical example of a fractal body is the “snowflake curve” (invented by Helga von Koch (1870-1924) in 1904. There are as many relationships between architecture, the arts, and mathematics as symmetry. The golden ratio, the Fibon

APA, Harvard, Vancouver, ISO, and other styles

14

Bonou, Malomon Aimé, Cocou Hubert Hounsossou, Epiphane Ayinon, Kossi Armel Helou, Julien Dossou, and Olivier Biaou. "High histological grade breast cancer morphological evaluation on mammogram using the box-counting fractal dimension." International Journal of Biomolecules and Biomedicine (IJBB) 11, no. 1 (2020): 15–20. https://doi.org/10.5281/zenodo.8318514.

Full text

Abstract:

To evaluate the high-grade breast cancer morphological complexity on mammogram. We conducted a retrospective study using an open source data got from <em>figshare repository</em>. These anonymized data were collected and used for a study approved by the institutional review board. Cranio-Caudal and Medio-lateral mammograms and their tumor segmented images from 66 patients subdivided in two groups high histological grade (n=23) low-grade (low and intermediate, n=41). From breast cancer image segmentation, we extracted fractal dimension using <em>Fraclac</em>, plugin of <em>ImageJ

APA, Harvard, Vancouver, ISO, and other styles

15

Juwitarty, Novita Anggraini, Kosala Dwidja Purnomo, and Kiswara Agung Santoso. "PENDETEKSIAN CITRA DAUN TANAMAN MENGGUNAKAN METODE BOX COUNTING." Majalah Ilmiah Matematika dan Statistika 20, no. 1 (2020): 35. http://dx.doi.org/10.19184/mims.v20i1.17221.

Full text

Abstract:

Different types of plants make identification difficult. Therefore, we need a system that can identify the similarity of the leaves based on a reference leaf. Extraction can be done by taking one part of the plant and the most easily obtained part is the leaf part. Natural objects such as leaves have irregular shapes and are difficult to measure, but this can be overcome by using fractal dimensions. In this research, image detection of plant leaves will be carried out using the box counting method. The box counting method is a method of calculating fractal dimensions by dividing images into sm

APA, Harvard, Vancouver, ISO, and other styles

16

Wang, Ji Zhe, and Qing Jie Guan. "Numerical Simulation of Cell Growth Pattern and Determination of Fractal Dimension of Cell Cluster." Advanced Materials Research 690-693 (May 2013): 1229–33. http://dx.doi.org/10.4028/www.scientific.net/amr.690-693.1229.

Full text

Abstract:

Life system behaves self-similar properties from microcosms to macrostructure. Based on the cell growth roles, the cell cluster growth process is simulated. The sandbox method and box counting are used for determining the fractal dimension of cell associated with the geometrical structure of growing deterministic fractals. The fractal dimension of cell shape is estimated according to the slope of line between the numbers of boxes and box size in double logarithm coordinates.

APA, Harvard, Vancouver, ISO, and other styles

17

Lee, Minhyeok, and Soyeon Lee. "Box-Counting Dimension Sequences of Level Sets in AI-Generated Fractals." Fractal and Fractional 8, no. 12 (2024): 730. https://doi.org/10.3390/fractalfract8120730.

Full text

Abstract:

We introduce a mathematical framework to characterize the hierarchical complexity of AI-generated fractals within the finite resolution constraints of digital images. Our method analyzes images produced by text-to-image models at multiple intensity thresholds, employing a discrete level set approach and box-counting dimension estimates. By conducting experiments on fractals created with the FLUX model at a resolution of 128×128, we identify a fully monotonic behavior in the dimension sequences for various box sizes, with inter-scale correlations surpassing 0.95. Pattern-specific dimensional gr

APA, Harvard, Vancouver, ISO, and other styles

18

Deng, Yuqian, Xiuxiong Liu, and Yongping Zhang. "Fractal Dimension Analysis of the Julia Sets of Controlled Brusselator Model." Discrete Dynamics in Nature and Society 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/8234108.

Full text

Abstract:

Fractal theory is a branch of nonlinear scientific research, and its research object is the irregular geometric form in nature. On account of the complexity of the fractal set, the traditional Euclidean dimension is no longer applicable and the measurement method of fractal dimension is required. In the numerous fractal dimension definitions, box-counting dimension is taken to characterize the complexity of Julia set since the calculation of box-counting dimension is relatively achievable. In this paper, the Julia set of Brusselator model which is a class of reaction diffusion equations from t

APA, Harvard, Vancouver, ISO, and other styles

19

AHAMMER, H., and M. MAYRHOFER-REINHARTSHUBER. "IMAGE PYRAMIDS FOR CALCULATION OF THE BOX COUNTING DIMENSION." Fractals 20, no. 03n04 (2012): 281–93. http://dx.doi.org/10.1142/s0218348x12500260.

Full text

Abstract:

The fractal dimensions of real world objects are commonly investigated using digital images. Unfortunately, these images are unable to represent an infinitesimal range of scales. In addition, a proper evaluation of the applied methods that encompass the image processing techniques is often missing. Several mathematical well-defined fractals with theoretically known fractal dimensions, represented by digital images, were investigated in this work. The very popular Box counting method was compared to a new image pyramid approach as well as to the Minkowski dilation method. Effects from noise and

APA, Harvard, Vancouver, ISO, and other styles

20

Xiang, Ming, Zhen Dong Cui, and Yuan Hong Wu. "A Fingerprint Image Segmentation Method Based on Fractal Dimension." Advanced Materials Research 461 (February 2012): 299–301. http://dx.doi.org/10.4028/www.scientific.net/amr.461.299.

Full text

Abstract:

Fractal analysis is becoming more and more popular in image segmentation community, in which the box-counting based fractal dimension estimations are most commonly used. In this paper, a novel fractal estimation algorithm is proposed. Both the proposed algorithm and the box-counting based methods have been applied to the segmentation of texture images. The comparison results demonstrate that the fractal estimation can differentiate texture images more effectively and provide more robust segmentations

APA, Harvard, Vancouver, ISO, and other styles

21

Yan, Loh Guan, Nuryazmin Ahmat Zainuri, and Mohd Zaki Nuawi. "Characterization of Musical Data Signals Resulting from Traditional Musical Instruments Using Fractal Features." Jurnal Kejuruteraan si6, no. 2 (2023): 167–78. http://dx.doi.org/10.17576/jkukm-2023-si6(2)-18.

Full text

Abstract:

Musical instruments are usually distinguished by their sound produced through human perception which may lead to misinterpretation due to auditory perception bias and other disturbances. Therefore, recognition using music signals is carried out to help characterize signals from different musical instruments. Fractal analysis is a mathematical tool used to study complex and irregular patterns in various systems. In this study, fractal analysis was used to study and analyze musical notes signal data from different instruments. The fractal analysis method used is the box counting method. The trad

APA, Harvard, Vancouver, ISO, and other styles

22

Sun, Hong Quan, and Jun Ding. "The Comparison of Fractal Dimensions of Cracks on Reinforced Concrete Beam." Advanced Materials Research 291-294 (July 2011): 1126–30. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.1126.

Full text

Abstract:

In the paper, fractal geometry is used to study the crack evolving process of reinforce concrete beams. The fractal dimensions on surface of the reinforced concrete beam and the mechanical properties of the beam have the linear relationships perfectly. In order to compare the accuracy of the fractal dimensions, box counting method and the digital image box method in practical engineering are used to calculate the fractal dimension separately. The advantages and the disadvantages of these methods are analyzed. And the calculating conditions of these two methods are obtained. The research result

APA, Harvard, Vancouver, ISO, and other styles

23

Jiang, Hongxiang, Changlong Du, Songyong Liu, and Kuidong Gao. "Fractal Characteristic of Rock Cutting Load Time Series." Discrete Dynamics in Nature and Society 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/915136.

Full text

Abstract:

A test-bed was developed to perform the rock cutting experiments under different cutting conditions. The fractal theory was adopted to investigate the fractal characteristic of cutting load time series and fragment size distribution in rock cutting. The box-counting dimension for the cutting load time series was consistent with the fractal dimension of the corresponding fragment size distribution, which indicated that there were inherent relations between the rock fragmentation and the cutting load. Furthermore, the box-counting dimension was used to describe the fractal characteristic of cutt

APA, Harvard, Vancouver, ISO, and other styles

24

Tanaka, M., Y. Kimura, A. Kayama, L. Chouanine, Reiko Kato, and J. Taguchi. "Image Reconstruction and Analysis of Three-Dimensional Fracture Surfaces Based on the Stereo Matching Method." Key Engineering Materials 261-263 (April 2004): 1593–98. http://dx.doi.org/10.4028/www.scientific.net/kem.261-263.1593.

Full text

Abstract:

A computer program of the fractal analysis by the box-counting method was developed for the estimation of the fractal dimension of the three-dimensional fracture surface reconstructed by the stereo matching method. The image reconstruction and fractal analysis were then made on the fracture surfaces of materials created by different mechanisms. There was a correlation between the fractal dimension of the three-dimensional fracture surface and the fractal dimensions evaluated by other methods on ceramics and metals. The effects of microstructures on the fractal dimension were also experimentall

APA, Harvard, Vancouver, ISO, and other styles

25

Lim, Michael, Alit Kartiwa, and Herlina Napitupulu. "Estimation of Citarum Watershed Boundary’s Length Based on Fractal’s Power Law by the Modified Box-Counting Dimension Algorithm." Mathematics 11, no. 2 (2023): 384. http://dx.doi.org/10.3390/math11020384.

Full text

Abstract:

This research aimed to estimate the length of the Citarum watershed boundary because the data are still unknown. We used the concept of fractal’s power law and its relation to the length of an object, which is still not described in other research. The method that we used in this research is the Box-Counting dimension. The data were obtained from the geographic information system. We found an equation that described the relationship between the length and fractal dimension of an object by substituting equations. Following that, we modified the algorithm of Box-Counting dimension by considerati

APA, Harvard, Vancouver, ISO, and other styles

26

PARKINSON, IAN H., and NIC L. FAZZALARI. "GOODNESS OF FIT ON A MODIFIED RICHARDSON PLOT BY RESIDUAL ANALYSIS." Fractals 08, no. 03 (2000): 261–65. http://dx.doi.org/10.1142/s0218348x00000275.

Full text

Abstract:

Modified Richardson plots obtained by a box counting method on outlines of trabecular bone were tested for linearity. The degree of deviation from true linearity was quantified. The results showed that although there was evidence of nonlinearity or serial correlation in the Richardson plots, the magnitude of deviation from true linearity was less than 0.3% for the residuals and less than 4% for the standard deviation of the residuals. This study shows that the modified box counting method for estimating overall fractal dimension or sectional fractal dimensions of trabecular bone is efficacious

APA, Harvard, Vancouver, ISO, and other styles

27

Nasr, Pedram, Hannah Leung, France-Isabelle Auzanneau, and Michael A. Rogers. "Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks." Gels 7, no. 2 (2021): 46. http://dx.doi.org/10.3390/gels7020046.

Full text

Abstract:

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of

APA, Harvard, Vancouver, ISO, and other styles

28

JÄRVENPÄÄ, ESA, MAARIT JÄRVENPÄÄ, ANTTI KÄENMÄKI, HENNA KOIVUSALO, ÖRJAN STENFLO, and VILLE SUOMALA. "Dimensions of random affine code tree fractals." Ergodic Theory and Dynamical Systems 34, no. 3 (2013): 854–75. http://dx.doi.org/10.1017/etds.2012.168.

Full text

Abstract:

AbstractWe study the dimension of code tree fractals, a class of fractals generated by a set of iterated function systems. We first consider deterministic affine code tree fractals, extending to the code tree fractal setting the classical result of Falconer and Solomyak on the Hausdorff dimension of self-affine fractals generated by a single iterated function system. We then calculate the almost sure Hausdorff, packing and box counting dimensions of a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in

APA, Harvard, Vancouver, ISO, and other styles

29

Tiwari, Ram Krishna, and Harihar Paudyal. "Fractal Structure of Seismic Signals of 2015 Gorkha-Kodari Earthquakes: A Box Counting Method." BMC Journal of Scientific Research 5, no. 1 (2022): 18–26. http://dx.doi.org/10.3126/bmcjsr.v5i1.50667.

Full text

Abstract:

Fractal dimension analysis is a computational image processing technique that allows assessing the degree of complexity in patterns. In seismology, fractal dimensions can be used to describe fractured surfaces quantitatively. The larger the fractal dimension the more rugged is the surface, the more irregular is the line, and the more complex is the pore space. For the present investigation the seismicwave signal of 40 earthquakes including one foreshock, main shock and 38 aftershocks (mb ≥ 5.0) of 2015 Gorkha-Kodari earthquakes from 2015/4/21 to 2016/11/27 were considered. The seismograms were

APA, Harvard, Vancouver, ISO, and other styles

30

Fan, Youping, Dai Zhang, and Jingjiao Li. "Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture." Advances in Materials Science and Engineering 2018 (November 1, 2018): 1–10. http://dx.doi.org/10.1155/2018/6019269.

Full text

Abstract:

The paper aims to understand how the fractal dimension and growth time of electrical trees change with temperature and moisture. The fractal dimension of final electrical trees was estimated using 2-D box-counting method. Four groups of electrical trees were grown at variable moisture and temperature. The relation between growth time and fractal dimension of electrical trees were summarized. The results indicate the final electrical trees can have similar fractal dimensions via similar tree growth time at different combinations of moisture level and temperature conditions.

APA, Harvard, Vancouver, ISO, and other styles

31

TANAKA, MANABU, ATSUSHI KAYAMA, RYUICHI KATO, and YOSHIAKI ITO. "ESTIMATION OF THE FRACTAL DIMENSION OF FRACTURE SURFACE PATTERNS BY BOX-COUNTING METHOD." Fractals 07, no. 03 (1999): 335–40. http://dx.doi.org/10.1142/s0218348x99000335.

Full text

Abstract:

In the box-counting method, positioning of images do not significantly affect the estimation of the fractal dimension of river pattern on the brittle fracture surface, and that of dimple pattern on the ductile fracture surface of materials. A reasonable estimation of the fractal dimension can be made using the box-counting method by a single measurement on the fracture surface pattern. The fractal dimension of dimple pattern in pure Zn polycrystals (about 1.50) is larger than that of river pattern in soda-lime glass (about 1.30). Personal difference in image processing does not have a large in

APA, Harvard, Vancouver, ISO, and other styles

32

Patiño-Ortiz, Miguel, Julián Patiño-Ortiz, Miguel Ángel Martínez-Cruz, Fernando René Esquivel-Patiño, and Alexander S. Balankin. "Morphological Features of Mathematical and Real-World Fractals: A Survey." Fractal and Fractional 8, no. 8 (2024): 440. http://dx.doi.org/10.3390/fractalfract8080440.

Full text

Abstract:

The aim of this review paper is to survey the fractal morphology of scale-invariant patterns. We are particularly focusing on the scale and conformal invariance, as well as on the fractal non-uniformity (multifractality), inhomogeneity (lacunarity), and anisotropy (succolarity). We argue that these features can be properly quantified by the following six adimensional numbers: the fractal (e.g., similarity, box-counting, or Assouad) dimension, conformal dimension, degree of multifractal non-uniformity, coefficient of multifractal asymmetry, index of lacunarity, and index of fractal anisotropy.

APA, Harvard, Vancouver, ISO, and other styles

33

Xu, Jie, and Giusepe Lacidogna. "A Modified Box-Counting Method to Estimate the Fractal Dimensions." Applied Mechanics and Materials 58-60 (June 2011): 1756–61. http://dx.doi.org/10.4028/www.scientific.net/amm.58-60.1756.

Full text

Abstract:

A fractal is a property of self-similarity, each small part of the fractal object is similar to the whole body. The traditional box-counting method (TBCM) to estimate fractal dimension can not reflect the self-similar property of the fractal and leads to two major problems, the border effect and noninteger values of box size. The modified box-counting method (MBCM), proposed in this study, not only eliminate the shortcomings of the TBCM, but also reflects the physical meaning about the self-similar of the fractal. The applications of MBCM shows a good estimation compared with the theoretical o

APA, Harvard, Vancouver, ISO, and other styles

34

Liu, Zheng, and Xiao Mei Liu. "Fractal Characteristics of Primary Phase Morphology in Semisolid A356 Alloy." Advanced Materials Research 535-537 (June 2012): 936–40. http://dx.doi.org/10.4028/www.scientific.net/amr.535-537.936.

Full text

Abstract:

Semisolid A356 alloy was prepared by low superheat pouring and slightly electro- magnetic stirring(LSPSES). The fractal dimensions of primary phase morphology in semisolid A356 alloy were researched by the calculating program written to calculate the fractal dimensions of box-counting in the image of primary phase morphology in semisolid A356 alloy. The results indicated that the primary phase morphology in the alloy was characterized by fractal dimension, and the morphology obtained by the different processing parameters had the different fractal dimension. The morphology at the different pos

APA, Harvard, Vancouver, ISO, and other styles

35

Tan, Piqiang, Yifan Yin, Deyuan Wang, Diming Lou, and Zhiyuan Hu. "The microscopic characteristics of particle matter and image algorithm based on fractal theory." E3S Web of Conferences 360 (2022): 01003. http://dx.doi.org/10.1051/e3sconf/202236001003.

Full text

Abstract:

The effects of ash and sulfur content on the morphology of particulate matter (PM) in diesel particle filter (DPF) were investigated with five different components of lubricants. The aggregate morphology of primary particles in diesel were analyzed using transmission electron microscopy (TEM). The fractal dimensions of carbon particles were calculated by box-counting method (BCM), differential box-counting method (DBC), relative differential box-counting method (RDBC) and MAD-based box counting method (MAD-DBC), and the results were compared. The results showed that the microstructure of PM de

APA, Harvard, Vancouver, ISO, and other styles

36

Maryenko, N. I., and O. Y. Stepanenko. "Fractal dimension of external linear contour of human cerebellum (magnetic resonance imaging study)." Reports of Morphology 27, no. 2 (2021): 16–22. http://dx.doi.org/10.31393/morphology-journal-2021-27(2)-03.

Full text

Abstract:

Fractal analysis is a method of mathematical analysis, which provides quantitative assessment of the spatial configuration complexity of the anatomical structures and may be used as a morphometric method. The purpose of the study was to determine the values of the fractal dimension of the outer linear contour of human cerebellum by studying the magnetic resonance images of the brain using the authors’ modification of the caliper method and compare to the values determined using the box counting method. Brain magnetic resonance images of 30 relatively healthy persons aged 18-30 years (15 men an

APA, Harvard, Vancouver, ISO, and other styles

37

Braverman, Boris, and Mauro Tambasco. "Scale-Specific Multifractal Medical Image Analysis." Computational and Mathematical Methods in Medicine 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/262931.

Full text

Abstract:

Fractal geometry has been applied widely in the analysis of medical images to characterize the irregular complex tissue structures that do not lend themselves to straightforward analysis with traditional Euclidean geometry. In this study, we treat the nonfractal behaviour of medical images over large-scale ranges by considering their box-counting fractal dimension as a scale-dependent parameter rather than a single number. We describe this approach in the context of the more generalized Rényi entropy, in which we can also compute the information and correlation dimensions of images. In additio

APA, Harvard, Vancouver, ISO, and other styles

38

He, Tao, Long Fei Cheng, Qing Hua Wu, Zheng Jia Wang, Lian Gen Yang, and Lang Yu Xie. "An Image Segmentation Calculation Based on Differential Box-Counting of Fractal Geometry." Applied Mechanics and Materials 719-720 (January 2015): 964–68. http://dx.doi.org/10.4028/www.scientific.net/amm.719-720.964.

Full text

Abstract:

Differential box-counting of fractal geometry has been widely used in image processing.A method which uses the differential box-counting to segment the gathered images is discussed in this paper . It is to construct a three-dimensional gray space and use the same size boxes to contain the three dimensional space.The number of boxes needed to cover the entire image are calculated .Different sizes of boxes can receive different number of boxes, so least squares method is used to calculate the fractal dimension. According to the fractal dimension parameters, appropriate threshold is chose to segm

APA, Harvard, Vancouver, ISO, and other styles

39

Alsaidi, Nadia M. G., Arkan J. Mohammed, and Wael J. Abdulaal. "Fingerprints Authentication Using Grayscale Fractal Dimension." Al-Mustansiriyah Journal of Science 29, no. 3 (2019): 106. http://dx.doi.org/10.23851/mjs.v29i3.627.

Full text

Abstract:

Characterizing of visual objects is an important role in pattern recognition that can be performed through shape analysis. Several approaches have been introduced to extract relevant information of a shape. The complexity of the shape is the most widely used approach for this purpose where fractal dimension and generalized fractal dimension are methodologies used to estimate the complexity of the shapes. The box counting dimension is one of the methods that used to estimate fractal dimension. It is estimated basically to describe the self-similarity in objects. A lot of objects have the self-s

APA, Harvard, Vancouver, ISO, and other styles

40

XIA, YUXUAN, JIANCHAO CAI, WEI WEI, XIANGYUN HU, XIN WANG, and XINMIN GE. "A NEW METHOD FOR CALCULATING FRACTAL DIMENSIONS OF POROUS MEDIA BASED ON PORE SIZE DISTRIBUTION." Fractals 26, no. 01 (2018): 1850006. http://dx.doi.org/10.1142/s0218348x18500068.

Full text

Abstract:

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribut

APA, Harvard, Vancouver, ISO, and other styles

41

Hermán, Peter, László Kocsis, and Andras Eke. "Fractal Branching Pattern in the Pial Vasculature in the Cat." Journal of Cerebral Blood Flow & Metabolism 21, no. 6 (2001): 741–53. http://dx.doi.org/10.1097/00004647-200106000-00012.

Full text

Abstract:

Arborization pattern was studied in pial vascular networks by treating them as fractals. Rather than applying elaborate taxonomy assembled from measures from individual vessel segments and bifurcations arranged in their branching order, the authors' approach captured the structural details at once in high-resolution digital images processed for the skeleton of the networks. The pial networks appear random and at the same time having structural elements similar to each other when viewed at different scales—a property known as self-similarity revealed by the geometry of fractals. Fractal (capaci

APA, Harvard, Vancouver, ISO, and other styles

42

ALEVIZOS, PANAGIOTIS D., and MICHAEL N. VRAHATIS. "OPTIMAL DYNAMIC BOX-COUNTING ALGORITHM." International Journal of Bifurcation and Chaos 20, no. 12 (2010): 4067–77. http://dx.doi.org/10.1142/s0218127410028197.

Full text

Abstract:

An optimal box-counting algorithm for estimating the fractal dimension of a nonempty set which changes over time is given. This nonstationary environment is characterized by the insertion of new points into the set and in many cases the deletion of some existing points from the set. In this setting, the issue at hand is to update the box-counting result at appropriate time intervals with low computational cost. The proposed algorithm tackles the dynamic box-counting problem by using computational geometry methods. In particular, we use a sequence of compressed Box Quadtrees to store the data p

APA, Harvard, Vancouver, ISO, and other styles

43

JOHNSEN, WILLIAM A., and CHRISTOPHER A. BROWN. "COMPARISON OF SEVERAL METHODS FOR CALCULATING FRACTAL-BASED TOPOGRAPHIC CHARACTERIZATION PARAMETERS." Fractals 02, no. 03 (1994): 437–40. http://dx.doi.org/10.1142/s0218348x94000600.

Full text

Abstract:

The objective of this work is to compare fractal-based, topographic characterization parameters calculated by several different fractal analysis methods. Four fractal characterization methods (compass, patchwork, box counting, and 2-point correlation) are systematically applied to five topographic data sets, which encompass a wide range of scale, and the results are compared. The compass and patchwork methods calculate similar values for the fractal dimension and smooth/rough crossover. The box and 2-point correlation methods calculate similar values for the fractal dimension. The compass and

APA, Harvard, Vancouver, ISO, and other styles

44

Liu, HongYan, Addie Bahi, and Frank K. Ko. "A one dimensional heat transfer model for wolverine (gulo-gulo) hair." International Journal of Clothing Science and Technology 30, no. 4 (2018): 548–58. http://dx.doi.org/10.1108/ijcst-08-2017-0108.

Full text

Abstract:

Purpose Wolverine hairs with superior heat transfer properties have been used as fur ruffs for extreme cold-weather clothing. In order to understand the exclusive mechanism of wolverine surviving in the cold areas of circumpolar, the purpose of this paper is to establish a one-dimensional fractional heat transfer equation to reveal the hidden mechanism for the hairs, and also calculate the fractal dimension of the wolverine hair using the box counting method to verify the proposed theory. The observed results (from the proposed model) found to be in good agreement with the box counting method.

APA, Harvard, Vancouver, ISO, and other styles

45

Maryenko, Nataliia I., and Oleksandr Yu Stepanenko. "COMPARATIVE ANALYSIS OF FRACTAL DIMENSIONS OF HUMAN CEREBELLUM: IMPACT OF IMAGE PREPROCESSING AND FRACTAL ANALYSIS METHODS." Wiadomości Lekarskie 75, no. 2 (2022): 438–43. http://dx.doi.org/10.36740/wlek202202120.

Full text

Abstract:

The aim: To compare the values of the fractal dimensions of human cerebellum obtained using different algorithms of image preprocessing and different methods of fractal analysis. Materials and methods: The study involved 120 people without structural changes in the brain (age 18-86 years, 55 men and 65 women). T1- and T2-weighted MR brain images were studied. Fractal analysis was performed using box counting and pixel dilatation methods. Fractal dimensions of cerebellar tissue as a whole, cerebellar cortex and its individual layers, cerebellar white matter were measured and compared to each ot

APA, Harvard, Vancouver, ISO, and other styles

46

Liu, Huabo, Fanjing Meng, and Shaozhen Hua. "4D Mapping of the Fracture Evolution in a Printed Gypsum-Like Core by Using X-Ray CT Scanning." Advances in Civil Engineering 2021 (April 17, 2021): 1–12. http://dx.doi.org/10.1155/2021/8820828.

Full text

Abstract:

The paper presents the use of micro-X-ray computed tomography (CT) system and associated automatic loading device in visualizing and analyzing the propagation of penny-shaped flaw in gypsum-like 3D printing specimen. During the loading process, a micro-X-ray computed tomography (CT) system was used to scan the specimen with a resolution of 30 × 30 μm2. The volumetric images of specimen were reconstructed based on two-dimensional images. Thus, the propagation of penny-shaped flaw in gypsum-like 3D printing specimen in spatial was observed. The device can record the evolution of the internal pen

APA, Harvard, Vancouver, ISO, and other styles

47

YU, BOMING, L. JAMES LEE, and HANQIANG CAO. "FRACTAL CHARACTERS OF PORE MICROSTRUCTURES OF TEXTILE FABRICS." Fractals 09, no. 02 (2001): 155–63. http://dx.doi.org/10.1142/s0218348x01000610.

Full text

Abstract:

It is found that the pore microstructures of textile fabrics, widely used in the manufacture of fiber-reinforced composites, exhibit the fractal characters. The fractal behaviors are described by the proposed analytical method and measured by the box-counting method for the three different types of textile fabrics: plain woven, four-harness, bidirectional-stitched fiberglass mats. The pore area fractal dimension is derived analytically and found to be the function of the porosity and architectural parameters of fabrics. The results indicate that the fractal characters are isotropic although th

APA, Harvard, Vancouver, ISO, and other styles

48

OSAKA, MOTOHISA, and NOBUYASU ITO. "LOCAL BOX-COUNTING TO DETERMINE FRACTAL DIMENSION OF HIGH-ORDER CHAOS." International Journal of Modern Physics C 11, no. 08 (2000): 1519–26. http://dx.doi.org/10.1142/s0129183100001474.

Full text

Abstract:

To determine the attractor dimension of chaotic dynamics, the box-counting method has the difficulty in getting accurate estimates because the boxes are not weighted by their relative probabilities. We present a new method to minimize this difficulty. The local box-counting method can be quite effective in determining the attractor dimension of high-order chaos as well as low-order chaos.

APA, Harvard, Vancouver, ISO, and other styles

49

Liu, Shulin, Xinxin Chen, Jianping Hu, Qishuo Ding, and Ruiyin He. "Identification of Box Scale and Root Placement for Paddy–Wheat Root System Architecture Using the Box Counting Method." Agriculture 13, no. 12 (2023): 2184. http://dx.doi.org/10.3390/agriculture13122184.

Full text

Abstract:

Root fractal analysis is instrumental in comprehending the intricate structures of plant root systems, offering insights into root morphology, branching patterns, and resource acquisition efficiency. We conducted a field experiment on paddy–wheat root systems under varying nitrogen fertilizer strategies to address the need for quantitative standardization in root fractal analysis. The study evaluated the impact of nitrogen fertilizer heterogeneity on root length and number. We established functional relationships and correlations among root fractal characteristics and root length across differ

APA, Harvard, Vancouver, ISO, and other styles

50

Stypa, Jörn. "Numerical Estimates of the Fractal Dimension of the Spatial Human Bronchial Tree by Two-Dimensional Box-Counting-Method." Fractals 06, no. 01 (1998): 87–93. http://dx.doi.org/10.1142/s0218348x98000109.

Full text

Abstract:

Photographs of the human bronchial trees were obtained from resin casts. After data editing, the fractal dimension of the contour of the bronchial tree was determined by the 2D box-counting-method (2D-BCM). Mathematical theorems about projections and intersections allow us to determine the fractal dimension of the spatial human bronchial tree.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!