COMPARATIVE STUDY OF FRACTAL BEHAVIOR IN QUASI-RANDOM AND QUASI-PERIODIC SPEECH WAVE MAP

Fractal behavior in the quasi-steady states of the two types of speech signals, namely, quasi-periodic and quasi-random, are studied. The signals of the first group consist of seven vowels and those for the second group consist of three variants each of three sibilants. Ten rendering of each of these signals by one native Bengali male speaker of 45 years of age are used as the signal database. Standard box-counting method is used for generating ln (pq) versus ln (1/r) curves. D0, Dq and the knee expanse (KE) of the curves, their interrelations and the projections on the source characteristics are the objects of analysis. D2>D0 is found to indicate locally dense nature of the map and are found to be associated mainly with some sibilants. Dq are found to be a family of simple polynomial functions of q for all signals. D0, Dq and KE are related to the nature of different signals and character of the sources generating the signals. The study of fractal dimensions and the generalized dimensions for these signals reveal intermittency behavior and multifractality, which indicate basically, turbulent source or sources for speech generation. That the quasi-periodic and the quasi-random sounds are fundamentally different is reflected in the behavior of generalized fractal dimensions.

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Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture

Advances in Materials Science and Engineering ◽

10.1155/2018/6019269 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10

Author(s):

Youping Fan ◽

Dai Zhang ◽

Jingjiao Li

Keyword(s):

Fractal Dimension ◽

Tree Growth ◽

Fractal Dimensions ◽

Moisture Level ◽

Growth Time ◽

Counting Method ◽

Box Counting ◽

Electrical Trees ◽

Box Counting Method ◽

Electrical Treeing

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

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A Modified Box-Counting Method to Estimate the Fractal Dimensions

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.58-60.1756 ◽

2011 ◽

Vol 58-60 ◽

pp. 1756-1761 ◽

Cited By ~ 1

Author(s):

Jie Xu ◽

Giusepe Lacidogna

Keyword(s):

Fractal Dimension ◽

Fractal Dimensions ◽

The Self ◽

Whole Body ◽

Counting Method ◽

Border Effect ◽

Self Similarity ◽

Box Counting ◽

Self Similar ◽

Box Counting Method

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 ones, which the biggest difference is smaller than 5%.

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Morphometric relations of fractal-skeletal based channel network model

Discrete Dynamics in Nature and Society ◽

10.1155/s1026022698000065 ◽

1998 ◽

Vol 2 (2) ◽

pp. 77-92 ◽

Cited By ~ 18

Author(s):

B. S. Daya Sagar ◽

Charles Omoregie ◽

B. S. Prakasa Rao

Keyword(s):

Network Model ◽

Fractal Dimensions ◽

Main Channel ◽

Second Order ◽

Counting Method ◽

Channel Network ◽

Channel Networks ◽

Box Counting ◽

Box Counting Method ◽

Channel Lengths

A fractal-skeletal based channel network (F-SCN) model is proposed. Four regular sided initiator-basins are transformed as second order fractal basins by following a specific generating mechanism with non-random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these F-SCNs are shown. The fractal dimensions of these fractal basins, channel networks, and main channel lengths (computed through box counting method) are compared with those of estimated length–area measures. Certain morphometric order ratios to show fractal relations are also highlighted.

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CALCULATING FRACTAL DIMENSIONS

International Journal of Modern Physics C ◽

10.1142/s0129183192000221 ◽

1992 ◽

Vol 03 (02) ◽

pp. 267-277 ◽

Cited By ~ 1

Author(s):

S. GOSHEN ◽

R. THIEBERGER

Keyword(s):

Parallel Implementation ◽

Fractal Dimensions ◽

Counting Method ◽

Box Counting ◽

Box Counting Method

An algorithm for calculating fractal dimensions by the box counting method is described. Parallel implementation of the algorithm is presented.

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A Successive Shift Box-Counting Method for Calculating Fractal Dimensions and Its Application in Identification of Faults

Acta Geologica Sinica - English Edition ◽

10.1111/j.1755-6724.2002.tb00091.x ◽

2010 ◽

Vol 76 (2) ◽

pp. 257-263 ◽

Cited By ~ 3

Author(s):

SHEN Xiaohua ◽

ZHOU Lejun ◽

LI Hongsheng ◽

SHEN Zhongyue ◽

YANG Shufeng

Keyword(s):

Fractal Dimensions ◽

Counting Method ◽

Box Counting ◽

Box Counting Method

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Comparative study on damage process of concrete subjected to uniaxial tensile and compression loads based on CT test and improved differential box counting method

Construction and Building Materials ◽

10.1016/j.conbuildmat.2021.122693 ◽

2021 ◽

Vol 285 ◽

pp. 122693

Author(s):

Le Zhang ◽

Faning Dang ◽

Weihua Ding ◽

Lin Zhu

Keyword(s):

Comparative Study ◽

Uniaxial Tensile ◽

Counting Method ◽

Box Counting ◽

Damage Process ◽

Ct Test ◽

Box Counting Method

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ACCURACY OF GENERALIZED DIMENSIONS ESTIMATED FROM GRAYSCALE IMAGES USING THE METHOD OF MOMENTS

Fractals ◽

10.1142/s0218348x09004302 ◽

2009 ◽

Vol 17 (03) ◽

pp. 351-363 ◽

Cited By ~ 8

Author(s):

E. PERFECT ◽

A. M. TARQUIS ◽

N. R. A. BIRD

Keyword(s):

Geometric Mean ◽

Maximum Deviation ◽

Counting Method ◽

Box Counting ◽

Order Of Magnitude ◽

Box Counting Method ◽

The Moment ◽

Generalized Dimensions ◽

Derivatives Of ◽

Grayscale Images

The moment-based box counting method of multifractal analysis is widely used for estimating generalized dimensions, Dq, from two-dimensional grayscale images. An evaluation of the accuracy of this method is needed to establish confidence in the resulting estimates of Dq. We estimated Dq from q = -10 to +10 for 23 random geometrical multifractal fields with different grid sizes, and known analytical Dq versus q functions. The fields were transformed to give normalized grayscale values between zero and one. Comparison of the estimated and analytical functions indicated the moment-based box counting method overestimates Dq by as much as 6.9% when q ≪ 0. The root mean square error, RMSE, for the entire range of q values examined ranged from 7.81 × 10-6 to 1.35 × 10-1, with a geometric mean of 6.50 × 10-3. The RMSE decreased with decreasing grid size and increasing heterogeneity. These trends appear to be largely due to the presence of zeros in the normalized grayscale fields. Variations in the slope of the log-transformed partition function, ln [χ(q,δ)], with box size resulted in the overestimation of Dq when q ≪ 0. An alternative procedure for estimating Dq was developed based on the numerical first derivatives of ln [χ(q,δ)]. Using this approach the maximum deviation in Dq values was only 1.2%, while the RMSE varied from 3.11 × 10-6 to 2.72 × 10-2, with a geometric mean of 2.57 × 10-4. When analyzing normalized grayscale fields, moment-based estimates of Dq should be interpreted with care. An order of magnitude increase in the accuracy of Dq can be achieved for such fields if the numerical first derivatives of ln [χ(q,δ)] are used in the analysis instead of standard linear regression.

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IMAGE PYRAMIDS FOR CALCULATION OF THE BOX COUNTING DIMENSION

Fractals ◽

10.1142/s0218348x12500260 ◽

2012 ◽

Vol 20 (03n04) ◽

pp. 281-293 ◽

Cited By ~ 7

Author(s):

H. AHAMMER ◽

M. MAYRHOFER-REINHARTSHUBER

Keyword(s):

Digital Images ◽

Fractal Dimensions ◽

Counting Method ◽

Image Pyramids ◽

Box Counting ◽

Aspect Ratios ◽

Box Counting Dimension ◽

Method Effects ◽

Box Counting Method ◽

Processing Techniques

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 altered aspect ratios were also considered. The new Pyramid method is quite identical to the Box counting method, but it is easier to implement. Additionally, the calculation times are much shorter and memory requirements are almost comparable.

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