• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2001년도 봄 학술발표회 논문집
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• pp.333-338
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• 2001

Fractal geometry is a non-Euclidean geometry which has been developed to quantitative analysis irregular or fractional shapes. Fractal dimension of irregular surface has fractal values ranging from 2 to 3 and of irregular line profile has fractal values ranging from 1 to 2. In this paper, quantitative analysis of crack growth patterns during the fracture processing of fiber-reinforced cement composites based on fractal geometry. The fracture behaviors of fiber reinforced mortar beams subjected to three-point loading in flexure. The beams all had a single notch depth, but varing volume fractions of polypropylene, cellulose fibers. The crack growth behaviors, as observed through the image processing system, and the box counting method was used to determine the fractal dimension, Df. The results showed that the linear correlation exists between fractal dimension and fracture energy of the fiber reinforced cement mortar.

• 한국해양공학회지
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• 제10권4호
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• pp.84-91
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• 1996

A fractal analysis on fracture surface of aluminium-particulate SiC composites was attempted. As the volume fraction of SiC in composites increases, the fractal dimension tends to increase. However, no correlation between the fractal dimension and the fracture toughness in terms of critical energy release rate was observed. Since the fractal dimension represents the roughness of fracture surface, the fracture toughness would be a function of not only fracture surface roughness but also additional parameters. Thus the applicability of fractal analysis to the estimation of fracture toughness must depend on the proper choice and interpretation of additioal paramerters. In this paper, the size of characteristic strctural unit for fracture was considered as an additional parameter. As a result, the size appeared to be a function of only volume fraction of SiC. Finally, a master curve for fracture toughness of aluminium-particulate SiC composites was proposed as a function of fractal dimension and volume fraction of SiC.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 2001년도 제34회 추계학술대회 개최
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• pp.53-58
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• 2001

Fractal dimension is the method to measure the roughness and the irregularity of something that cannot be defined obviously by Euclidean dimension. And the analysis method of this dimension don't need perfect, accurate boundary and color like analysis lot diameter, perimeter, aspect or reflectivity of wear particles or surface. If we arranged the morphological characteristic of various wear particle by using the characteristic of fractal dimension, it might be very efficient to the diagnosis of driving condition. In order to describe morphology of various wear particle, the wear test was carried out under friction experimental conditions. And fractal descriptors was applied to boundary and surface of wear particle with image processing system. These descriptors to analyze shape and surface wear particle are boundary fractal dimension and surface fractal dimension.

• East Asian Economic Review
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• 제18권4호
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• pp.367-394
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• 2014

In this study, we examined the fractal structure of the Nikkei225, HangSeng, Shanghai Stock Exchange and Straits Times Index of Singapore. Empirical analysis was performed via non-parametric, semi-parametric long memory tests and also fractal dimension calculations. In order to avoid spurious long memory features, besides the Detrended Fluctuations Analysis (DFA), we also used Smith's (2005) modified GPH method. As for fractal dimension calculations, they were conducted via Box-Counting and Variation (p=1) tests. According to the results, while there is no long memory property in log returns of any index, we found evidence for long memory properties in the volatility of the HangSeng, the Shanghai Stock Exchange and the Straits Times Index. However, we could not find any sign of long memory in the volatility of Nikkei225 index using either the DFA or modified GPH test. Fractal dimension analysis also demonstrated that all raw index prices have fractal structure properties except for the Nikkei225 index. These findings showed that the Nikkei225 index has the most efficient market properties among these markets.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 1998년도 제28회 추계학술대회
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• pp.115-123
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• 1998

The morphological analysis of wear particle is a very effective means for machine condition monitoring and fault diagnosis. In order to describe morphology of various wear particle, the wear test was carried out under different experimental conditions. And fractal descriptors was applied to boundary and surface of wear particle with image processing system. These descriptors to analyze shape and surface wear particle are shape fractal dimension and surface fractal dimension. The shape fractal dimension can be derived from the boundary profile and surface fractal dimension can be determined by sum of intensity difference of surface pixel. The morphology of wear particles can be effectively obtained by two fractal dimensions.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 2001년도 제33회 춘계학술대회 개최
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• pp.30-35
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• 2001

The morphological analysis of wear particle is a very effective means for machine condition monitoring and fault diagnosis. In order to describe morphology of various wear particle, the wear test was carried oui under friction experimental conditions. And fractal descriptors was applied to boundary and surface of wear particle with image processing system. These descriptors to analyze shape and surface wear particle are share fractal dimension and surface fractal dimension. The boundry fractal dimension can be derived from the boundary profile and surface fractal dimension can be determined b)r sum of intensity difference of surface pixel. The morphology of wear particles can be effectively obtained by two fractal dimensions.

• 대한치과교정학회지
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• 제46권5호
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• pp.323-330
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• 2016

Objective: The purpose of this study was to determine whether the results of fractal analysis can be used as criteria for midpalatal suture maturation evaluation. Methods: The study included 131 subjects aged over 18 years of age (range 18.1-53.4 years) who underwent cone-beam computed tomography. Skeletonized images of the midpalatal suture were obtained via image processing software and used to calculate fractal dimensions. Correlations between maturation stage and fractal dimensions were calculated using Spearman's correlation coefficient. Optimal fractal dimension cut-off values were determined using a receiver operating characteristic curve. Results: The distribution of maturation stages of the midpalatal suture according to the cervical vertebrae maturation index was highly variable, and there was a strong negative correlation between maturation stage and fractal dimension (-0.623, p < 0.001). Fractal dimension was a statistically significant indicator of dichotomous results with regard to maturation stage (area under curve = 0.794, p < 0.001). A test in which fractal dimension was used to predict the resulting variable that splits maturation stages into ABC and D or E yielded an optimal fractal dimension cut-off value of 1.0235. Conclusions: There was a strong negative correlation between fractal dimension and midpalatal suture maturation. Fractal analysis is an objective quantitative method, and therefore we suggest that it may be useful for the evaluation of midpalatal suture maturation.

• Imaging Science in Dentistry
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• 제38권3호
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• pp.147-151
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• 2008

Purpose : The purpose of this study was to investigate whether fractal analysis of periapical and panoramic radiographs was useful in predicting osteoporosis risk. Materials and Methods : 37 postmenoposal women between the age of 42 and 79 were classified as normal and osteoporosis group according to the bone mineral density of lumbar vertebrae and periapical and panoramic radio-graphs were taken. Fractal dimensions at periapical areas of mandibular first molars were calculated to differentiate the two groups. Results : The mean fractal dimensions of normal group on periapical and panoramic radiographs were $1.413{\pm}0.079$, $1.517{\pm}0.071$ each. The mean fractal dimensions of osteoporotic group on periapical and panoramic radiographs were $1.498{\pm}0.086$, $1.388{\pm}0.083$ each. The mean fractal dimension from peripaical radiographs of osteoporotic group was statistically significantly higher than that of normal group. The mean fractal dimension from panoramic radiographs of osteoporotic group was statistically significantly lower than that of normal group. Conclusion : Fractal analysis using periapical and panoramic radiographs was useful in predicting osteoporosis.

• 패션비즈니스
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• 제22권1호
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• pp.135-147
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• 2018

Since the 20th century, there has been a growing interest in the new concept of fractals, a combination of mathematics and art, and the attempt to study the creative spatial aspects of the concept is being made. The purpose of this research is to examine artistic characteristics of fractal dimension and then analyze the types of fractal dimensions expressed in the fashion. Previous literature on fractals and dimension, and visual data on art and fashion collected over the Internet were used for analysis. Fractal dimension refers to the spatial concept of structural dimension of geometrical self-similarity. An analysis of the types of fractals seen in fashion revealed spatial expansion, the repetition in continual figures, superposition accordant to different sizes, and shades of different shapes. The aesthetic characteristics of fractal dimension appearing in fashions were examined based on analyses of fractal dimension types; the inherent characteristics of self-similarity, superimposition, and atypicality were found. Results obtained from this study are expected to be used as basic materials for the application of the design of fractal dimension into various perspectives of fashion.

• Tribology and Lubricants
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• 제22권5호
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• pp.276-281
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• 2006

The fractal dimension is quantitatively to define the irregular characteristic of the shape in natural. It can be useful in describing morphological characteristics of various wear particles. This paper was undertaken to diagnose failure condition for sliding members in lubrication by fractal dimension. It will be possible to diagnose wear mechanism, friction and damage state of machines through analysis of shape characteristics for wear particle on driving condition by fractal parameters. In this study, the calculating and analyzing methods of fractal dimensions were constructed for the condition monitoring and wear particle analysis in lubricant condition. So, we carried out the Friction and wear test with the ball on disk type tester, and the fractal parameters of wear particle in lubricated conditions were calculated. Fractal parameters were defined as texture fractal dimension ($D_{t}$), structure fractal dimension ($D_{s}$) and total fractal dimension (D).