• East Asian Economic Review
• /
• v.18 no.4
• /
• pp.367-394
• /
• 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.

• Imaging Science in Dentistry
• /
• v.31 no.1
• /
• pp.35-42
• /
• 2001

Purpose: To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Materials and Methods : Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10×20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We compared fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Results: Fractal dimension at interdental crest area of normal group was 1.979±0.018 and that of patient group 1.971±0.012 (p>0.05). Fractal dimension at furcation area of normal group was 1.986±0.024 and that of patient group 1.974±0.015 (p<0.05). The ratio of fractal dimension at interdental crest area to interdental middle 1/3 of normal group was 1.003±0.015 and that of patient group 0.993±0.018 (p<0.05). The ratio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006±0.018 and that of patient group 0.994±0.018 (p<0.05). Conclusion : The ratio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis.

• The korean journal of orthodontics
• /
• v.46 no.5
• /
• pp.323-330
• /
• 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.

• 한국HCI학회:학술대회논문집
• /
• 2008.02a
• /
• pp.618-622
• /
• 2008

In this paper, we suggest new music composition algorithm based on fractal theory. User can define and control fractal shape by setting an initial state and production rules in L-System. We generate an asymmetric fractal tree based on L-System and probability. Then a music is generated by the fractal tree image using sonification techniques. We introduce two composition algorithm using the fractal tree. First, monophonic music can be generated by mapping x and y axis to velocity and pitch, respectively Second, harmonic music also can be generated by mapping x and y axis to time and pitch, respectively Using our composition algorithm, user can easily generate a music which has repeated pattern created by recursive feature of fractal, and a music which has structure similar to fractal tree image.

• Wind and Structures
• /
• v.31 no.4
• /
• pp.363-371
• /
• 2020

Proper understanding of offshore wind speed variability is of essential importance in practice, which provides useful information to a wide range of coastal and marine activities. In this paper, long-term wind speed data recorded at various offshore stations are analyzed in the framework of fractal dimension analysis. Fractal analysis is a well-established data analysis tool, which is particularly suitable to determine the complexity in time series from a quantitative point of view. The fractal dimension is estimated using the conventional box-counting method. The results suggest that the wind speed data are generally fractals, which are likely to exhibit a persistent nature. The mean fractal dimension varies from 1.31 at an offshore weather station to 1.43 at an urban station, which is mainly associated with surface roughness condition. Monthly variability of fractal dimension at offshore stations is well-defined, which often possess larger values during hotter months and lower values during winter. This is partly attributed to the effect of thermal instability. In addition, with an increase in measurement interval, the mean and minimum fractal dimension decrease, whereas the maximum and coefficient of variation increase in parallel.

• The Journal of the Korea Contents Association
• /
• v.7 no.12
• /
• pp.322-332
• /
• 2007

We consider a deformation method suitable for fractal. In IFS fractal, the position of a point is characterized by its code as well as by its coordinates. Code has a meaning of address for fractal. If we move a point by changing its code, the resulting movement shows fractal behavior. We propose three deformation methods based on code information. For the deformation vector of a point in fractal, 1) we use the vector of a given vector field at the point obtained by code transformation, 2) we use the vector constructed by adding predefined displacement vectors according to the code information of the point. Both methods show a fractal-like character as well as an ordinary continuous deformation character. Also, 3) we can deform fern-fractal more naturally by restricting its deforming region using code form.

• Journal of Korea Water Resources Association
• /
• v.37 no.11
• /
• pp.889-896
• /
• 2004

The fractal advection-diffusion equation (ADE) is a generalization of the classical AdE in which the second-order derivative is replaced with a fractal order derivative. While the fractal ADE have been analyzed with a stochastic process In the Fourier and Laplace space so far, in this study a fractal ADE for describing solute transport in rivers is derived with a finite difference scheme in the real space. This derivation with a finite difference scheme gives the hint how the fractal derivative order and fractal diffusion coefficient can be estimated physically In contrast to the classical ADE, the fractal ADE is expected to be able to provide solutions that resemble the highly skewed and heavy-tailed time-concentration distribution curves of contaminant plumes observed in rivers.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.4 no.4
• /
• pp.434-440
• /
• 2003

Since Jacquine introduced the image coding algorithm using fractal theory, many fractal image compression algorithms providing good quality at low bit rate have been proposed by Fisher and Beaumount et al.. But a problem of the previous implementations is that the decoding rests on an iterative procedure whose complexity is image-dependent. This paper proposes an iterative-free fractal image decoding algorithm to reduce the decoding time. In the proposed method, under the encoder previously with the same codebook image as an initial image to be used at the decoder, the fractal coefficients are obtained through calculating the similarity between the codebook image and an input image to be encoded. As the decoding process can be completed with received fractal coefficients and predefined initial image without repeated iterations, the decoding time could be remarkably reduced.

• Imaging Science in Dentistry
• /
• v.38 no.3
• /
• pp.147-151
• /
• 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.

• Journal of Fashion Business
• /
• v.22 no.1
• /
• pp.135-147
• /
• 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.