• KSBB Journal
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• v.9 no.5
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• pp.512-517
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• 1994

The morphology of fungal growth, which is an important variable for separability and rheological property of fermented medium, was quantified with fractal geometry. Fractal dimensions were determined for submerged growth of two industrially important fungi, Aspergillus niger and Aspergillus oryzae. The tendency of pellet formation was related to the fractal dimension of fungi.

• Advances in concrete construction
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• v.16 no.3
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• pp.141-153
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• 2023

In order to develop and take full advantage of pasture fiber and waste concrete, this article studied how different amounts of pasture fiber influenced the toughness and pore structure of concrete with different replacement rates of recycled fine aggregate. Pasture fiber recycled concrete constitutive equations were established under idealized stiffness and toughness damage rate, based on fracture energy and damage mechanics theories. The relationship between pore structure and toughness was studied utilizing nuclear magnetic resonance and fractal theory. The toughness of text groups (0% (JZ), 10% (ZS10), 20% (ZS20)) first increased and then decreased with increasing amounts of pasture fiber, based on the damage rate of toughness. The toughness of concrete samples with recycled fine aggregate and pasture fiber is negatively correlated to the fractal dimension of small and medium-sized pores with a pore size of 0-500 nm. At a replacement rate of 10% of the recycled fine aggregate, the fractal dimension of the air voids (r: 500-9000 nm, i.e., Lg(r) ∈ [2.7, 3.9]) shows a gradual decrease with the increase of grass fiber dosage, indicating that with such a replacement rate of the recycled fine aggregate, the increase of pasture fiber can reduce the complexity of the pore structure of the air voids (500-9000 nm).

• Imaging Science in Dentistry
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• v.35 no.2
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• pp.91-96
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• 2005

Purpose : To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Materials and Methods Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER Computerized Dental X-ray $System^{(R)}$. Fractal dimensions were calculated three times at each area by Scion Image $PC^{(R)}$ program. Rectangular region of interest $(30\times30)$ were selected at apical lesion and normal apex of each image. Results : The fractal dimension at apical lesion of first diagnosis $(L_0)$ is $0.940{\pm}0.361$ and that of normal area $(N_0)$ is $1.186{\pm}0.727(p<0.05)$. Fractal dimension at apical lesion of 6 months after endodontic treatment $(L_1)$ is $1.076{\pm}0.069$ and that of normal area $ (N_1)$ is $1.192{\pm}0.055(p<0.05)$. Fractal dimension at apical lesion of 1 year after endodontic treatment $(L_2)$ is $1.163{\pm}0.074$ and that of normal area $(N_2)$ is $1.225{\pm}0.079(p<0.05)$. After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. Conclusion : The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.33 no.5
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• pp.494-498
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• 2007

Purpose: This study was done to know the usefulness of fractal analysis when evaluating the radiologic changes after decompression on jaw bone cystic lesions using fractal analysis. Materials and methods: 30cases of cystic lesions were followed up after decompression. Panoramic image was used to observe radiologic changes around the cystic lesion. The part of the panoramic image which showed radiologic change was defined as region of interest(ROI); The fractal dimension of the ROI was calculated using box-counting method. Results: Using sign-rank test, there was a statistically significant difference in fractal dimensions after decompression therapy(P<0.0001). The fractal dimensions statistically increased after decompression(the median of D:0.12). Conclusions: The ROI after decompression showed higher fractal dimensions which offer the objective proof of the bone healing around cystic lesions after decompression treatment.

• Proceedings of the KSRS Conference
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• 2007.10a
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• pp.29-32
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• 2007

Tidal channel development is influenced by sediment type, grain size, composition and tidal current. Tidal channels are usually characterized by channel development, density and shape. Quantitative analysis of tidal channels using remotely sensed data have rarely been studied. The objective of this study is to quantify tidal channels in terms of fractal dimension and compare different inter-tidal channel patterns. For the fractal analysis, we used Box counting method which had been successfully applied to streams, coastlines and others linear features. For a study, the southern part of Ganghwado tidal flats was selected where is famous for high dynamics of tidal currents and vast tidal flats. This area has different widths and lengths of tidal channels. IKONOS and Komsat-2 MSC images were used for extracting tidal channels, and the Box counting method was applied to obtain fractal dimensions (D) for each tidal channel. Yeochari area possesses channels with linear pattern and less dense development and accordingly show low D values ranging from 1.037 to 1.038. On other hands, area (near Donggumdo and Yeongjongdo ) of dendrites channel pattern and dense development resulted in high D values from 1.2057 to 1.2667. Also, area possesses channels with linear pattern had low density about $18{\sim}24%$. Area of dendritic channel pattern had high density about $34{\sim}69%$. The difference of fractal dimensions about 0.2 according to channel development in tidal flats is relatively large enough to use as an index for tidal channel classification. Also, area where channels showed linear pattern had low density about $18{\sim}24%$. Area of dendritic channel pattern had high density about $34{\sim}69%$. Using fractal dimension and density, it would be possible to quantify the tidal channel development in association with surface characteristics.

• Imaging Science in Dentistry
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• v.33 no.2
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• pp.113-119
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• 2003

Purpose : To evaluate the relationship between morphometric analysis of bone microstructure from digital radiographic image and trabecular bone strength. Materials and Methods : One hundred eleven bone specimens with 5 mm thickness were obtained from the mandibles of 5 pigs. Digital images of specimens were taken using a direct digital intraoral radiographic system. After selection of ROI (100 × 100 pixel) within the trabecular bone, mean gray level and standard deviation were obtained. Fractal dimension and the variants of morphometric analysis (trabecular area, periphery, length of skeletonized trabeculae, number of terminal point, number of branch point) were obtained from ROI. Punch sheer strength analysis was performed using Instron (model 4465, Instron Corp., USA). The loading force (loading speed 1 mm/min) was applied to ROI of bone specimen by a 2 mm diameter punch. Stress-deformation curve was obtained from the punch sheer strength analysis and maximum stress, yield stress, Young's modulus were measured. Results: Maximum stress had a negative linear correlation with mean gray level and fractal dimension significantly (p<0.05). Yield stress had a negative linear correlation with mean gray level, periphery, fractal dimension and the length of skeletonized trabeculae significantly (p < 0.05). Young's modulus had a negative linear correlation with mean gray level and fractal dimension significantly (p < 0.05). Conclusions : The strength of cancellous bone exhibited a significantly linear relationship between mean gray level, fractal dimension and morphometric analysis. The methods described above can be easily used to evaluate bone quality clinically.

• The Journal of Engineering Geology
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• v.9 no.2
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• pp.119-134
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• 1999

Joints developed around the Moryang fault were investigated by traverse and inventory methods in order to characterize their orientation, spacing and density. The results of the traverse method show that the orientation of the dominant joint sets of the study area is NNE and EW, and that joint spacing distribution is a negative exponential distribution to the center of the fault and a log-normal distribution to the margin of the fault. The results of the inventory method show that the orientation of the dominant joint sets on joint map is NW and NE, and that joint density tends to increase toward the center of the fault. Fractal dimension was determined by using Box-counting method and Cantor's dust method to quantify the distribution of joint network and to evaluate the dimension around the fault. The dimension determined by Box-counting method ranges from 1.31 to 1.70 and shows the tendency of increasing value toward the center of the fault. Comparing fractal dimension by Box-counting method with joint density, fractal dimension is directly proportional to joint density. Nevertheless, fractal dimension could be varied due to the different distribution patterns of the joints with same density. The dimensions determined by Cantor's dust method show different values with respect to the orientation of scan lines. This results form the anisotropy of joint distribution.

• Journal of Welding and Joining
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• v.16 no.5
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• pp.108-118
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• 1998

This study proposes th analysis and evaluation method of time series ultrasonic signal using the chaos feature extraction for ultrasonic pattern recognition. Features extracted from time series data using the chaos time series signal analyze quantitatively weld defects. For this purpose, analysis objective in this study is fractal dimension and Lyapunov exponent. Trajectory changes in the strange attractor indicated that even same type of defects carried substantial difference in chaosity resulting from distance shifts such as 0.5 and 1.0 skip distance. Such differences in chaosity enables the evaluation of unique features of defects in the weld zone. In quantitative chaos feature extraction, feature values of 4.511 and 0.091 in the case of side hole and 4.539 and 0.115 in the case of vertical hole were proposed on the basis of fractal dimension and Lyapunov exponent. Proposed chaos feature extraction in this study can enhances ultrasonic pattern recognition results from defect signals of weld zone such as side hole and vertical hole.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.11
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• pp.152-165
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• 1998

This study proposes the analysis and evaluation method of time series ultrasonic signal using the chaoral post-process system for precision rate enhancement of ultrasonic pattern recognition. Chaos features extracted from time series data for analysis quantitatively weld defects For this purpose, feature extraction objectives in this study are fractal dimension, Lyapunov exponent, shape of strange attrator. Trajectory changes in the strange attractor indicated that even same type of defects carried substantial difference in chaoticity resulting from distance shifts such as nearby 0.5, 1.0 skip distance. Such difference in chaoticity enables the evaluation of unique features of defects in the weld zone. In quantitative chaos fenture extraction, feature values of 0.835 and 0.823 in the case of slag inclusion and 0.609 and 0.573 in the case of crack were suggested on the basis of fractal dimension and Lyapunov exponent. Proposed chaoral post-process system in this study can enhances precision rate of ultrasonic pattern recognition results from defect signals of weld zone, such as slag inclusion and crack.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.817-821
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• 1997

Ever since the nonlinearity of machine tool dynamics was established, researchers attempted to make use of this fact to devise better monitoring, diagnostics and system, which were hitherto based on linear models. Theory of chaos, which explains many nonlinear phenomena comes handy for furthering the analysis using nonlinear model. In this study, measuring system will be constructed using multi-sensor (Tool Dynamometer, Acoustic Emission) in end millingprocess. Then, it will be verified that cutting force is low-dimensional deterministic chaos calculating Lyapunov exponents, Fractal dimension, Embedding dimension. Aen it will be investigated that the relations between characteristic parameter caculated form sensor signal and tool wear.