• Journal of Korea Water Resources Association
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• v.54 no.1
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• pp.49-60
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• 2021

This study presents a methodology to estimate two distinct fractal dimensions of natural river basin by using fractal tree concept. To this end, an analysis is performed on fractal features of a complete drainage network which consists of all possible drainage paths within a river basin based on the growth process of fractal tree. The growth process of fractal tree would occur only within the limited drainage paths possessing stream flow features in a river basin. In the case of small river basin, the bifurcation process of network is more sensitive to the growth step of fractal tree than the meandering process of stream segment, so that various bifurcation structures could be generated in a single network. Therefore, fractal dimension of network structure for small river basin should be estimated in the form of a range not a single figure. Furthermore, the network structures with fractal tree from this study might be more useful information than stream networks from a topographic or digital map for analysis of drainage structure on small river basin.

• Journal of The Korean Astronomical Society
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• v.41 no.6
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• pp.157-161
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• 2008

We have estimated the fractal dimension of the molecular clouds associated with the Hii region Sh 156 in the Outer Galaxy. We selected the $^{12}CO$ cube data from the FCRAO CO Survey of the Outer Galaxy. Using a developed code within IRAF, we identified slice-clouds (2-dimensional clouds in velocity-channel maps) with two threshold temperatures to estimate the fractal dimension. With the threshold temperatures of 1.8 K, and 3 K, we identified 317 slice-clouds and 217 slice-clouds, respectively. There seems to be a turn-over location in fractional dimension slope around NP (area; number of pixel) = 40. The fractal dimensions was estimated to be D = $1.5\;{\sim}\;1.53$ for $NP\;{\geq}\;40$, where $P\;{\propto}\;A^{D/2}$ (P is perimeter and A is area), which is slightly larger than other results. The sampling rate (spatial resolution) of observed data must be an important parameter when estimating fractal dimension. Fractal dimension is apparently invariant when varying the threshold temperatures applied to slice-clouds identification.

• 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.32 no.4
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• pp.201-206
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• 2002

Purpose : To evaluate the radiographic change of operation sites after orthognathic surgery using the digital image processing and fractal analysis. Materials and Methods : A series of panoramic radiographs of thirty-five randomly selected patients who had undergone mandibular orthognathic surgery (bilateral sagittal split ramus osteotomy) without clinical complication for osseous healing, were taken. The panoramic radiographs of each selected patient were taken at pre-operation (stage 0), 1 or 2 days after operation (stage 1), 1 month after operation (stage 2), 6 months after operation (stage 3), and 12 months after operation (stage 4). The radiographs were digitized at 600 dpi, 8 bit, and 256 gray levels. The region of interest, centered on the bony gap area of the operation site, was selected and the fractal dimension was calculated by using the tile-counting method. The mean values and standard deviations of fractal dimension for each stage were calculated and the differences among stage 0, 1, 2, 3, and 4 were evaluated through repeated measures of the ANOVA and paired t-test. Results : The mean values and standard deviations of the fractal dimensions obtained from stage 0, 1, 2, 3, and 4 were 1.658±0.048, 1.580±0.050, 1.607±0.046, 1.624±0.049, and 1.641 ±0.061, respectively. The fractal dimensions from stage 1 to stage 4 were shown to have a tendency to increase (p < 0.05). Conclusion: The tendency of the fractal dimesion to increase relative to healing time may be a useful means of evaluating post-operative bony healing of the osteotomy site.

• Imaging Science in Dentistry
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• v.40 no.3
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• pp.123-129
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• 2010

Purpose : To evaluate the effect of surgical treatment of ligature-induced peri-implantitis in dogs using fractal analysis. Also, the capabilities of fractal analysis as bone analysis techniques were compared with those of histomorphometric analysis. Materials and Methods : A total of 24 implants were inserted in 6 dogs. After a 3-months, experimental periimplantitis characterized by a bone loss of about 3 mm was established by inducing with wires. Surgical treatment involving flap procedure, debridement of implants surface with chlorhexidine and saline (group 1), guided bone regeneration (GBR) with absorbable collagen membrane and mineralized bone graft (group 2), and $CO_2$ laser application with GBR (group 3) were performed. After animals were sacrificed in 8 and 16 weeks respectively, bone sections including implants were made. Fractal dimensions were calculated by box-counting method on the skeletonized images, made from each region of interest, including five screws at medial and distal aspects of implant, were selected. Results : Statistically significant differences in the fractal dimensions between the group 1($0.9340{\pm}0.0126$) and group 3($0.9783{\pm}0.0118$) at 16 weeks were found (P<0.05). The fractal dimension was statistically significant different between 8($0.9395{\pm}0.0283$) and 16 weeks in group 3 (P<0.05). These results were similar with the result of the evaluation of new bone formation in histomorphometric analysis. Conclusions : Treatment of experimental peri-implantitis by using $CO_2$ laser with GBR is more useful than other treatments in the formation of new bone and also the tendency of fractal dimension to increase relative to healing time may be a useful means of evaluating.

• Archives of design research
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• v.15 no.1
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• pp.5-14
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• 2002

Fractal which was named by Mandelbrot in 1975 and its theory have been taken notice of many fields of scholarship, namely mathematics, physics, geography, architecture, art, philosophy and so on. If we approach Fractal on the basis of the designing cogitation, it can be used not only as one of materials to take a crease thinking in design, also as a due of the methods to assess the design problem with a new point of view. Based on above background, in this study, it was studied on the graphic artist, Morits Collelius Escher who has been well known as the great artist of illusion," and on the attributes of Fractal which were contained in his various work\ulcorner As a reset, the four attributes, namey ′fractal dimension′, ′self-similarity, ′recursiveness′and ′infinity were founded in his works. Also, it was founded that Escher had employed the attributes of Fractal in his almost works for "the representation of the condition of unified-duality," that is to say, for the union of two different dimensions. After this, it is expected that this study shoed be extended to the development of the principle of Fractal-Design on the basis of ′Fractal which can be defined as the phenomenon of repetitious pattern between chaos and order and′the formative beauty of Fractal′.

• Journal of Electrochemical Science and Technology
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• v.14 no.2
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• pp.194-204
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• 2023

Models based on diffusion-limited aggregation (DLA) have been extensively used to explore the mechanisms of dendritic particle aggregation phenomena. The physical and chemical properties of systems in which DLA aggregates emerge are given in their fractal. In this paper, we present a comprehensive study of the growth of electrodeposited copper dendrites in flat plate electrochemical cells from a fractal perspective. The effects of growth time, applied voltage, copper ion concentration, and electrolyte acidity on the morphology and fractal dimension of deposited copper were examined. 'Phase diagram' set out the variety of electrodeposited copper fractal morphology analysed by metallographic microscopy. The box counting method confirms that the electrodeposited dendritic structures manifestly exhibit fractal character. It was found that with the increase of the voltage and copper ion concentration. The fractal copper size becomes larger and its morphology shifts towards a dendritic structure, with the fractal dimension fluctuating around 1.60-1.70. In addition, the morphology of the deposited copper is significantly affected by the acidity of the electrolyte. The increase in acidity from 0.01 to 1.00 mol/L intensifies the hydrogen precipitation side reactions and the overflow path of hydrogen bubbles affects the fractal growth of copper dendrites.

• KSTLE International Journal
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• v.3 no.2
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• pp.75-78
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• 2002

The surface morphology of oil-lubricated surfaces fer hydraulic piston motors is believed to be extremely effective in contact mechanics, adhesion, friction and weak In order to describe morphology of various rubbed surfaces on driving conditions, the wear test was carried out under different experimental conditions in an oil-lubricated system. And fractal descriptors were applied to rubbed surfaces of hydraulic members and analyzed through an image processing system. These descriptors to analyze surface structure are fractal dimension. Surface fractal dimensions can be determined by sum of intensity difference of surface pixel. The morphology of rubbed surfaces can be effectively obtained by fractal dimension.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.755-759
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• 2000

The determination of surface topography is believed to be extremely important in the areas of contact mechanics, adhesion and friction. In order to describe topography of various frictional surface. the wear test was carried out under different experimental conditions in dry friction. And fractal descriptors was applied to frictional surface of laser modified steel with image processing System. These descriptors to analyze surface structure are fractal dimension. Surface fractal dimension can be determined by sum of intensity difference of surface pixel. Topography of frictional surface can be effectively obtained by fractal dimensions.

• Journal of the Korean institute of surface engineering
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• v.43 no.1
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• pp.12-16
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• 2010

The morphology of the passivated surface of stainless steel (SS) was quantitatively characterized based on fractal geometry. In particular, the surface irregularities of the passivated 304 and 439 SSs were comparatively analyzed in terms of their self-similar fractal dimensions. The passivated surface of 439 SS in an acid-based electrolyte proved to have a higher fractal dimension, as compared to that of 304 SS, esp. at a scale of several tens of nanometers, strongly indicating the higher irregularity of the passivated surface. It is anticipated that the fractal approach suggested herein might be effectively utilized to analyze the irregularity of the steel surface and/or the compactness of the oxide film.