• Archives of design research
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• v.17 no.1
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• pp.211-220
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• 2004

The Chaos theory of complexity and Fractal theory which became a prominent figure as a new paradigm of natural science should be understood not as whole, and not into separate elements of nature. Fractal Dimensions are used to measure the complexity of objects. We now have ways of measuring things that were traditionally meaningless or impossible to measure. They are capable of describing many irregularly shaped objects including man and nature. It is compatible method of application to express complexity of nature in the dimension of non-fixed number by placing our point of view to lean toward non-linear, diverse, endless time, and complexity when we look at our world. Fractal Dimension allows us to measure the complexity of an object. Having a wide application of fractal geometry and Chaos theory to the art field is the territory of imagination where art and science encounter each other and yet there has not been much research in this area. The formative word has been extracted in this study by analyzing objective data to grasp formative principle and geometric characteristic of (this)distinct figures of Fractals. With this form of research, it is not so much about fractal in mathematics, but the concept of self-similarity and recursiveness, randomness, devices expressed from unspeakable space, and the formative similarity to graphic design are focused in this study. The fractal figures have characteristics in which the structure doesn't change the nature of things of the figure even in the process if repeated infinitely many times, the limit of the process produces is fractal. Almost all fractals are at least partially self-similar. This means that a part of the fractal is identical to the entire fractal itself even if there is an enlargement to infinitesimal. This means any part has all the information to recompose as whole. Based on this scene, the research is intended to examine possibility of analysis of fractals in geometric characteristics in plasticity toward forms in graphic design. As a result, a beautiful proportion appears in graphic design with calculation of mathematic. It should be an appropriate equation to express nature since the fractal dimension allows us to measure the complexity of an object and the Fractla geometry should pick out high addition in value of peculiarity and characteristics in the complex of art and science. At the stage where the necessity of accepting this demand and adapting ourselves to the change is gathering strength is very significant in this research.

• Journal of Korea Water Resources Association
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• v.45 no.9
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• pp.943-957
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• 2012

In this study, a technique based on Fractal Theory with Erosion Model was developed to interpolate the river morphology data at the border area between river bed and river side where both surface and under water surveyings can not be committed easily. Three dimensional river morphology data along the Ara River was generated by the developed technique. The Ara River is an artificially constructed waterway for vessels between the Han River and West Sea of Korea. The result was compared with the survey data by RMSE of 0.384, while the IDW interpolation result has RMSE of 0.802. Consequently, the developed river morphology data interpolation technique using Erosion Model based Fractal Theory is conceived to be superior to the IDW which has been generally used in generating the river morphology data.

• Korean Journal of Soil Science and Fertilizer
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• v.40 no.3
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• pp.189-195
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• 2007

Using fractal dimensionality theory proposed by Riew and Sposito (1991), we attempted to analyze quantitatively the characteristics of porous distribution for built-in soils in the mini-lysimeter and artificial seed-bed media. The 2" stainless core soil samples were taken from lysimeter soils. Artificial seed-bed media were compacted in the acrylic core filled with raw materials consisted of cocopeat, zeolite and perlite. N (Constant number of partitioned group size smaller media volumes) and r (Self-similarity ratio) parameters consisting of fractal dimension D=log(N)/log(1/r) were obtained by Excel Programme using the Riew and Sposito's fractal model. The pore distribution of tested media was screened in pore size and its occurring frequency. The results reveal that the distribution range of pores is wider in the lysimeter soils than in the seed-bed media, while average size of pores in the media is smaller in lysimeter core soils than in seed-bed media.

• Korean Journal of Agricultural Science
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• v.41 no.4
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• pp.379-384
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• 2014

In general, fractal analysis which is based on self-similarity as a basic theory has been mainly used to define the characteristics of complex mathematical figures, however, considering its basic theory, it can be also used to analyze the surface ununiformity of unknown materials. In this study, the soil samples were collected from the reclaimed (remodelled) agricultural fields which mean that the external soil is artificially piled up (mainly up to 1m) on the lands, Naju, Jellanam-do and Gumi, Gyeongsangbuk-do, and the conventional agricultural fields, Anseong, Gyeonggi-do and Hwasoon, Jellanam-do, and compared using fractal dimension analysis on the basis of the results of chemical properties. The score of fractal dimension ($D_0$) for organic matter was lower in Hwasoon (1.46) and Naju (1.58) than Anseong (1.86) and Gumi (1.96), and this trend showed similarly in soil pH. On the basis of the results of chemical properties, fine textured-soils (Hwasoon and Naju) and conventional agricultural fields were chemically uniform compared to coarse textured-soils (Anseong and Gumi) and the reclaimed. Therefore, it is required to develop technical methods for integrated soil management to the reclaimed lands.

• Korean Institute of Interior Design Journal
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• v.23 no.1
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• pp.88-95
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• 2014

This study intended arousal of other viewpoints that deal with and understand spaces and shapes, by describing the concept of 'dimensions' into visual patterns. Above all, the core concept of spatial dimensions was defined as 'expandability'. Then, first, the 'golden ratio', 'Fibonacci sequence', and 'fractal theory' were defined as elements of each dimension by stage. Second, a 'unit cell' of one dimension as 'minimum unit particles' was set. Next, Fibonacci sequence was set as an extended concept into two dimensions. Expansion into three dimensions was applied to the concept of 'self-similarity repetition' of 'Fractal'. In 'fractal dimension', the concept of 'regularity of irregularity' was set as a core attribute. Plus, Platonic solids were applied as a background concept of the setting of the 'unit cell' from the viewpoint of 'minimum unit particles'. Third, while 'characteristic patterns' which are shown in the courses of 'expansion' of each dimension were embodied for the visual expression forms of dimensions, expansion forms of dimensions are based on the premise of volume, directional nature, and concept of axes. Expressed shapes of each dimension are shown into visually diverse patterns and unexpected formative aspects, along with the expression of relative blank spaces originated from dualism. On the basis of these results, the 'unit cell' that is set as a concept of theoretical factor can be defined as a minimum factor of a basic algorism caused by other purpose. In here, by applying diverse pattern types, the fact that meaning spaces, shapes, and dimensions can be extracted was suggested.

• Water for future
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• v.28 no.5
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• pp.117-127
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• 1995

The application and analysis for the scale considering GIUH model proposed by the authors in this issue have been performed for the leemokjung sub-basin in the Pyungchang basin one of IHP representative basin in Korea. Scales of topographic maps for model application and fractal analysis are 1:25,000, 1:50,000 and 1:100,000. The ratio between successive scales is therefore constant. Link lengths were measured using a curvimeter with the resolution of 1 mm. Richardson's method was employed to have fractal dimension of streams. Apparent alternations of parameters were found in accordance with variations of map scale. And this tendency could mislead physical meanings of parameters because model parameters had to preserve their own value in spite of map scale change. It was found that uses of fractal transform and Melton's law could help to control the scale problem effectively. This methodlogy also could emphasize the relationship between network and basin to the model. To verify the applicability of GIUH proposed in this research, the model was compared with the exponential GIUH model. It is proven that proposed 2-parameter gamma GIUH model can better simulate the corresponding runoff from any given flood events than exponential GIUH model. The result showed that 2-parameter gamma GIUH model and fractal theory could be used for deriving scale considered IUH of the basin.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.6
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• pp.2730-2747
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• 2016

Due to the limitation of the bandwidth resource and capture resolution of depth cameras, low resolution depth maps should be up-sampled to high resolution so that they can correspond to their texture images. In this paper, a novel depth map up-sampling algorithm is proposed by exploiting the fractal internal self-referential feature. Fractal parameters which are extracted from a depth map, describe the internal self-referential feature of the depth map, do not introduce inherent scale and just retain the relational information of the depth map, i.e., fractal transforms provide a resolution-independent description for depth maps and could up-sample depth maps to an arbitrary high resolution. Then, an enhancement method is also proposed to further improve the performance of the up-sampled depth map. The experimental results demonstrate that better quality of synthesized views is achieved both on objective and subjective performance. Most important of all, arbitrary resolution depth maps can be obtained with the aid of the proposed scheme.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.11
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• pp.611-616
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• 2004

In this paper, we introduce a very fast and efficient fractal coding scheme by using the spatial prediction on ultra-small atomic range blocks. This new approach drastically speeds up the encoding while improving the fidelity and the compression ratio. The affine transformation coefficients between adjacent range blocks induced by this method often have good correlations thereby the compression ratios can further be improved. The proposed method leads to improved rate-distortion performance compared to previously reported pure fractals, and it is faster than other state-of-the-art fractal coding methods.

• Journal of the Korean Geotechnical Society
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• v.31 no.4
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• pp.19-29
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• 2015

Nowadays, the importance of the information management of construction sites to achieve the goal of safety construction. This management uses the collaborated analysis of in-situ monitoring data and numerical analysis, especially of an earth retaining structures of excavation sites. In this paper, the fractal theory was applied to actually monitored data from various excavation sites to develop the alternative interpolation technique which could predict the displacement behavior of unknown location around the monitoring locations and the future behavior of the monitoring locations with the steps of excavation. Data, mainly from inclinometer, were collected from various sites where retaining structures were collapsed during construction period, as well as from normal sites with the characteristics of geology, excavation method etc. In the analyses, Hurst exponent (H) was estimated with monitored periods using the Rescaled range analysis (R/S analysis) method applying the H in simulation processes. As the results of the analyses, Hurst exponents were ranged from 0.7 to 0.9 and showed the positive correlation of H > 1/2. The simulation processes, then, with the Hurst exponent estimated by Rescaled range analysis method showed reliable results. In addition, it was also expected that the variation of Hurst exponents with the monitoring period could instruct the abnormal behavior of an earth retaining structures to directors or operators. Therefore it was concluded that fractal theory could be applied for predicting the lateral displacement of unknown location and the future behavior of an earth retaining structures to manage the safety of construction sites during excavation period.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.233-236
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• 2008

Recently, the development and application of unmaned robots are increasing in various fields including surveillance and reconnaissance, planet exploration and disaster relief. Unmaned robots are usually controlled from distance using radio communications but they should be equipped with autonomous travelling function to cope with unexpected terrains and obstacles. This means that unmanned robots should be able to evaluate terrain's characteristics quantitatively using mounted sensors so as to traverse harsh natural terrains autonomously. For this purpose, this paper presents an algorithm for extracting terrain information from elevation maps as an early step of traversability analysis. Slope and roughness information are extracted from a world terrain map based on least squares method and fractal theory, respectively. The effectiveness of the proposed algorithm is verified on both fractal and real terrain maps.