• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.2
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• pp.93-99
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• 2013

Fractal theory has been adopted as an effective tool for modelling complex and irregular natural phenomena facing in the fields of Computer Science, Engineering, Medical, Climatology and so on. In this paper, we presents an algorithm which enhances the performance of the triangular prism method(TPM) which has been widely used for fractal dimension extraction of natural terrains and images. For this, existing sampling methods are analyzed and a new sampling method which takes their merits is proposed. The effectiveness of the proposed algorithm is tested on fractal terrain maps and its performance is compared with that of other methods.

• 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).

• Journal of Navigation and Port Research
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• v.38 no.1
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• pp.45-52
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• 2014

Fractal theory has been widely used to quantify the complexity of remotely sensed digital elevation models and images. Despite successful applications of fractals to a variety of fields including computer graphics, engineering and geosciences, the performance of fractal estimators depends highly on data sampling. In this paper, we propose an algorithm for computing the fractal dimension based on the triangular prism method and a new sampling method. The proposed sampling method combines existing two methods, that is, the geometric step method and the divisor step method to increase pixel utilization. In addition, while the existing estimation methods are based on $N{\times}M$ window, the proposed method expands to $N{\times}M$ window. The proposed method is applied to generated fractal DEM, Brodatz's image DB and real images taken in the campus to demonstrate its feasibility.

• Journal of the Korean Society of Costume
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• v.51 no.2
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• pp.181-192
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• 2001

Men study the nature in two ways. Scientists and mathematicians inquire a branch of those two ways. Mathematical formulations are the tools and the expressions of their nature. Meanwhile, the other branch, the art, alms for different inquiry. Instead of formulating the nature, the artists create their masterpieces from their ultimate source, the Mother Nature. For thousands of years these two branches have grown together, influencing each others work. Some mathematicians find that formulation, are not enough to fully express the beauty of nature. It is believed that such a simple expression, formula, easily omits the careful details of nature. The nature is simply too chaotic to be shaped with a formula. Of those mathematicians, Mandelbrot, one of the first to realize this matter, introduced the world of fractal geometry. Fractals give new possibilities. It allows us not to limit ourselves to linear prospect, rather a whole new view of this chaotic beauty of the nature. A popular practice to understand fractals is in costume design. The artistic characteristic and organization mechanism is appalled to costumes. Meanwhile, another practice, rather aggressive, is using computer to create an image of fractals. This image is then used for motives to generate artistic expressions. Computer and paper ironing technique is used for fashion illustration in this research. The works were synthesized arid transformed from computer programs. To add more traditional painting touch to this work, Paper ironing technique was used. Since the of effect of this technique is so random, irregular, and unordered, it corresponds to fractal consideration. This thesis asserts an another prospect to fractal as a structural way of describing nature ailed fashion illustration, rather than restricting it to only mathematical theory.

• Journal of Sasang Constitutional Medicine
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• v.12 no.1
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• pp.24-36
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• 2000

Purpose : Many believe that the Sasang mentioned in the I Ching and the Sasang of Sasang Medicine (as expounded by Dr. Lee Je-ma in the book Longevity and Life Preservation in Oriental Medicine) refer to different concepts. This is untrue. In order to understand the thought patterns of Dr. Lee Je-ma and his book, it is necessary to first understand the concepts of the I Ching. The I Ching was the most respected text in Dr. Lee Je-ma time, and served as the foundation upon which his medicine stood. The purpose of this research is to understand the concept of Sasang in the I Ching and how it applies to the Sasang medicine. Method : The authors first defined the term Sasang according to the theory of I Ching. It was then discussed in relation to theories of modern science. Inferences were made as to how Sasang corresponds to the terminologies and concepts of modern science. The characteristics of Sasang interpreted through modern science were then applied to the physiology, pathology and pharmacology of Sasang Medicine. Results and Conclusion : 1. The Sasang theory of the I Ching organizes seemingly random and isolated natural phenomena into four distinct groups according to various attributes. The particular characteristics representing each of these four categories are known as Sasang. 2. The Sasang theory of I Ching has a strong correlation to the Theory of Relativity and the Theory of Complementarity, as well as the Digital and Fractal Theories. 3. By applying the Sasang Theory to various fields, the seemingly unrelated principles of physics, chemistry, biology and medicine can be seen as parts of a whole. 4. Sasang Medicine categorizes human morphology, physiology and pharmacology into four categories according to the characteristics defined by the Sasang Theory of the I Ching. 5. Grouping new discoveries of modern physics, chemistry, biology and medicine according to the Sasang Theory will bring to light the intricacies of the Sasang Theory while facilitating the incorporation of modern science into Sasang Medicine.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.3 no.3
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• pp.177-182
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• 2002

In this paper, we present a mathematical theory and algorithm consoucting some fractal sets. Among such fractal sets, the degree-n bifurcation set as well as the Julia sets is defined by extending the concept of the Mandelbrot set to the complex polynomial $Z^n$+c($c{\epsilon}C$, $n{\ge}2$). Some properties of the degree-n bifurcation set and the Julia sets have been theoretically investigated including the symmetry, periodicity, boundedness, and connectedness. An efficient algorithm constructing both the degree-n bifurcation let and the Julia sets is proposed using theoretical results. The mouse-operated software called "MANJUL" has been developed for the effective construction of the degree-n bifurcation set and the Julia sets in graphic environments with C++ programming language under the windows operating system. Simple mouse operations can construct ann magnify the degree-n bifurcation set as well af the Julia sets. They not only compute the component period but also save the images of the degree-n bifurcation set and the Julia sets to visually confirm various properties and the geometrical structure of the sets. A demonstration has verified the useful versatility of MANJUL.of MANJUL.

• Korean Journal of Ecology and Environment
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• v.44 no.1
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• pp.58-65
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• 2011

This study aims to investigate the settling velocity of aggregates of cohesive sediment (floc) and its relationship with sediment size, density and fractal dimension. A system of commercial camera and macro-lens is used for the experiment. Through the image-analysis technique, the image taken by the camera system is analyzed. For the experiment, kaolinite and a natural sediment sampled at Lake Apopka in Florida have been tested. From this study, it is known that kaolinite and Lake Apopka sediments show different behaviors mainly depending on the organic matter content. Samples of kaolinite with less organic contents show a more definite trend to follow a fractal theory and relatively strong relationships between the settling velocity, density, fractal dimension and floc size compared to the Lake Apopka sediments rich in organics.

• Geomechanics and Engineering
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• v.1 no.4
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• pp.323-335
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• 2009

Gravels forming part of the base of flexible pavements experience abrasion and crushing as a result of static and dynamic loads. Abrasion takes place when the sharp corners of the particles of gravel are removed as a result of compressive and shear loads. As a result of abrasion, the particles change in shape. Crushing is caused by the fragmentation of the particles into a mixture of many small particles of varying sizes. In this study, the abrasion and crushing of gravels are evaluated experimentally and analytically. The laboratory component of this study involves gravels that were subjected to abrasion and dynamic compression tests. The evaluation of the abrasion and crushing experienced by the gravel was carried out using fractals. In this study, the fractal dimension concept from fractal theory is used to evaluate: (a) the changes in shape, and (b) the crushing (fragmentation) of the original particles of gravel. It was determined that the fractal dimension of the profile of the particles decreased as a result of abrasion. With respect to crushing, the fragmentation fractal dimension was found to increase with the degree of breakage of the gravel. To understand the influence of crushing on the permeability of the gravels, the hydraulic conductivity of the gravels was measured before and after crushing. The hydraulic conductivity of the gravels was found to decrease with an increase in their level of crushing. Also, changes in the angle of friction of the granular materials as a result of abrasion was calculated using the Krumbein's roundness chart. The angle of friction of the granular materials was found to decrease as a result of abrasion.

• Proceedings of the Korean Information Science Society Conference
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• 1999.10b
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• pp.622-624
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• 1999

모핑 애니메이션은 컴퓨터 그래픽스 및 많은 응용에서 이용되고 있다. 모핑 애니메이션에서는 대부분 이미지들을 동영상 편집기 등을 이용하므로 많은 저장 공간을 필요로 한다. 본 논문에서는 이를 해결하는 한 방법으로 프랙탈 기법을 사용한다. 예를 보이기 위해 두 개의 나무 모핑 애니메이션을 보인다.

• Journal of Korea Multimedia Society
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• v.6 no.1
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• pp.89-96
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• 2003

This paper propose the new method witch is adopted in extracting character features and recognizing numeric characters using fractal dimension and modified Henon Attractor of the Chaos Theory. Firstly, it gets features of mesh feature, projection feature and cross distance feature from numeric character images And their feature hi converted into time series data. Then using the modified Henon system suggested in this paper, it gets last features of numeric character image after calculating Natural Measure and information bit which art meant fractal dimension. Finally, numeric character recognition is performed by statistically finding out the each information bit showing the minimum difference against the normalized pattern database. An Experimental result shows 100% character classification rates for 10 digits and 90% of recognition rates in real situation and the recognition speed was 26 characters per second.