• Communications of Mathematical Education
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• v.38 no.2
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• pp.247-261
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• 2024

This study propose the educational potential of an activity that solves the task of one-stroke drawing of complex figures using a drag-and-drop type educational programming language such as Scratch. The problem of determining whether a given shape is capable of one-stroke drawing is a separate problem from actually finding the path of one-stroke drawing and implementing it through programming. In particular, finding a path that allows one-stroke drawing of complex shapes with regularity and implementing it through programming requires problem-solving capabilities based on the convergence of various mathematical knowledge. Accordingly, in this study, problems related to one-stroke drawing concerning polygon-related shapes, tessellation-related shapes, and fractal shapes were presented, and the results of one-stroke drawing programming of the shapes were exemplified. In addition, the mathematical knowledge and computational thinking elements necessary for the solution of the illustrated problem were analyzed. This study is significant as a new example of the mathematics education that combines mathematics and information.

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.2
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• pp.59-64
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• 2004

Most features of nature and phenomena we encounter in many branches of science are inherently very irregular and have fractal aspects. Thus the analysis of them with the traditional methods such as a differential operator may result in their ill-posed problems. To settle these problems, one may use several type of mean filters which smooth the input signal. However when a given function or data are complex in their nature, there may be loss of some original information during these process. In this paper, we utilized the tangent plane method instead of mean filters for the purpose of less loss of information and more smoothness. After then we attempt to take more accurate edges for the irregular image on the basis of the Otzu threshold. Finally we introduce the effective edge extracting method which use the fractal dimension representing the complexity of the given image.

• 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.

• Proceedings of the Korean Information Science Society Conference
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• 2002.10d
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• pp.454-456
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• 2002

압축 방법에는 크게 손실(lossy)압축과 무손실(lossless)압축으로 나눌 수 있다. 그 중 프랙탈 이미지 압축은 lossy 압축의 한가지 방법으로서 개별적인 화소들에 대한 자료를 저장하기보다는, 영상 생성을 위한 명령이나 방식을 저장하는 방법이다. 특히 이미지의 내에 자기유사성(self-similarity)과 중복성(Redundancy)을 이용하여 관련성을 발견하고 수학적인 공식으로 표현하려는 방식이다. 그러나 이미지를 Domain과 Range로 블록화 한 후 유사한 이미지를 찾아내는 데 걸리는 시간이 상당히 길다. 여기에서는 Domain과 Range의 외곽선의 기울기의 부호를 이용하여 블록을 16가지로 클래스화 하여서, 전체의 Domain 블록을 탐색하는 데 걸리는 시간을 줄이고자 하였다. 전체 탐색을 하는 경우보다 10배 이상의 속도향상을 보였고, 이미지에 따라서는 PSNR 값의 손실도 없음을 보였다.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2004.06a
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• pp.89-94
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• 2004

우리가 일반적으로 다루는 많은 대상들은 대부분 복잡하고 불규칙적인 형태를 지니고 있다. 이로 인해 보통 사용하는 미분연산자와 같은 전통의 수학적 기법들은 경우에 따라 심각한 불량 문제(ill-posed problem)를 야기하여 부정확한 결과를 나타내기도 한다. 이의 해결을 위해 전처리 과정으로 평활화를 위한 여러 가지 mean filter를 사용하기도 한다. 그렇지만 원 자료가 근본적으로 복잡한 경우 위 과정으로 오히려 중요 정보가 소실될 수도 있다. 이에 본 논문에서는 먼저 전처리로서 흔히 사용되는 각종 평균필터 대신 손실을 최소화하면서 곡면의 부드러움(smoothness)을 유도할 수 있는 접평면 접근 방식을 이용하고. 아울러 대상 영상의 복잡도에 연동한 프랙탈 차원을 적용하여 보다 효과적으로 영상의 경계를 추출하고자 했다.

• The Mathematical Education
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• v.37 no.1
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• pp.115-138
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• 1998

We seek the possibility of introduction of Fractals to the high school math. curriculum through identifying Fractals teaching programs appropriate for the scopes and sequences in math. education for the high school students. We presented the contents of Fractal theory suitable for the high school students. The following subjects were chosen to be introduced; self-similarity, Fractal dimension, Cantor set, Sierpinsky triangle, Sierpinsky carpel Koch curve, Koch island, perimeter estimate of rugged profiles drawn on paper, and chaos game. We developed the working papers and the criteria for appraisal. Each working paper focuses on the activities in which students can solve the given problems, understanding the characteristics and ideas of Fractals. The working papers were given to the second year students who take science course, and the degree of achievements were analyzed based on the appraisal criteria. The results show that it is possible to introduce Fractals to the high school students.

• 한국해양학회지
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• v.29 no.3
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• pp.228-238
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• 1994

The change of sea-level is a good indicator of the change of climate during the Quaternary period. The sea-levels in the world have been changing very irregularly during that time. The pattern of the Quaternary sea-level change was assumed to be a stochastic fractal in this study. We measured fractal dimensions of the Holocene sea-levels of the Hudson river estuary and the Delaware coast. A box counting method gave almost the same values. i.e., D=1.358 for the Hudson sea-level changes and D+1.346 for the Delaware sea-level changes. the ability of the inverse method of fractal interposea-levels. IFIF reproduction the realistic sea-levels for the both of them. The delaware sea-level data made less statistical errors for the interpolation of IFIF than the Hudson and the Delaware sea-levels. IFIF reproduction the realistic sea-levels for the both of them. The Delaware sea-level data made less statistical errors for the interpolation of IFIF than the Hudson sea-level data. This suggests that the Delaware sea-level data are more reliable than the Hudson sea-level data was calculated from the fractal dimension of the Delaware sea-level data. Fractal interpolation functions (FIF) was used to reconstruct the peleosea-levels of the Korean coasts and the Atlantic Ocean coasts of the United States. The Korean Peleosea-level change generacted by FIF is different from the peleosea-level change of the eastern U.S.. The Korean peleosea-levels are much higher than the eastern U.S. Paleosea-levels, comparing to each other from the present to 8,000 BP.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.59-76
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• 2006

This research focuses on the relationship between mathematics and visual art from a perspective of chaos theory which emerged under the influence of post-modernism. Culture and history, which transform dynamically with the passing of time, are models of complexity. Especially, when the three periods of Medieval, Renaissance, and 17-18 Centuries are observed, the Renaissance period is phase transition phenomenon era between Medieval and 17-18 Centuries. The transition stage between the late Medieval times and the Renaissance; and the stage between the Renaissance and the Modern times are also phase transitions. These phenomena closely resemble similarity in Fractal theory, which includes the whole in a partial structure. Phase transition must be preceded by fluctuation. In addition to the pioneers' prominent act of creation in the fields of mathematics and visual an serving as drive behind change, other socio-cultural factors also served as motivations, influencing the transformation of the society through interdependency. In particular, this research focuses on the fact that scientific minds of artists in the Renaissance stimulated the birth of Perspective Geometry.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.13 no.10
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• pp.834-839
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• 2000

The structural properties that SEM photograph of ZnO varistors surface studied by fractal mathematics program were investigated to verify the relations of electrical characteristics. The SEM photograph of ZnO varistors surface were changed by binary code and the grain shape of that were analyzed by fractal dimension. The void of ZnO varistors surface was found by fractal program. The relation between grain density and electrical properties depend on fractal dimension. The grain size in ZnO varistors surface was decreased by increasing of Sb$_2$O$_3$ addition. The spinel structure was formed by Sb$_2$O$_3$addition and it was depressed the ZnO grain formation. The grain size of ZnO by Sb$_2$O$_3$addition were from 5 to 10[${\mu}{\textrm}{m}$]. Among of ZnO varistors, fractal dimension of ZnO4 was very high as a 1.764. The density of grain boundary in ZnO2 and ZnO3 varistors surface was 15[%] by formed spinal structure. The breakdown electric field of ZnO2 that fractal dimension has 1.752 was very high to be 8.5[kV/cm]. When the fractal dimensin was high, the grain shape of ZnO varistors was complex and the serial layers of ZnO grain was increased.

• Journal of the Korea Computer Graphics Society
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• v.1 no.2
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• pp.248-253
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• 1995

Mandelbrot에 의하여 제안된 Random Fractal은 현실감 있는 지형의 모델링을 가능하게 하였으며. Fournier등은 수학적으로 매우 복잡한 Fractal이론을 단순화한 중간점 분할 알고리즘(Midpoint Subdivision Algorithm)을 고안하여 다양한 형태의 지형 모델링에 매우 성공적인 결과를 얻게 되었다. 그러나, Random Fractal을 응용한 여러 종류의 알고리즘들은 이것의 특성으로 인하여, 생성되는 지형의 형태를 예측하기 어려운 단점이 있다. 따라서, 본 논문에서는 중간점 분할 알고리즘을 이용하여 사용자가 원하는 형태의 지형을 모델링할 수 있는 방법에 대하여 논하였다. 전체적인 지형의 모델링 과정을 크게 전역 제어와 지역 제어의 두 단계로 구분하여, 전역 제어 단계에서 전체 지형의 개략적인 형태를 제어하여 모델링한 후 지역 제어 단계에서의 세부적인 형태제어를 통하여 최종적으로 사용자가 원하는 형태의 지형을 모델링할 수 있는 방법을 제안하였다. 또한, GUI(Graphical User Interface)를 이용하여 전역 제어와 지역 제어에서 생성되는 전체 지형의 형태를 wire frame을 이용하여 실시간에 회전시키며 점검할 수 있도록 하여 세부적인 수정을 용이하게 하였다.