• 한국게임학회 논문지
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• 제14권6호
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• pp.109-118
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• 2014

이미지 디자인 등에 사용하기에 용이한 정다각형의 회전대칭성을 갖는 프랙탈 생성에 대해 연구하였다. Loocke의 논문[13]에서 사용한 방법과 같이 회전, 축소 아핀함수를 기반으로 하되 제곱근(square root)함수 대신 줄리아 셋(Julia set)을 생성하는 함수들로 확장하여 IFS(iterated function systems)를 구성하였다. 그 결과 줄리아 셋의 모양에 바탕을 둔 회전 대칭적 프랙탈을 생성할 수 있었으며, 줄리아 셋의 모양이 잘 나타나지 않는 경우에는 IFS 생성 알고리즘의 확률적 함수선택 부분을 변경하여 줄리아 셋의 모양이 뚜렸해지도록 할 수 있음을 보였다. 또한 줄리아 셋의 모양을 지수의 변화를 통해 변형하는 방법을 제안하였다.

• 대한수학회논문집
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• 제13권2호
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• pp.281-287
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• 1998

We define a new form of fractals, called the braked subsimilar set from a self similar set and find the relation between their fractal dimensions.

• 한국산학기술학회논문지
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• 제3권3호
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• pp.177-182
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• 2002

이 논문에서는 맨델브로트집합의 개념을 n차 복소 다항식 Zⁿ+c(c∈C, n≥2)에 확장하여 n차 분기집합 및 줄리아 집합을 정의하고, 이 집합의 대칭성, 유계성 및 연결성 등에 관하여 이론적으로 연구하였다. 그 연구결과를 이용하여 n차 분기집합 및 줄리아 집합을 효율적으로 작성하는 알고리즘을 고안하고, C++컴퓨터 언어를 사용하여 마이크로소프트사의 윈도우 운영체제하에서 사용자가 마우스를 조작하여 n차 분기집합 및 줄리아 집합을 구성할 수 있도록 소프트웨어 MANJUL을 개발하는 것이 본 논문의 목적이다. MANJUL 소프트웨어의 중요한 특징으로서 CUI(graphical user interfaces) 환경에서 단순한 마우스 조작을 통하여 n차 분기집합 및 줄리아 집합을 작성하고 그 일부분을 확대함은 물론, n차 분기집합 성분의 주기등을 계산 및 저장함으로써, 이 집합들의 다양한 이론적 성질과 기하학적 구조를 시각적으로 확인할 수 있도록 하였다.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2009년도 IWAIT
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• pp.655-658
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• 2009

Fractal dimension has been used for texture analysis as it is highly correlated with human perception of surface roughness and applied to quantifying the structures of wide range of objects in biology and medicine. On the other hand, the evaluation of the human skin state is based solely on the subjective assessment of clinicians; this assessment may vary from moment to moment and from rater to rater. Therefore we attempt to analysis of skin texture image using fractal dimension and discuss its application to evaluating human skin state. It can be helpful for extracting human features and also can be useful for detection of many human skin diseases. This paper presents a method to calculate fractal dimension of skin with use of camera lens magnification. We take multiple pictures frequently from skin with different camera lens magnification as a magnification factor of fractal set, and counting the number of objects (cells) in each picture as a number of self similar pieces of fractal set.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권3호
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• pp.191-196
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• 2007

The main components in the generalized Mandelbrot sets are under a theoretical investigation for their parametric boundary equations. Using the boundary geometries, a fast construction algorithm is introduced for the generalized Mandelbrot set. This fast algorithm definitely reduces the construction CPU time in comparison with the naive algorithm. Its graphic implementation displays the mysterious and beautiful fractal sets.

• 방송공학회논문지
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• 제4권2호
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• pp.127-133
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• 1999

기존의 이산 웨이브렛 변환 기반 플랙탈 영상 압축은 프랙탈 부호화시 고정된 블럭 크기를 사용하므로 낮은 비트율에서 PSNR을 감소시킨다. 본 논문에서는 플랙탈 부호화시 가변 블록 크기를 사용하여 PSNR을 개선하는 이산 웨이브렛 기반 프랙탈 영상 부호화를 제안한다. 제안된 방법에서는 먼저 이산 웨이브렛 변환 계수들의 절대값을 최하고, 같은 공간 영역에 해당하는 다른 고주파 부대역의 이산 웨이브렛 변환 계수들을 묶어서 레인지 블록과 도메인 블록을 만든다. 그리고 각각의 레인지 블록 레벨의 레인지 블록에 대한 프랙탈 코드를 지정하고, 프랙탈 부호화,\ulcorner0\ulcorner부호화와 스칼라 양자화중 하나를 선택하여 만든 집합인 결정 트리 C를 만들고 스칼라 양자화기의 집합 q를 선택한다. 웨이브렛 계수, 프랙탈 코드와 결정 트리를 적응적 산술 부호화기를 사용하여 엔트로피 nq호화 한다. 제안된 방법은 낮은 비트율에서 PSNR을 개선하고 복원 영상의 블록킹 현상을 제거한다. 실험 결과를 통해서 제안한 방법은 기존의 프랙탈 부호화 방법과 웨이브렛 변환 부호화 방법에 비해 더 좋은 PSNR과 더 높은 압축율을 얻었다.

• 한국실내디자인학회논문집
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• 제23권1호
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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.

• Applied Microscopy
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• 제51권
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• pp.6.1-6.9
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• 2021

Histopathology is a well-established standard diagnosis employed for the majority of malignancies, including breast cancer. Nevertheless, despite training and standardization, it is considered operator-dependent and errors are still a concern. Fractal dimension analysis is a computational image processing technique that allows assessing the degree of complexity in patterns. We aimed here at providing a robust and easily attainable method for introducing computer-assisted techniques to histopathology laboratories. Slides from two databases were used: A) Breast Cancer Histopathological; and B) Grand Challenge on Breast Cancer Histology. Set A contained 2480 images from 24 patients with benign alterations, and 5429 images from 58 patients with breast cancer. Set B comprised 100 images of each type: normal tissue, benign alterations, in situ carcinoma, and invasive carcinoma. All images were analyzed with the FracLac algorithm in the ImageJ computational environment to yield the box count fractal dimension (Db) results. Images on set A on 40x magnification were statistically different (p = 0.0003), whereas images on 400x did not present differences in their means. On set B, the mean Db values presented promising statistical differences when comparing. Normal and/or benign images to in situ and/or invasive carcinoma (all p < 0.0001). Interestingly, there was no difference when comparing normal tissue to benign alterations. These data corroborate with previous work in which fractal analysis allowed differentiating malignancies. Computer-aided diagnosis algorithms may beneficiate from using Db data; specific Db cut-off values may yield ~ 99% specificity in diagnosing breast cancer. Furthermore, the fact that it allows assessing tissue complexity, this tool may be used to understand the progression of the histological alterations in cancer.

• Journal of Electrochemical Science and Technology
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• 제14권2호
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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.

• 호남수학학술지
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• 제27권3호
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• pp.405-419
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• 2005

We present some properties characterizing the Mandelbrot set of quadratic rational maps. Any quadratic rational map is conjugate to either $z^2+c$ or ${\lambda}(z+1/z)+b$. For ${\mid}{\lambda}{\mid}=1$, we find the figure of the Mandelbrot set $M_{\lambda}$, the set of parameters b for which the Julia set of ${\lambda}(z+1/z)+b$ is connected. It is seen to be the whole complex plane if ${\lambda}{\neq}1$, but it is intricate fractal if ${\lambda}=1$. This supplements the work already investigated for the case ${\mid}{\lambda}{\mid}>1$.