프랙탈 기법에 의한 지형의 특성분석

권기욱(Kee Wook Kwon),지형규(Hyung Kyu Jee),이종달(Jong Dal Lee) 한국지역지리학회 2005 한국지역지리학회지 Vol.11 No.6

본 연구에서는 지형이 위치별로 자기 상사성을 가진다는 전제하에 프랙탈 차원을 이용한 지형의 복잡성을 표현해 보고자 한다. 특히 수치지도 분석기법에서 표면적 요소를 산정하여 프랙탈 차원을 산정하도록 한다. 또한 프랙탈 차원과 지형 형상요소들과의 관계를 규명하고, 프랙탈 차원의 통계적 대표치로서의 기능에 대해 고찰해 보려 한다. 본 연구에서는 GIS기법을 적용하여 지형의 프랙탈 특성을 구하였다. 길이를 이용하여 하천이나 해안선의 1차원적 프랙탈 특성을 구하는 것에서 벗어나 면적의 개념 즉, 투영면적과 표면적을 이용하여 지형의 2차원적 프랙탈 특성을 구해보았다. 그리고 프랙탈 차원과 평균경사도와의 상관관계를 검토해 보았다. 연구결과 다음과 같은 결론을 얻게 되었다. 1) 프랙탈 차원을 구하기 위한 척도로서 표면적을 사용한 경우에서도 일반적 프랙탈 차원의 특성과 같이 지형의 복잡성과 비례관계의 성질을 나타내었다. 2) 본 연구에서 제안한 표면적을 이용한 프랙탈 차원은 영천지역에서는 2.10~2.24이고 의성지역은 2.02~2.15으로 나타났다. 이 값들은 통상 알려진 지형의 프랙탈 차원인 2.10~2.20의 범위에 든다. 3) 평균경사도와 프랙탈 차원의 상관관계는 평균경사도가 25˚이상인 지역에서 결정계수 R2값이 25˚이하인 지역에 비해 30% 정도 작아진다. 그러므로 모든 지형의 거침도를 표현하기 위해선 프랙탈차원이 알맞을 것으로 본다. 본 연구결과를 통해 투영면적과 표면적을 이용한 프랙탈 차원 산정공식이 유효함을 확인하였다. 그러나 본 기법이 충분히 타당성을 인정받기 위해선 연구대상지역의 확대를 통하여 경사도와 표면적, 프랙탈 차원과의 상관관계를 더욱 명확히 할 필요가 있다. 향후 연구에선 지형의 복원에 적용 할 수 있을 것이며 fBm모델을 이용하여 교통류 해석에도 적용이 가능할 것이다. In this study, GIS method has been used to get fractal characteristics. Using the projected area and surface area, 2 dimensional fractal characteristic of terrain was found out. Correlation of fractal dimension and mean slope were also checked over. Results are as below. 1) To get a fractal dimension, the method which is using the surface area is also directly proportional to complexity of the terrain as other fractal dimension. 2) Fractal dimensions using the surface area, that is proposed in this thesis are carried out as below : Uiseong : 2.02~2.15 Yeongcheon : 2.10~2.24 These values are in a range of fractal 2.10~2.20 dimensions which has known. 3) Correlation of mean slope and fractal dimension is diminished about 30% in a region which is more than 25˚ of mean slope. So, in this region using the fractal dimension method is better than using the mean slope. From this study, on formula using the projected area and surface area is still good to get a fractal dimension that has been found. But to confirm this method the region of research should be wider and be set up the correlation of mean slope, surface area and fractal dimension. It can be applicable to restoration of terrain and traffic flow analysis in the future research.

감쇠비를 고려한 가속도 신호의 프랙탈 해석

윤문철(Moon-Chul Yoon) 한국기계가공학회 2013 한국기계가공학회지 Vol.12 No.5

To analyze the dynamic acceleration characteristics, it is necessary to identify the acceleration model using some methods that can represent the dynamic properties well. In this sense, fractal methods were used for the verification of characteristics of an acceleration signal. To estimate and analyze the geometry of acceleration signal, a fractal interpolation and its analysis was introduced in this paper. The chaotic nature of acceleration signal was considered in fractal modeling. In this study the fractal signal modeling has brought a focus within the scope of the fractal interpolation and fractal dimension. And a new idea of fractal dimension has been introduced and discussed considering the damping ratio and amplitude for its dynamic properties of the signal. The fractal dimension of acceleration with respect to the scaling factor using fixed data points of 1000 points was calculated and discussed. The acceleration behaviors of this results show some different characteristics. And this fractal analysis can be applied to other signal analysis of several machining such as pendulum type grinding and milling which has many dynamic properties in the signal.

Application of Fractal Geometry to Architectural Design

Myung-Sik Lee 대한건축학회 2014 Architectural research Vol.16 No.4

Contemporary architecture tends to deconstruct modern architecture based on rationalization just like reductionism and functionalism and secedes from it. It means change from mechanical to organic and ecological view of the world. According to these changes, consideration of a compositive relationship presented variety and complexity in architecture. Thus, the modern speculation based on rationalism cannot provide an alternative interpretation about complicated architectural phenomena. At this point in time, the purpose of this study is to investigate the possibilities of the fractal as an alternative tool of analysis and design in contemporary architecture. In this study, two major aspects are discussed. First, the fractal concepts just like ‘fractal dimension’, ‘box-counting dimension’ and ‘fractal rhythm’ can be applied to analysis in architecture. Second, the fractal formative principles just like ‘scaling’, ‘superimposition trace’, ‘distortion’ and ‘repetition’ can be applied to design in architecture. Fractal geometry similar to nature’s patterned order can provide endless possibilities for analysis and design in architecture. Therefore further study of fractal geometry should be conducted synthetically from now on.

펄프ㆍ제지 산업에서의 프랙탈 기하 원리 및 그 응용

고영찬(Young Chan Ko),박종문(Jong-Moon Park),신수정(Soo-Jung Shin) 한국펄프·종이공학회 2015 펄프.종이기술 Vol.47 No.4

Until Mandelbrot introduced the concept of fractal geometry and fractal dimension in early 1970s, it has been generally considered that the geometry of nature should be too complex and irregular to describe analytically or mathematically. Here fractal dimension indicates a non-integer number such as 0.5, 1.5, or 2.5 instead of only integers used in the traditional Euclidean geometry, i.e., 0 for point, 1 for line, 2 for area, and 3 for volume. Since his pioneering work on fractal geometry, the geometry of nature has been found fractal. Mandelbrot introduced the concept of fractal geometry. For example, fractal geometry has been found in mountains, coastlines, clouds, lightning, earthquakes, turbulence, trees and plants. Even human organs are found to be fractal. This suggests that the fractal geometry should be the law for Nature rather than the exception. Fractal geometry has a hierarchical structure consisting of the elements having the same shape, but the different sizes from the largest to the smallest. Thus, fractal geometry can be characterized by the similarity and hierarchical structure. A process requires driving energy to proceed. Otherwise, the process would stop. A hierarchical structure is considered ideal to generate such driving force. This explains why natural process or phenomena such as lightning, thunderstorm, earth quakes, and turbulence has fractal geometry. It would not be surprising to find that even the human organs such as the brain, the lung, and the circulatory system have fractal geometry. Until now, a normal frequency distribution (or Gaussian frequency distribution) has been commonly used to describe frequencies of an object. However, a log-normal frequency distribution has been most frequently found in natural phenomena and chemical processes such as corrosion and coagulation. It can be mathematically shown that if an object has a log-normal frequency distribution, it has fractal geometry. In other words, these two go hand in hand. Lastly, applying fractal principles is discussed, focusing on pulp and paper industry. The principles should be applicable to characterizing surface roughness, particle size distributions, and formation. They should be also applicable to wet-end chemistry for ideal mixing, felt and fabric design for papermaking process, dewatering, drying, creping, and post-converting such as laminating, embossing, and printing.

Morphological Analysis of Wear Particles using Fractal Parameters

Y. S. CHO,H. S. PARK 한국트라이볼로지학회 2002 한국트라이볼로지학회 학술대회 Vol.2002 No.10

The fractal dimension is the characteristics that can quantitatively define the irregularity in natural. It is useful in describing the morphology of various rubbed surface for hydraulic piston motor instead of the stylus profiling method. But fractal parameters had not constructed on the morphological characteristic of rubbed surface because of the insufficient knowledge about a conception of fractal dimension. In this study, for the purpose of applying fractal parameters practically, we have suggested way to establish the morphological characteristic of rubbed surface with fractal parameters, and we carried out an experiment on the lubricant friction and wear by using Ball-ON-Disk type tester. Materials were the brass and the bronze which are used to slipper-pad in the hydraulic piston motor. We searched tor fractal parameters of surface structure with the digital image processing, Surface fractal dimension can be determined by Slim of intensity difference of surface pixel. Using the image processing and fractal parameters for rubbed surface in the friction and wear test, morphology of rubbed surface can be effectively obtained by fractal dimensions.

FRACTAL DIMENSIONS OF INTERSTELLAR MEDIUM: II. THE MOLECULAR CLOUDS ASSOCIATED WITH THE H_II REGION SH 156

Lee, Young-Ung,Kang, Mi-Ju,Kim, Bong-Kyu,Jung, Jae-Hoon,Kim, Hyun-Goo,Yim, In-Sung,Kang, Hyung-Woo,Choi, Ji-Hoon The Korean Astronomical Society 2008 Journal of The Korean Astronomical Society Vol.41 No.6

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.

프랙탈(Fractal) 원리를 통한 도자 표현 연구

김은지(Kim, Eun Ji),박재연(Park, Jae Yeon) 한국전시산업융합연구원 2015 한국과학예술융합학회 Vol.22 No.-

본 연구의 배경 및 목적은 다음과 같다. 최근 새로운 자연과학적 발견에 기초하여 자연의 패턴이 갖는 복잡성을 설명해 주는 이론인 ‘프랙탈(Fractal)’이 대두되고 있다. 프랙탈은 자연과학과 예술이 융합된 학문으로 새로운 미학을 제시해 주는 이론이라 할 수 있다. 프랙탈은 철학, 수학, 물리학 등의 다양한 학문 분야에서 영향을 미치고 있으며, 예술가, 디자이너들에게 새로운 조형적 변수로 적용되어짐에 따라 회화, 입체, 설치 등 현대 조형작품에서 그 사례를 찾을 수 있다. 융합의 시대가 도래된 지금 프랙탈 아트라는 새로운 장르가 탄생되었듯 과학과 예술의 창조성이 서로 융합되어 그 가치를 더하고 있다. 이에 따라 프랙탈이라는 자연에 기초를 둔 디자인은 더욱더 필요성이 제기되고 있으며, 이를 위해 기초교육과 조형교육의 융합적인 학문의 중요성이 날로 증대되고 있다. 프랙탈의 기본적 개념은 하나의 개체에서 시작하여 유사한 형상이 반복되는 알고리즘(algorithm)을 통해 무한히 생성되어 재귀되는 ‘자기유사성’, ‘프랙탈 차원’, ‘비선형성’ 을 특징으로 하고 있다. 본 연구의 연구방법 및 내용, 그 결과는 다음과 같다. 프랙탈의 원리가 적용된 현대 조형의 사례를 분석함으로써 회화, 건축, 설치, 도자 분야에서 나타나는 규칙과 패턴은 자연현상에 본질적인 법칙이 내재된 프랙탈 이론으로 설명될 수 있다. 그에 따라 디자인 조형 요소로서의 가능성을 확립하고, 자연계 법칙에 의해 구조와 기능적인 면에서 이상적인 형태인 육각형을 차용하여 작품에 적용하였다. 이는 자연물에서 보여지는 프랙탈 원리를 연구자의 작품에 응용함으로써 자연의 원리가 갖는 함축적인 의미를 더해 자연과학과 예술의 융합을 창조적으로 표현하고자 한다. 이에 본 연구의 목적은 법칙성이 내재된 자연과학 안에서 디자인적 조형 요소를 추출하여 적용함으로써 프랙탈의 다양한 조형적 가능성을 제시하고, 향후 다학제적 연구가 더욱 증대될 것이다. Background and objectives of this study are as follows. Fractal which is a theory explaining the complexity of natural patterns based on a new natural scientific discovery has emerged recently. Fractal can be explained as a fusion study of the natural science and art that it comes forth with a new aesthetic point of view. Fractal has influenced in the various fields of study, such as philosophy, mathematics, physics, or so; therefore, it can be found at many modern formative arts like as paintings, three dimensional sculptures and installation art since it has been applied to a new formative variable by many artists and designers. The value of Fractal art is rising; likewise, it was born by the result of mixing creativities of science and art in the era of fusion at present. For these reasons, the necessity of the fractal design based on nature has been increasing as the importance of fusion studies of basic and art education has become increasing. The fundamental concept of fractal has special features named "self-similarity", "fractal dimension", and "non linearity". These are reflexive infinite formation through "algorithm", which is a repetition of similar phenomenon that starts from an initial state. Methods, contents, and results of this study are as follows. By analyzing examples of modern formative art works applying fractal principles, certain rules and patterns appeared in the painting, architecture, installation, and the ceramic art field could be explained by the fractal theory, containing the essential rules in nature. Accordingly, a hexagon shape which is an ideal form following natural orders in terms of structural and functional aspects was applied to this work. This means the fractal theory is used for expressing combination of natural science and art creatively along with the implication of nature principles. This study aims to suggest various formative possibilities of fractal by extracting formative design elements from the natural science within a specific generality and it would make fusion studies increase in future.

화학적 특성과의 비교 분석을 통한 프랙탈 차원을 이용한 풍화도 추정

노수각,손영환,봉태호,박재성,Noh, Soo-Kack,Son, Young-Hwan,Bong, Tae-Ho,Park, Jae-Sung 한국농공학회 2012 한국농공학회논문집 Vol.54 No.2

The processes of chemical and physical weathering occur simultaneously. The objective of this study was to estimate the degree weathered using fractal dimension through comparison with chemical characteristic of soil samples from Pohang (PH) and Kimpo (KP). Comparing chemical characteristics with fractal dimension, $SiO_2$, $Na_2O$, $K_2O$ content decreased and loss of ignition increased as fractal dimension increased. And fractal dimension showed high correlation with CWI while ATI, STI CIW, PI, CIA and RR demonstrated different degrees of correlation with fractal dimension. The tendency of the changes in oxide content and chemical weathering index with increasing fractal dimension appeared to be similar with the chemical changes due to weathering. Therefore, fractal dimension could be a good indicator representing the extent of weathering and chemical changes.

윤활 작동조건에 따른 마멸분 형태특징 분석을 위한 프랙탈 차원 해석 방법

조연상(Yonsang Cho),전성재(Sungjae Jun),우규성(Kyusung Woo),박흥식(Heungsik Park) 한국트라이볼로지학회 2006 한국트라이볼로지학회 학술대회 Vol.2006 No.6

The fractal dimension is quantitatively to define the irregular characteristic of the shape in natural. It can be useful in describing morphological characteristics of various wear particles. This paper was undertaken to diagnose failure condition for sliding members in lubrication by fractal dimension. It will be possible to diagnose wear mechanism, friction and damage state of machines through analysis of shape characteristics for wear particle on driving condition by fractal parameters. In this study, the calculating and analyzing methods of fractal dimensions were constructed for the condition monitoring and wear particle analysis in lubricant condition. So, we carried out the Friction and wear test with the ball on disk type tester, and the fractal parameters of wear particle in lubricated conditions were calculated. Fractal parameters were defined as texture fractal dimension(Dt), structure fractal dimension(Ds) and total fractal dimension(D).

윤활유 중의 마멸입자의 프랙탈 형상특징 추출 방법

우규성(Kyusung Woo),조연상(Yonsang Cho),김동호(Dongho Kim),예규현(Gyooheon Ye),박흥식(Heungsik Park) 한국트라이볼로지학회 2006 한국윤활학회지(윤활학회지) Vol.22 No.5

The fractal dimension is quantitatively to define the irregular characteristic of the shape in natural. It can be useful in describing morphological characteristics of various wear particles. This paper was undertaken to diagnose failure condition for sliding members in lubrication by fractal dimension. It will be possible to diagnose wear mechanism, friction and damage state of machines through analysis of shape characteristics for wear particle on driving condition by fractal parameters. In this study, the calculating and analyzing methods of fractal dimensions were constructed for the condition monitoring and wear particle analysis in lubricant condition. So, we carried out the Friction and wear test with the ball on disk type tester, and the fractal parameters of wear particle in lubricated conditions were calculated. Fractal parameters were defined as texture fractal dimension (D₁), structure fractal dimension (Ds) and total fractal dimension (D).