• Journal of The Korean Digital Architecture Interior Association
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• v.9 no.3
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• pp.15-23
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• 2009

Chaos theory, qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems, is dominant paradigm in the twenty first century. Fractal geometry, as an expressed form of chaos, now influences many areas such as architecture, art, music, economics, literature, etc. The purpose of this study is to analyze fractal geometry and fractal formative elements in architectural design. There are scaling, superimposition, distortion, deformation and repetition in the fractal form generator that can be applied to design concept and process in architecture. This study shows fractal geometry can be the architectural form creation method. Fractal geometry similar to nature's patterned order can be provided endless possibilities for design analysis and methodology in architecture. Therefore the further study of fractal geometry should progress synthetically through the basis of the study.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.47 no.4
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• pp.177-186
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• 2015

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.

• International Journal of Internet, Broadcasting and Communication
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• v.15 no.2
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• pp.175-180
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• 2023

Fractal geometry, a relatively new branch of mathematics, was first introduced by Benoit Mandelbrot in 1975. Since then, its applications have expanded into various fields of natural science. In fact, it has been recognized as one of the three significant scientific discoveries of the mid-20th century, along with the Dissipative System and Chaos Theory. With the help of fractal geometry, designers can create intricate and expressive artistic patterns, using the concept of self-similarity found in nature. The impact of fractal geometry on the digital art world is significant and its exploration could lead to new avenues for creativity and expression. This paper aims to explore and analyze the development and applications of fractal geometry in digital art design. It also aims to showcase the benefits of applying fractal geometry in art creation and paves the way for future research on sacred geometry.

• KCI Concrete Journal
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• v.14 no.1
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• pp.30-35
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• 2002

The fractal geometry is a non-Euclidean geometry which describes the naturally irregular or fragmented shapes, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cementitious composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is apparent.ent.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.1
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• pp.18-26
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• 2002

With the introduction of Fractal notation, various fields of engineering adopted fractal notation to express characteristics of geometry involved and one of the most frequently applied areas was turbulence. With research on turbulence regarding the surface as fractal geometry, attempts to analyze turbulent premised flame as fractal geometry also attracted attention as a tool for modeling, for the flame surface can be viewed as fractal geometry. Experiments focused on disclosure of flame characteristics by measuring fractal parameters were done by researchers. But robust principle or theory can't be extracted. Only reported modeling efforts using fractal dimension is flame speed model by Gouldin. This model gives good predictions of flame speed in unstrained case but not in highly strained flame condition. In this research, approaches regarding fractal dimension of flame as one representative value is pointed out as a reason for the absence of robust model. And as an extort to establish robust modeling, Presents methods treating fractal dimension as statistical variable. From this approach flame characteristics reported by experiments such as Da effect on flame structure can be seen quantitatively and shows possibility of flame modeling using fractal parameters with statistical method. From this result more quantitative model can be derived.

• Architectural research
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• v.16 no.4
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• pp.175-183
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• 2014

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.

• The Research Journal of the Costume Culture
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• v.18 no.4
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• pp.703-716
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• 2010

The objective of the study is to analyze expressions of modern fashion in relation to design principle of a science theory, fractal geometry, in order to identify various and multi-layered expressions of fashion. As for methodology, the study interprets principle and characteristics of fractal geometry based on literature review in areas of linguistic, philosophy, sociology and science. The research identifies expressive characteristics of fractal through empirical studies, and applies them to fashion in order to analyze how fractal design principles are reflected in modern fashion in terms of form and significance. Fractal aesthetics pursue order, balance, diversity and openness among disorder and insecurity. They are closely related to the function of modern fashion that works as a multi-layered code, instead of being confined to conventional idea about fashion that "functions" as "wear."

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.333-338
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• 2001

Fractal geometry is a non-Euclidean geometry which has been developed to quantitative analysis irregular or fractional shapes. Fractal dimension of irregular surface has fractal values ranging from 2 to 3 and of irregular line profile has fractal values ranging from 1 to 2. In this paper, quantitative analysis of crack growth patterns during the fracture processing of fiber-reinforced cement composites based on fractal geometry. The fracture behaviors of fiber reinforced mortar beams subjected to three-point loading in flexure. The beams all had a single notch depth, but varing volume fractions of polypropylene, cellulose fibers. The crack growth behaviors, as observed through the image processing system, and the box counting method was used to determine the fractal dimension, Df. The results showed that the linear correlation exists between fractal dimension and fracture energy of the fiber reinforced cement mortar.

• Korean Institute of Interior Design Journal
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• no.37
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• pp.12-20
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• 2003

The purpose of this study is to propose a new design principles and to analyze the pattern of art and architecture applying fractal concepts. As this study is based on fractal geometry as a natural science, 1 intented to explain the concepts and provide some methods of generating fractal properties. Two major aspects are discussed. Frist, fractals are geometric shapes that are self-similar, in other words, they iterate a basic shape at ever increasing a decreasing dimensions. Self-similarity, irregularity, and scaling are fundamental characteristics of fractal geometry. Second, the fractal concepts of art and design can be analyzed and used as a critical tool. In both criticism and design, fractals provides a tool In fine, fractal geometry can be provided endless possibilities for artists and designers intended in expressing the more complex underlying rhythms and organic patterns of nature.

• Journal of Fashion Business
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• v.21 no.5
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• pp.136-150
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• 2017

3D printing has grown tremendously as the most noteworthy new technology in the manufacturing industries. In addition, the rapid development of computer science technology with 3D printing has created a new paradigm called Fractal Geometry, or a new form of digital art. This study explores the formative characteristics of 3D printing jewelry based on presentation of fractal geometry by classification of 3D printing jewelry's morphological types that except for producible shape with traditional mold manufacturing methods. The results of the study are as follows. The morphological characteristics of 3D printed jewelry are divided into their constitutive shapes by the repetition of the unit. The organic shape determined by superposition or overlapping, the systematic shape by distortion caused by distortion, and the variation in scaling by scaling. The formative characteristics, which are drawn from a study on the shape expression of 3D printed jewelry design using fractal geometry, consist of continuity, geometrical characteristics, and exaggeration. Continuity creates a new and self-assigned new space through a recursive structure through a cyclic structure that is formed along a single directional basis. The geometry of the geometry forms a three-dimensional and constructive structure comprised of the same size and structure of the same sized unit under the mathematical order of the geometry of Fractal's geometry. Exaggeration demonstrates the informal beauty and the maximization of the shape by expanding the scaling or superposition of a unit, by scaling the scale or he distortion of the units.