• Title/Summary/Keyword: Fractal shapes

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A Study on the Fractal and Chaos Game (프랙털 도형과 카오스 게임 탐구)

  • Kim, Soohwan;Yoon, Joonseo;Jo, Minjoon
    • Communications of Mathematical Education
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    • v.33 no.2
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    • pp.67-84
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    • 2019
  • The purpose of this study is to investigate the effectiveness of intensive inquiry activity through intensive camp for 2 hours and 3 days in summer vacation and 100 hours of classes from March to December 2018 by selecting 2 middle school students using OKMINDMAP for creative education. It is the result. The teacher was the assistant, and the research problem was selected by two students themselves, and the variation of the fractal dimension was investigated and the Chaos game was shown to be possible in the modified Sierpinski triangle.

A Study on Modularity Concepts of Furniture Design - Focus on Fractal Concepts - (모듈화(Modularity) 개념이 적용된 가구디자인 연구 - 프랙탈 개념을 중심으로 -)

  • Lee, Hyun-Jung
    • Journal of the Korea Furniture Society
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    • v.21 no.5
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    • pp.380-391
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    • 2010
  • Modular furniture's colors, materials, finishing materials and quantities are determined by users' tastes and it's diverse functions, shapes and sizes are determined by the spaces of users. That is, modules satisfy the diversity of consumers, meet differentiated individuals' tastes and enable communications with consumers rather than delivering one-way messages of designers. The contemporary spaces of the 21st century have been gradually shifting from uniform spaces attaching weight on individuals' individuality and tastes and along with it, the consumption of expensive custom-made furniture and foreign branded furniture is increasing to satisfy those small numbers of consumers who want to express diversified individuality. The modular furniture as a concept which is the most suitable to Mass Customization can be produced in large quantities while considering the diverse needs and tastes of individuals and it does not have absolute shapes or sizes. The concept of modular furniture shows similarities to the creation of fractals that forms shapes by self similarities, repeats and similar transformations which is in the same context as the characteristics of a modular design that presents diversity with scales, materials and jointing points. Fractals will be combined with the digital media of today to present great plasticity and influence designers more heavily. Pursuit of new modeling is a requisite for the creation of future spaces and it will require continuous creativity and the transformable modular furniture will contribute to the satisfaction of diverse consumers' needs. This study is to propose the modular furniture that considers the diversity of the public in the 21st century and their individuality and that will enable interactions between designers and consumers.

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Chaotic Vibrations of a Cantilevered Beam with Stops to Limit Motions (차단판에 의해 운동이 제한된 외팔보의 혼돈 진동)

  • Choi, Bong-Moon;Ryu, Bong-Jo;Kim, Young-shik;Koo, Kyung-Wan
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.66 no.12
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    • pp.1852-1865
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    • 2017
  • The vibration of the structures with restrained motion has long been observed in various engineering fields. When the motion of vibrating structure is restrained due to the adjacent objects, the frequencies and the mode shapes of the structure change and its vibration characteristics becomes unpredictable, in general. Although the importance of the study on this type of vibration model increases in many engineering areas, most studies conducted so far are limited to the theoretical study on dynamic responses of the structure with stops, including some experimental works. Specially, the study on the nonlinear phenomena due to the impact between the structure and the stops have been mainly performed theoretically. In the paper, both numerical analyses and experiments are conducted to study the chaotic vibration characteristics of the nonlinear motion and the dynamic response of a cantilevered beam which has restrained motion at the free end by the stops. Results are presented for various magnetic forces and gaps between the beam and stops. The conclusions are as follows : Firstly, Numerical simulation results have a good agreement with experimental ones. Secondly, the effect of higher modes of beams are increased with increasing magnitude of exciting force, and displacement and velocity curves become more complicated shapes. Thirdly, nonlinear characteristics tend to appear greatly with increasing magnitude of exciting force, and fractal dimension is increased.

A Preliminary Study on the Adjustment of Forest-based Wildlife Protection Area (산림기반 야생동식물보호구역 조경을 위한 기초연구)

  • Jang, Gab-Sue
    • Journal of the Korean Institute of Landscape Architecture
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    • v.36 no.1
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    • pp.62-69
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    • 2008
  • This study was conducted in order to recommend forest-based wildlife protection areas in Chung-nam Province using several basic habitat conditions. The conditions used in this study were the forest patch size with the potential to keep wildlife animals safe, the distance from water sources, and the availability of food for wildlife. The fractal dimension index was also used to find the edge line dynamics, which can influence on habitat conditions for edge species. The natural conservation management indices including a forest map (indicating the level of forest age), a slope map, and an elevation map were used to find the forest patches with enough space for wildlife to live on. Water resources and their buffer areas were considered as factors to protect the space as an ecological corridor. Deciduous trees and trees mixed with deciduous trees and conifers were chosen to provide wildlife animals their food. In total, 525 forest patches were chosen and recommended for the wildlife protection area. Five of these forest patches were recommended as wildlife protection areas managed by the provincial government. The other 520 forest patches were recommended to protect local wildlife animals and be managed by each county or city. These forest patches were located around the Geum-buk and Geum-nam mountains, and the forest patches are important resources as habitats to keep wildlife in the area. An ecological network consists of these separate forest patches with the ecological integration. A fractal dimension index was used to divide forest patches into several categories in order to find how patches are shaped. The forest patches with longer edges or more irregular shapes have a much higher possibility of being inhabited by various types of edge species. Through comparison of the wildlife protection areas recommended in this study to the current wildlife protection areas, we recognized that the current wildlife protection areas need boundary adjustments in order for wildlife animals to survive by themselves with water sources and food.

The Quantitative Evaluation of Catchment Plan-Form Elongation (집수평면의 신장도에 대한 정량적 평가)

  • Kim, Joo-Cheol;Lee, Sang-Jin;Noh, Joon-Woo
    • Journal of Korea Spatial Information System Society
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    • v.11 no.3
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    • pp.1-8
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    • 2009
  • In this study the concepts on the elongation, compactness and equivalent ellipse of catchment plan-forms are applied to the real basins considering their theoretical frameworks. The catchment plan-forms and corresponding equivalent ellipses, obtained from GIS, are inspected on downstream directions. As a result the catchment plan-forms seem to be the population of the basin shapes which come from the random interaction between two conjectures on Hack's law being controversial recently. The ratio of the maximum and minimum inertia moments of the catchment plan-form Ri is more sensitive to evaluate the elongation of the basin shapes than the ratio of the main channel length and diameter of circle which has the same area as the catchment plan-form E. The catchment plan-forms compactness measures show distinct aspects according to their different definitions. These results are caused by the difficulties to quantification of the shapes and the composite consideration with more than two compactness measures and the fractal analysis are therefore required to recover them.

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Effects of Dual-Coagulant Performance (이중응집이 응집공정에 미치는 영향)

  • Kim, Hee-Geun;Moon, Byung-Hyun;Kim, Seung-Hyun
    • Journal of Korean Society of Water and Wastewater
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    • v.19 no.1
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    • pp.92-97
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    • 2005
  • This research is to investigate the effect of the dual coagulant using inorganic coagulants($AICl3{\cdot}6H2O$) and polymer on the coagulant process. Jar-test was conducted by using Kaolin injected raw water. PDA(Photometric Dispersion Analyzer) equipment in order to analyze the size of the particles and the characteristics of the shapes. The change in the rate of sample ores' residual deposited after coagulants were also compared. According to the result derived from this experiment, the concentration of inorganic coagulant reduced 50% and the residual was lower by using dual coagulants compared to using single coagulant. However the dual coagulant required sufficient mixing time, and affected particle characteristics, with the effect of the injection order of coagulants, the simultaneous injection of inorganic coagulant and polymer showed the most effective in the particle removal.

Tectonic Strategies in Architectonic Fashion Design (건축적 패션 디자인의 구조적 전략)

  • Yim, Eunhyuk
    • Journal of Fashion Business
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    • v.18 no.1
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    • pp.164-181
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    • 2014
  • As the boundary between fashion and architecture is getting blurred, the interactions of the two fields are turning out abundant as well as essential. This study investigates the tectonic strategies in architectural fashion design as a novel aesthetic in the 21st century by combining literary survey and case analysis on architecture and contemporary fashion. The tectonic strategies in the works of architectural fashion designers were categorized as follows: organic geometry, technological garment construction, and independent space. Organic geometry transforms basic geometric shapes into subtle organic forms after being thrown on the body. Technological garment construction explores the garment structure and volume by applying the structural principle of suspension and fractal geometry. Independent space refers to maintaining the firm three-dimensionality of garment structure which keeps the distance from the body, assuming the similarity to architecture.

Vibration Characteristics of a Cantilevered Beam with Restrained Motions (제한된 운동을 갖는 외팔보의 진동특성)

  • 최봉문;류봉조;윤충섭
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2000.05a
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    • pp.578-582
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    • 2000
  • When the motion of vibrating structure is restrained due to the adjacent objects, the frequencies and the mode shapes of the structure change and its vibration characteristics becomes unpredictable, in general. Although the importance of the study on this type of vibration model increases in many engineering areas, most studies conducted so far are limited to the theoretical study on dynamic responses of the structure with the separation plate, including some experimental works. In the paper, both numerical analyses and experiments are conducted to study the chaotic vibration characteristics and the dynamic response of a fixed-free beam which has restrained motion at the free end by the separation plates. Results are presented for various magnetic forces and gaps between stops.

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A Study on the Development of Geometry as the Natural Laws and the Concepts of Space - Focus on the Whitehead's theories of natural laws - (자연법칙으로서 기하학과 공간 개념의 전개에 관한 연구 - 화이트헤드의 자연법칙 학설을 중심으로 -)

  • Hwang, Tae-Joo
    • Korean Institute of Interior Design Journal
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    • v.19 no.2
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    • pp.90-98
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    • 2010
  • The concepts of laws like regularity or persistence or recurrence those are discovered in nature, became the essential elements in speculative philosophy, study and scientific technology. Western civilization was spread out by these natural laws. As this background, this study is aimed to research the theories of natural laws and the development of geometry as the descriptive tools and the development aspects of the concepts of space. According to Whitehead's four theories on the natural laws, the result of this study that aimed like that as follows. First, the theories on the immanence and imposition of the natural laws were the predominant ideas from ancient Greek to before the scientific revolution, the theory on the simple description like the positivism made the Newton-Cartesian mechanism and an absolutist world view. The theory on the conventional interpretation made the organicism and relativism world view according to non-Euclidean geometry. Second, the geometrical composition of ancient Greek architecture was an aesthetics that represented the immanence of natural laws. Third, in the basic symbol of medieval times, the numeral symbol was the frame of thought and was an important principal of architecture. Fourth, during the Renaissance, architecture was regarded as mathematics that made the order of universe to visible things and the geometry was regarded as an important architectural principal. Fifth, according to the non-Euclidean geometry, it was possible to present the natural phenomena and the universe. Sixth, topology made to lapse the division of traditional floor, wall and ceiling in contemporary architecture and made to build the continuous space. Seventy, the new nature was explained by fractal concepts not by Euclidean shapes, fractal presented that the essence of nature had not mechanical and linear characteristic but organic and non-linear characteristic.

A Study on the Self-similarity Found in Fashion Design - Focusing on the Designs of Viktor & Rolf - (패션디자인에 나타나는 자기유사성에 관한 연구 - Viktor & Rolf의 디자인을 중심으로 -)

  • Kim, Yonson
    • Journal of the Korean Society of Costume
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    • v.64 no.7
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    • pp.97-113
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    • 2014
  • The study aims to determine the significance and characteristics of self-similarity inherent in natural objects or phenomena, the existence of self-similarity in design created by fashion designers, and the traits and internal significance implied in self-similarity and their effects on fashion. The subject of the study is Viktor & Rolf, and the scope of the study is the collections created from 2001 to 2014, which include designs implemented in their early years and those unveiled in the media. Self-similarity means attributes of a fractal structure appearing without change in the original form, even after modification of scale or direction in terms of shape or phenomena. As self-similarity is applied to the arts and design sectors, it leads people to pay attention to fundamental characteristics and intrinsic forms as a factor of expressing a unique creative world. Analysis of Viktor & Rolf collections generated ribbons, overlapping/juxtaposition, side decorations and exaggerated design elements as basic units of self-similarity. These factors had self-similarity rates as high as 84%. Self-similarity was established as design elements formed in the incipient stage were repeated in a certain form, and continued for a long period of time. It served as an element that recognizes design and a fashion designer at the same time. Characteristics of self-similarity appearing in Viktor & Rolf collections can be summarized as homeostasis based on an equivalent relationship, balance based on self-organization, reducibility into essential elements, and uniqueness based on odd shapes. These characteristics influenced the pursuit of consistent brand image, the maintenance of a fashion designer's creative world, the formation of styles and the expression of a fashion designer's identity.