• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.6
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• pp.1492-1511
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• 2013

A novel, chaotic map that is based on concatenated torus automorphisms is proposed in this paper. As we know, cat map, which is based on torus automorphism, is highly chaotic and is often used to encrypt information. But cat map is periodic, which decreases the security of the cryptosystem. In this paper, we propose a novel chaotic map that concatenates several torus automorphisms. The concatenated mechanism provides stronger chaos and larger key space for the cryptosystem. It is proven that the period of the concatenated torus automorphisms is the total sum of each one's period. By this means, the period of the novel automorphism is increased extremely. Based on the novel, concatenated torus automorphisms, two application schemes in image encryption are proposed, i.e., 2D and 3D concatenated chaotic maps. In these schemes, both the scrambling matrices and the iteration numbers act as secret keys. Security analysis shows that the proposed, concatenated, chaotic maps have strong chaos and they are very sensitive to the secret keys. By means of concatenating several torus automorphisms, the key space of the proposed cryptosystem can be expanded to $2^{135}$. The diffusion function in the proposed scheme changes the gray values of the transferred pixels, which makes the periodicity of the concatenated torus automorphisms disappeared. Therefore, the proposed cryptosystem has high security and they can resist the brute-force attacks and the differential attacks efficiently. The diffusing speed of the proposed scheme is higher, and the computational complexity is lower, compared with the existing methods.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1997.10a
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• pp.181-184
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• 1997

Practical applications of learning systems usually involve complex domains exhibiting nonlinear behavior and dilution by noise. Consequently, an intelligent system must be able to adapt to nonlinear processes as well as probabilistic phenomena. An important class of application for a knowledge based systems in prediction: forecasting the future trajectory of a process as well as the consequences of any decision made by e system. This paper examines the robustness of data mining tools under varying levels of noise while predicting nonlinear processes in the form of chaotic behavior. The evaluated models include the perceptron neural network using backpropagation (BPN), the recurrent neural network (RNN) and case based reasoning (CBR). The concepts are crystallized through a case study in predicting a Henon process in the presence of various patterns of noise.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.1 s.94
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• pp.150-160
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• 1999

본 논문은 ‘파트 1’에 그 기초를 두었으며, 실제 실험 상황에의 응용예를 들었다. 보편적인 ‘이중-우물 위치 진동기(double-well potential vibrator)'를 외부 공기압 감쇠기를 장치할 수 있도록 수정하였다. 감쇠는 높음 또는 낮음 으로 조정할 수 있도록 하였다. 이 실험계는 주기운동부터 카오스 운동까지 다양한 동적 특성을 보여준다. 힘-위상(Force-Stare Mapping) 방법이 선형상태 및 카오스상태에 응용되었으며, 특히 감쇠의 높고 낮음의 파악에 그 중점을 두었다. 그리고 , 부분발산지수들(Short term averaged Lyapunov exponents)의 합이 또한 감쇠를 파악함과 동시에 높은 감쇠에서 낮은 감쇠로의 변화를 감시할 수 있음을 보였다. 이 두가지 방법들을 비교하였으며 논하였다.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.2
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• pp.95-105
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• 2001

In this paper, in order to control uncertain chaotic system, an adaptive fuzzy control(AFC) scheme is developed for the multi-input/multi-output plants represented by the Takagi-Sugeno(T-S) fuzzy models. The proposed AFC scheme provides robust tracking of a desired signal for the T-S fuzzy systems with uncertain parameters. The developed control law and adaptive law guarantee the boundedness of all signals in the closed-loop system. In addition, the chaotic state tracks the state of the stable reference model(SRM) asymptotically with time for any bounded reference input signal. The suggested AFC design technique is applied for the control of an uncertain Lorenz system based on T-S fuzzy model such as stabilization, synchronization and chaotic model following control(CMFC).

• Wind and Structures
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• v.25 no.6
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• pp.589-608
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• 2017

A novel probabilistic approach is presented for estimating the equivalent static wind loads that produce a static response of the structure, which is "equivalent" in a probabilistic sense, to the extreme dynamic responses due to the unsteady pressure random field induced by the wind. This approach has especially been developed for complex structures (such as stadium roofs) for which the unsteady pressure field is measured in a boundary layer wind tunnel with a turbulent incident flow. The proposed method deals with the non-Gaussian nature of the unsteady pressure random field and presents a model that yields a good representation of both the quasi-static part and the dynamical part of the structural responses. The proposed approach is experimentally validated with a relatively simple application and is then applied to a stadium roof structure for which experimental measurements of unsteady pressures have been performed in boundary layer wind tunnel.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.843-856
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• 2009

In possibility framework, we propose two risk measures named Fuzzy Value-at-Risk and Fuzzy Conditional Value-at-Risk, based on Credibility measure. Two portfolio optimization models for fuzzy portfolio selection problems are formulated. Then a chaos genetic algorithm based on fuzzy simulation is designed, and finally computational results show that the two risk measures can play a role in possibility space similar to Value-at-Risk and Conditional Value-at-Risk in probability space.

• Journal of the Society of Disaster Information
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• v.11 no.4
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• pp.542-547
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• 2015

This study is discussing with respect to the access sector for terrorism response based on the thinking and methodology of complex systems theory, which is mainly used in many disciplines today to effectively respond to complex multi-environment change its purpose there. As a result, Butterfly Effect, fractal & self-similarity, self-organization, emergence, coevolution, edge of chaos the applicability of the corresponding field of terrorism through the complex system theory as metaphorical will be able to navigate.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.5
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• pp.606-613
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• 2003

As a technical method for controlling chaotic dynamics, this paper presents a predictive control for chaotic systems based on radial basis function networks(RBFNs). To control the chaotic systems, we employ an on-line identification unit and a nonlinear feedback controller, where the RBFN identifier is based on a suitable NARMA real-time modeling method and the controller is predictive control scheme. In our design method, the identifier and controller are most conveniently implemented using a gradient-descent procedure that represents a generalization of the least mean square(LMS) algorithm. Also, we introduce a projection matrix to determine the control input, which decreases the control performance function very rapidly. And the effectiveness and feasibility of the proposed control method is demonstrated with application to the continuous-time and discrete-time chaotic nonlinear system.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.743-754
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• 2014

Investigations of regular and chaotic vibrations of the autoparametric pendulum absorber suspended on a nonlinear coil spring and a magnetorheological damper are presented in the paper. Application of a semi-active damper allows controlling the dangerous motion without stooping of system and additionally gives new possibilities for designers. The investigations are curried out close to the main parametric resonance. Obtained numerical and experimental results show that the semi-active suspension may reduce dangerous motion and it also allows to maintain the pendulum at a given attractor or to jump to another one. Moreover, the results show that, for some parameters, MR damping may transit to chaotic motions.