• Proceedings of the KOSOMBE Conference
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• v.1995 no.05
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• pp.281-284
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• 1995

This paper describes a complexity measure algorithm based on nonlinear dynamics(chaos theory). In order to quantify complexity or regularity of biomedical signal, this paper proposed fractal dimension-1 and fractal dimension-2 algorithm with digital filter. Approximate entropy algorithm which measure a system regularity are also compared. In this paper investigate what we quantify of biomedical signal. These quantified complexity measure may be a useful information about human physiology.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.8
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• pp.99-108
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• 1994

In this paper an image compression technique based on fractal theory using iterated contractive transformation is analysed and an improved image coder is suggested. Existing methods used the classifier proposed by Ramamurthi and Gersho which utilize the properties of neighboring pixels in the spatial domain. In this paper DCT-based classification is applied to 512$\times$512 images and PSNR improvement of 0.4~2.7 dB is obtained at lower bit rate over conventional algorithms. In addition the effect of varying the domain block size and quantization step size of the luminance shift parameter on the compression ratio and the image quality is compared and analysed.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.980-982
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• 1995

Image coding based on a fractal theory of iterated transformations presents highly compressed image. In this paper, we compress image using the partitioning method which devides image adaptively in horizon and vertical axis. This method can encode image more compactly than the quadtree partitioning method. The maximum range size can be selected as $32{\times}32$ blocks and the minimum size can be $4{\times}4$ blocks. And the domain size is twice as many as the range size.

• East Asian mathematical journal
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• v.25 no.3
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• pp.229-245
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• 2009

G. Cantor gave a deep influence to the society of mathematics in many ways, especially in the set theory. It is important for gifted and talented high school students in mathematics to understand the Euler constant and the fractal dimension of the Cantor set in a heuristic sense. On the historic basis of mathematics and the standard of high school students, we give the teaching method for the talented high school student to understand them better. Further we introduce the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs distribution and its first moment. We hope that from these topics, the gifted and talented students in mathematics will have insight in the analysis of mathematics.

• The KIPS Transactions:PartB
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• v.9B no.6
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• pp.715-726
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• 2002

In this paper, we construct real-time moving picture encoder based on fractal theory by using general purpose digital signal processors. The constructed encoder is implemented using two fixed-point general DSPs (ADSP2181) and performs image encoding by three stage pipeline structure. In the first pipeline stage, the image grabber acquires image data from NTSC standard image signals and stores digital image into frame memory. In the second stage, the main controller encode image dada using fractal algorithm. The last stage, output controller perform Huffman coding and result the coded data via RS422 port. The performance tests of the constructed encoder shows over 10 frames/sec encoding speed for QCIF data when all the frames are encoded. When we encode the images using the interframe and redundency based on the proposed algorithms, encoding speed increased over 30 frames/sec in average.

• Journal of Korea Multimedia Society
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• v.13 no.2
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• pp.298-307
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• 2010

The grass is one of important components that cover the wide surfaces in the application such as game or real time simulation. Actually, it not easy to render effectively numerous grasses that grow over the wide terrain. To solve the difficulty, we must find a solution to the two contradictions in terms : quality and calculation cost. As a solution to the above-mentioned task, in this paper, we propose an efficient method to represent the natural grasses by introducing fractal theory and instancing technique. Although the existing grass representation methods make use of a simple rule of applying a basic grass model repeatedly in rendering process, on the contrary we take advantage of the basic property of fractal's self-similarity and we devise a natural representation method suited to the given environment by introducing two important growth factors such as nature of terrain and quantity of light, and finally we apply a GPU-based shader instancing technique to rendering numerous grass models in real-time.

• CELLMED
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• v.5 no.2
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• pp.9.1-9.14
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• 2015

The so-called "Needham's Grand Question" (NGQ) can be formulated as why modern science was developed in Europe despite the earlier successes of science and technology in ancient China. Numerous answers have been proposed. In this review, it will be pointed out that traditional Chinese natural philosophy (TCNP) and traditional Chinese medicine (TCM) are in fact dealing with problems of highly complex dynamical systems of Nature and human beings. Due to the lack of mathematical machinery in dealing with such complex phenomena, a holistic approach was taken by ancient Chinese instead. It was very successful for the first eighteen centuries. In the recent three centuries, however, the reductionist and mechanistic viewpoints of Western natural philosophy, sciences, and medicine have been prevalent all over the world up to now. The main obstacle in preventing the advancement of TCM, TCNP and its sciences is actually the lacking of proper mathematical tools in dealing with complex dynamical systems. Fortunately, the tools are now available and a "chaotic wave theory of fractal continuum" has been proposed recently. To give the theory an operational meaning, three basic laws of TCNP are outlined. These three laws of wave/field interactions contrast readily with those of Newton's particle collisions. Via the proposed three laws, TCM, TCNP and its sciences can be unified under the same principles. Finally, an answer to NGQ can be accurately given. It is hoped that this review will help promoting a genuine understanding of natural philosophy, sciences, and medicine in an ecumenical way.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.179-184
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• 2005

Empirical findings on interet rate dynamics imply that short rates show some long memories and non-Markovin. It is well-known that fractional Brownian motion(fBm) is a proper candidate for modelling this empirical phenomena. fBm, however, is not a semimartingale process. For this reason, it is very hard to apply such processes for asset price modelling. With some modifications, this paper investigate the fBm interest rate theory, and obtain a pure discount bond price and Greeks.

• Proceedings of the Korea Information Processing Society Conference
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• 2000.04a
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• pp.240-243
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• 2000

웹 환경에서 모핑 애니메이션들은 전송량의 증가에 따른 과부하를 줄이기 위하여 소스들을 다운 로드 하여 자신의 컴퓨터에서 실행하여 통신 트래픽을 해소하고자 한다. 이때의 애니메이션들은 기하학적 프리미티들을 이용하여 만든 동화상들로 자연스러운 실세계 등의 모습을 표현하기에는 무리가 있다. 본 논문에서는 이러한 문제들을 해결하는 한 방법이면서 보다 다양한 자연의 랜덤한 모습을 보이기 위해 랜덤프랙탈을 사용 한다.

• Communications of Mathematical Education
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• v.27 no.2
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• pp.165-177
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• 2013

Mathematics teaching is often more effective when teachers connect the contents of mathematics with history, culture, and social events. In the history of mathematics, the 'paradigm' theory from Thomas Kuhn's scientific revolution is very effective to explain the revolutionary process of development in mathematics, and his theory has been widely quoted in the history of science and economics. However, it has not been appropriate to use his theory in the other fields. This is due to the fact that the scope of Kuhn's paradigm theory is limited to mathematics and science. In this study, this researcher introduced pan-paradigm as a general concept that encompasses all, since through any relation in the field of mathematics and architecture, Thomas Kuhn's theory of paradigm does not explain the phenomena. That is, at the root of various cultures there exist always a 'collective unconsciousness' and 'demands of the times,' and these two factors by synergism form values and controlling principles common to various parts of the culture, and this synergism leads the cultural activities, the process of which is a phenomenon called pan-paradigm.