• 한국학교수학회논문집
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• 제4권1호
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• pp.29-36
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• 2001

This paper gives an example of experimental mathematics education which leads students to understand logically the problem of Fractal and Infinity.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.13-22
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• 1998

Fractals which represent many of the sets in various scien-tific fields as well as in nature is geometrically too complicate. Then we usually use Hausdorff dimension to estimate their geometrical proper-ties. But to explain the fractals from the hausdorff dimension induced by the Euclidan metric are not too sufficient. For example in digi-tal communication while encoding or decoding the fractal images we must consider not only their geometric sizes but also many other fac-tors such as colours densities and energies etc. So in this paper we define the dimension matrix of the sets by redefining the new metric.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권2호
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• pp.91-105
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• 2002

The study of fractal hedgehogs is a recent development in the ambit of fractal theory and nonlinear analysis. The intent of this paper is to present a study of fractal hedgehogs along with some of their special constructions. The main result is a new fractal hedgehog theorem. As a consequence, a fractal projective hedgehog theorem of Martinez-Maure is obtained as a special case, and several fractal hedgehogs and similar images are discussed.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제5권1호
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• pp.1-12
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• 2001

Generating fractal images by graphing calculators such as TI_92 combines several important features, which convey the excitement of a living, changing mathematics appropriate to secondary or post-secondary students. The topic of fractal geometry can be illustrated using natural objects such as snowflakes, leaves and ferns. These complex and natural forms are often striking fantastic and beautiful. The examples highlight the fact that complex, natural behaviors can result from simple mathematical rules such as those embodied in iterated function systems(IFS). The visual splendor beauty of fractals, in concert with their ubiquity in nature, revels the intellectual beauty of nonlinear mathematics in a compelling way. The window is now open for students to experience and explore some of the wonder of fractal geometry.

• 한국전기전자재료학회논문지
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• 제20권2호
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• pp.183-187
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• 2007

Fractal mathematics is being highlighted as a research method for classification of image. But the application of Fractal dimension(FD) has been requited the complicated calculation method because of its complex repetition progressing. In this paper, it has been developed the new approach method to express the Fractal Dimension(FD) for aging level calculation and estimation system of outside insulator using special image processing algorithm. As a result after FD testing, the recognized aging estimation of FD has a very characteristics compared to the conventional visual inspection.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권3호
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• pp.191-196
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• 2007

The main components in the generalized Mandelbrot sets are under a theoretical investigation for their parametric boundary equations. Using the boundary geometries, a fast construction algorithm is introduced for the generalized Mandelbrot set. This fast algorithm definitely reduces the construction CPU time in comparison with the naive algorithm. Its graphic implementation displays the mysterious and beautiful fractal sets.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.279-295
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• 2019

In this paper, using local fractional integrals on fractal sets $R^{\alpha}(0<{\alpha}{\leq}1)$ of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.

• 한국전기전자재료학회논문지
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• 제13권10호
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• pp.834-839
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• 2000

The structural properties that SEM photograph of ZnO varistors surface studied by fractal mathematics program were investigated to verify the relations of electrical characteristics. The SEM photograph of ZnO varistors surface were changed by binary code and the grain shape of that were analyzed by fractal dimension. The void of ZnO varistors surface was found by fractal program. The relation between grain density and electrical properties depend on fractal dimension. The grain size in ZnO varistors surface was decreased by increasing of Sb$_2$O$_3$ addition. The spinel structure was formed by Sb$_2$O$_3$addition and it was depressed the ZnO grain formation. The grain size of ZnO by Sb$_2$O$_3$addition were from 5 to 10[${\mu}{\textrm}{m}$]. Among of ZnO varistors, fractal dimension of ZnO4 was very high as a 1.764. The density of grain boundary in ZnO2 and ZnO3 varistors surface was 15[%] by formed spinal structure. The breakdown electric field of ZnO2 that fractal dimension has 1.752 was very high to be 8.5[kV/cm]. When the fractal dimensin was high, the grain shape of ZnO varistors was complex and the serial layers of ZnO grain was increased.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2003년도 추계학술대회 논문집 Vol.16
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• pp.567-570
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• 2003

Fractal mathematics is being highlighted as a research method for classification of image. But the application of Fractal dimension(FD) has been required the complicated calculation method because of its complex repetition progressing. In this paper, it has been developed the new approach method to express the Fractal Dimension(FD) for aging level calculation and estimation system of outside insulator using special image processing algorithm. As a result after FD testing, the recognized aging estimation of FD has a very characteristics compared to the conventional visual inspection.

• 대한수학회논문집
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• 제13권2호
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• pp.281-287
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• 1998

We define a new form of fractals, called the braked subsimilar set from a self similar set and find the relation between their fractal dimensions.