• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.66-71
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• 2003

Profiles of naturally fractured surfaces of three sedimentary rock samples were plotted from the measured data using a mechanical profilometer. Fractal dimension of these profiles were computed and statistical F-test indicates that fractal dimension (FD) values can be used as a parameter for distinguishing the rock types. The comparison between FD values and a commonly used profile-roughness parameter called the Mayer's $Z_2$ parameter shows the superiority of the FD values as roughness estimator. Two-dimensional fractal roughness parameters of the same naturally fractured rock surfaces were also studied from their scanning electron microscopic (SEM) images at various magnification levels. The most suitable level of magnification of the SEM images for the study of the 2-D fractal roughness parameter was identified. The values of 2-D fractal roughness parameter for three different rocks were also compared using different methods of fractal dimensioning.

• Journal of the korean society of oceanography
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• v.35 no.1
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• pp.11-15
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• 2000

The scaling behavior of random fractals and multifractals is investigated numerically on the seabottom depth in the seabottom topography. In the self-affine structure the critical length for the crossover can be found from the value of standard deviations for the seabottom depth. The generalized dimension and the spectrum in the multifractal structure are discussed numerically, as it is assumed that the seabottom depth is located on a two-dimensional square lattice. For this case, the fractal dimension D$_0$ is respectively calculated as 1.312476, 1.366726, and 1.372243 in our three regions, and our result is compared with other numerical calculations.

• Journal of Korea Game Society
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• v.14 no.6
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• pp.109-118
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• 2014

We studied the creation of fractal images with polygonal rotation symmetry. As in Loocke's method[13] we start with IFS of affine functions that create polygonal fractals and extends the IFS by adding functions that create Julia sets instead of adding square root functions. The resulting images are rotationally symmetric and Julia set shaped. Also we can improve fractal images by modifying probabilistic IFS algorithm, and we suggest a method of deforming Julia set by changing exponent value.

• Research in Mathematical Education
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• v.5 no.1
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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.

• Economic and Environmental Geology
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• v.29 no.4
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• pp.523-528
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• 1996

In Korean topography the behaviors of random fractals and multifractality are analytically and numerically studied on the mountain heights shown between $128{\sim}129^{\circ}E$ and $37{\sim}38^{\circ}N$. The phase transitions on the fractal structure are approximately found at the critical length $N_c=2000m$ from the values of standard deviations that it varies with both the longitudinal and latitudinal lengths. In the multifractal structure we assume that the mountain heights divided by the intervals of 20 m are located on the horizontal plane in two dimensional square lattice, and estimate the values of the generalized dimension and the scaling exponents by using the the box counting method for the three cases of square area ($1{\times}1km^2$, $2{\times}2km^2$, $4{\times}4km^2$).

• The Journal of Natural Sciences
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• v.8 no.2
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• pp.77-82
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• 1996

New very low bit rate segmentation image coding technique is proposed by segmenting image into textually homogeneous regions. Regions are classified into on of three perceptually distinct texture classes (perceived constant intensity (class I), smooth texture (class II), and rough texture (class III) using the human Visual System (HVS) and the fractals. To design very low bit rate image coder, it is very important to determine nonoverlap and overlap segmentation method for each texture class. Good quality reconstructed images are obtained with about 0.10 to 0.21 bit per pixel (bpp) for many different types of imagery.

• Journal of Astronomy and Space Sciences
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• v.40 no.1
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• pp.29-33
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• 2023

An unexplained acceleration on the order of 10^-8 cm s^-2, which is close to cH, where c is the speed of light and H is the Hubble constant, is detected in gravitationally bound systems of different scales, from the solar system to clusters of galaxies. We found that any test body located inside a fractal structure with fractal dimension D = 2 experiences acceleration of the same order and confirmed the previous work that photons propagating through this structure decrease the frequency owing to gravitational redshift. The acceleration can be directed against the movement of the test body. The fractal distribution of the matter should be at scales of at least hundreds of megaparsecs to a few gigaparsecs for the existence of this acceleration.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.583-605
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• 2024

This paper discusses the properties of attractors of Type 1 IFS which construct self similar fractals on product spaces. General results like continuity theorem and Collage theorem for Type 1 IFS are established. An algebraic equivalent condition for the open set condition is studied to characterize the points outside a feasible open set. Connectedness properties of Type 1 IFS are mainly discussed. Equivalence condition for connectedness, arc wise connectedness and locally connectedness of a Type 1 IFS is established. A relation connecting separation properties and topological properties of Type 1 IFS attractors is studied using a generalized address system in product spaces. A construction of 3D fractal images is proposed as an application of the Type 1 IFS theory.

• 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.

• Journal of Periodontal and Implant Science
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• v.43 no.5
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• pp.209-214
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• 2013

Purpose: To assess bony trabecular changes potentially caused by loading stress around dental implants using fractal dimension analysis. Methods: Fractal dimensions were measured in 48 subjects by comparing radiographs taken immediately after prosthesis delivery with those taken 1 year after functional loading. Regions of interest were isolated, and fractal analysis was performed using the box-counting method with Image J 1.42 software. Wilcoxon signed-rank test was used to analyze the difference in fractal dimension before and after implant loading. Results: The mean fractal dimension before loading ($1.4213{\pm}0.0525$) increased significantly to $1.4329{\pm}0.0479$ at 12 months after loading (P<0.05). Conclusions: Fractal dimension analysis might be helpful in detecting changes in peri-implant alveolar trabecular bone patterns in clinical situations.