• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.341-354
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• 2009

The purpose of this study is to show the Fractals activities for mathematically gifted students, and to analyze the constructions on Fractals of the mathematically gifted. The subjects of this study were 5 mathematically gifted students in the Gifted Education Institut and also 6th graders at elementary schools. These activities on Fractals focused on constructing Fractals with the students' rules and were performed three ways; Fractal cards, colouring rules, Fractal curves. Analysis of collected data revealed in as follows: First, the constructions on Fractals transformed the ratios of lines and were changed using oblique lines or curves. Second, to make colouring rules on Fractals, students presented the sensitivities of initial and fractal dimensions on Fractals. In conclusion, this study suggested the importance of communication and mathematical approaches in the mathematics classrooms for the mathematically gifted.

• The Mathematical Education
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• v.37 no.1
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• pp.115-138
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• 1998

We seek the possibility of introduction of Fractals to the high school math. curriculum through identifying Fractals teaching programs appropriate for the scopes and sequences in math. education for the high school students. We presented the contents of Fractal theory suitable for the high school students. The following subjects were chosen to be introduced; self-similarity, Fractal dimension, Cantor set, Sierpinsky triangle, Sierpinsky carpel Koch curve, Koch island, perimeter estimate of rugged profiles drawn on paper, and chaos game. We developed the working papers and the criteria for appraisal. Each working paper focuses on the activities in which students can solve the given problems, understanding the characteristics and ideas of Fractals. The working papers were given to the second year students who take science course, and the degree of achievements were analyzed based on the appraisal criteria. The results show that it is possible to introduce Fractals to the high school students.

• Journal of the Korea Society for Simulation
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• v.4 no.1
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• pp.113-119
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• 1995

In 3D computer graphics, fractal techniques have been applied to terrain models. Even though fractal models have become popular for recreating a wide variety of the shapes found in nature, a specific 3D terrain model such as Uleung Island could not be formulated by statistical fractals easily owing to the random effects. However, by locating the midpoints on the edges and the surface of a specific terrain such as Uleung Island, a similar shape of the terrain model can be simulated. This paper shows the way of simulating 3D Uleung Island terrain model by the statistical fractals wherein the subdivision algorithm is used.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.491-507
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• 2023

The aim of this paper is to study the descriptive set-theoretic complexity of the Hewitt-Stromberg measure and dimension maps.

• ETRI Journal
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• v.27 no.6
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• pp.713-724
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• 2005

This paper focuses on the problem of key-frames coding and proposes a new promising approach based on the use of fractals. The summary, made of a set of key-frames selected from a full-length video sequence, is coded by using a 3D fractal scheme. This allows the video presentation tool to expand the video sequence in a "natural" way by using the property of the fractals to reproduce the signal at several resolutions. This feature represents an important novelty of this work with respect to the alternative approaches, which mainly focus on the compression ratio without taking into account the presentation aspect of the video summary. In devising the coding scheme, we have taken care of the computational complexity inherent in fractal coding. Accordingly, the key-frames are first wavelet transformed, and the fractal coding is then applied to each subband to reduce the search range. Experimental results show the effectiveness of the proposed approach.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.323-341
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• 2020

In this note, we investigate the multifractal analogues of the Hewitt-Stromberg measures and dimensions in a probability space.

• IE interfaces
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• v.17 no.spc
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• pp.46-51
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• 2004

In order to quickly respond to the rapidly changing manufacturing environment, it is imperative for the system to have such capabilities as flexibility, adaptability, reusability, etc. One of the promising approaches for new manufacturing paradigm satisfying those capabilities is the fractal manufacturing system (FrMS). The FrMS can be optimized by reorganizing the structure of fractals through the dynamic restructuring process (DRP) to deal with the changes of environment. Through the DRP, the logical connections between fractals and roles of fractals are autonomously changed. To determine an appropriate fractal structure, certain rules are needed to build and evaluate alternative structures for fractals involved in the DRP. In this paper, an algorithm for the DRP-, which is invoked when some equipment are unavailable, is introduced and explained with examples.

• Korean Journal of Computational Design and Engineering
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• v.22 no.2
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• pp.172-180
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• 2017

The fractal structures, which include Sierpinski and Pascal triangular fractals, have provided many mathematical interests. In this study, the hydrodynamic and mechanical properties of the triangular fractals were investigated, and their application to the design of various artificial bone scaffolds has been implemented via CAD modeling, computational analysis and mechanical testing. The study proved that the Sierpinski and Pascal triangular fractal structures could effectively be applied to bone scaffold design and manufacturing regarding permeability and mechanical stiffness.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1073-1097
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• 2022

In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure 𝓗^q,t_𝜇 and multifractal packing measure 𝓟^q,t_𝜇 of Cartesian product sets by means of the measure of their components. This is done by investigating the density result introduced in [34]. As a consequence, we get the inequalities related to the multifractal dimension functions, proved in [35], by using a unified method for all the inequalities. Finally, we discuss the extension of our approach to studying the multifractal Hewitt-Stromberg measures of Cartesian product sets.

• Journal of applied mathematics & informatics
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• v.5 no.1
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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.