• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.927-933
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• 2020

We characterize Möbius functions mapping the unit disc of the complex plane contractively into itself. We then give a procedure to produce Möbius iterated function systems on the unit disc.

• Proceedings of the Korea Society of Design Studies Conference
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• 1995.11a
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• pp.86-87
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• 1995

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.155-162
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• 2013

Although the snowflake curve, the boundary of the Koch snowflake, is one of the well-known fractals, there is no iterated function system (IFS) for it in the literature. In this study, we give an IFS for this familiar closed curve.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.681-699
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• 2020

In this paper, topological entropy of iterated function systems (IFS) on one dimensional spaces is considered. Estimation of an upper bound of topological entropy of piecewise monotone IFS is obtained by open covers. Then, we provide a way to calculate topological entropy of piecewise monotone IFS. In the following, some examples are given to illustrate our theoretical results. Finally, we have a discussion about the possible applications of these examples in various sciences.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.113-121
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• 2002

We construct lots of non-self similar fractal sets called generalized Markov attractors for a given (hyperbolic) iterated function system and calculated bounds of their Hausdorff dimensions.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.789-805
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• 2005

In this paper we consider analogous of Gronwall-type inequalities involving iterated integrals in the inequality (1.2) for functions when the function u in the right-hand side of the in­equality (1.2) is replaced by the function $u^P$ for some p. These inequalities are effective tools in the study of a system of an integral equation. We also provide some integral inequalities involving iterated integrals.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.11
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• pp.6810-6814
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• 2014

The concept of IFS (Iterated Function System) was applied to compress and transmit image data efficiently. To compress the image data with IFS, self-similarity was used to search a similar block. To improve the coding performance for the iterated function system with natural images, the image will be formed of properly transformed parts of itself to minimize the coding error. The simulation results using the proposed IFS represent high PSNR performance and improved compression efficiency with the coefficient of a recursive function.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.173-179
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• 2020

Let X be a compact space and Λ a finite index set. We deal with dynamical properties of iterated function systems on X. For an iterated function system 𝓕 on X, we prove that 𝓕 is c-expansive if and only if 𝓕^k is also c-expansive for each k ∈ ℕ. Furthermore we prove that the c-expansiveness of 𝓕 is equivalent to the original expansiveness of the shift map of it.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.765-800
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• 2022

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

• Communications of Mathematical Education
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• v.9
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• pp.283-297
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• 1999

수학에서는 컴퓨터를 활용해야 하고, 사회생활에서는 수학을 활용해야 한다. 이런 의미에서 엑셀을 수업 시간에 활용하는 것이 필요하다. 수학II의 일차변환을 엑셀을 어떻게 활용할 수 있는 가를 제시한다. 일차변환의 응용으로서, 이동을 포함시킨 아핀변환을 이용하여 프랙탈을 생성하는 방법을 찾아본다. 프랙탈을 생성하기 위해서는 IFS(Iterated Function System)에 의해 수 만번의 합성변환을 필요하므로 소프트웨어가 필수적이다. 여기서는 Fanstic Fractals 프로그램을 이용하여 직관적으로 얻은 그림에서 변환 행렬의 값을 구하여, 엑셀에서 두 가지 방법으로 분석하였다.