On the symmetric sierpinski gaskets
Commun. Korean Math. Soc. 1997 Vol. 12, No. 1, 157-163
Hyun-Jong Song, Byung-Sik Kang
Pukyung National University, Kosin Univesity
Abstract : Based on a $n$-regular polygon $P_n$, we show that $r_n =1/(2 \displaystyle{\sum^{[(n-4)/4]+1}_{j=0}}\cos 2j\pi/n)$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $\Cal G_n = \{f_i \vert 1 \leq i \leq n\}$. Moreover we see that for any odd $n$, the ratio $r_n$ is still valid for just-touching I.F.S. $\Cal H_n = \{f_i \circ R \vert 1 \leq i \leq n \}$ yielding another symmetric gasket $H_n$ where $R$ is the $\pi / n$-rotation with respect to the center of $P_n$.
Keywords : Fractal gasket, Scaling factor, Iterated function system
MSC numbers : Primary 28A80, Secondary 58F08
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society.
(Rm.1109) The first building, 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd