On the symmetric sierpinski gaskets

On the symmetric sierpinski gaskets

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ 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. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover w...

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Veröffentlicht in:Communications of the Korean Mathematical Society 1997, Vol.12 (1), p.157-163
Hauptverfasser: Song, Hyun-Jong, Kang, Byung-Sik
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description Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ 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. $g_n = {f_i $\mid$ 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 $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.
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title On the symmetric sierpinski gaskets
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