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📁 分形理论及算法
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m">1</A></TD>
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m">5</A></TD>
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m">6</A></TD>
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/1001.h=
tm">10</A></TD>
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/EP.htm=
">=CE=B2=C9=F9</A></TD>
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    <TD><A=20
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/701.ht=
m">7.1</A></TD>
    <TD><A=20
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/702.ht=
m">7.2</A></TD>
    <TD><A=20
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/703.ht=
m">7.3</A></TD>
    <TD><A=20
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/704.ht=
m">7.4</A></TD>
    <TD><A=20
      =
href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/705.ht=
m">7.5</A></TD></TR></TBODY></TABLE></FONT></CENTER>
<HR width=3D"100%">

<H2>7.4 =
=B6=D4=B3=C6=B0=DF=CD=BC=B5=C4=B5=C8=C4=DC=C3=E6=BB=AD=B7=A8</H2>
<P>=CE=AA=C1=CB=B5=C3=B5=BD<I>q</I>=B4=CE=D0=FD=D7=AA=B6=D4=B3=C6=CD=BC=B0=
=B8=A3=AC=BF=C9=D2=D4=CF=C8=BD=AB=B9=FE=C3=DC=B6=D9=BA=AF=CA=FD=D7=F6=C6=BD=
=BB=AC=BB=AF=B4=A6=C0=ED=A3=AC=B5=C3=B5=BD=D0=C2=B5=C4=B9=FE=C3=DC=B6=D9=C1=
=BF H^((o))_<I>q</I>=A3=BA</P>
<P>
<UL>H^((0))_<I>q</I>=3D=A1=C6^<I>q</I>_(j=3D1)cos=A3=FB<I>x</I>cos[2=A6=D0=
j/<I>q</I>]+=20
  =
<I>y</I>sin[2=A6=D0j/<I>q</I>]=A3=FD=3D=A1=C6^<I>q</I>_(j=3D1)cos(=A6=CE_=
j)=3D<I>E</I>,</UL>
<P></P>
<P>=C6=E4=D6=D0</P>
<P>
<UL><I>=A6=CE_j</I>=3D<I>re_j</I>=A3=AC<I>j</I>=3D1,=A1=AD=A3=AC<I>q</I>=A3=
=AC<BR><I>r</I>=3D(<I>x</I>,<I>y</I>),<BR><I>e_j</I>=3Dcos(2=A6=D0/<I>q</=
I>)j+sin(2=A6=D0/<I>q</I>)j,</UL>
<P></P>
<P>=D4=DA=D5=E2=C0=EF=A6=CE_j=CA=C7=CA=B8=C1=BFr=D4=DAe_j=B7=BD=CF=F2=C9=CF=
=B5=C4=CD=B6=D3=B0=B3=A4=B6=C8=A1=A3=BE=D9=C0=FD=CB=B5=C3=F7=A3=AC=B5=B1<=
I>q</I>=3D3=CA=B1=A3=AC=A6=CE_j=C8=A1=D6=B5=C8=E7=CF=C2=A3=BA </P>
<P>
<UL><I>=A6=CE</I>_1=3D[-<I>x</I>+SQRT(3)<I>y</I>]/2,<BR><I>=A6=CE</I>_2=3D=
[-<I>x</I>-SQRT(3)<I>y</I>]/2=A3=AC<BR><I>=A6=CE</I>_3=3D<I>x</I>.</UL>
<P></P>
<P>
<CENTER><IMG=20
src=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/p712.JP=
G"=20
width=3D600>
<P></P>
<P>=CD=BC7.12 =
=CE=E5=B4=CE=B6=D4=B3=C6=B0=DF=CD=BC=A1=A3=D7=F3=CD=BC=B5=C4=B7=B6=CE=A7=CA=
=C764=A6=D0=A1=C164=A6=D0=A3=AC=D3=D2=CD=BC=B5=C4=B7=B6=CE=A7=CA=C716=A6=D0=
=A1=C116=A6=D0. </P></CENTER>
<P>=B5=B1<I>q</I>=3D4=CA=B1=A3=AC<I>=A6=CE_j</I>=B5=C4=C8=A1=D6=B5=C8=E7=CF=
=C2=A3=BA</P>
<P>
<UL><I>=A6=CE</I>_1=3D<I>y</I>=A3=AC<BR><I>=A6=CE</I>_2=3D-<I>x</I>,<BR><=
I>=A6=CE</I>_3=3D-<I>y</I>,<BR><I>=A6=CE</I>_4=3D<I>x</I>.</UL>
<P></P>
<P>=B7=D6=B1=F0=C1=EE=AA=B5<I>E</I>/=AA=B5<I>x</I>=3D0,=AA=B5<I>E</I>/=AA=
=B5<I>y</I>=3D0,=BF=C9=D2=D4=C7=F3=B3=F6<I>E</I>=B5=C4=D7=EE=B4=F3=D6=B5=BA=
=CD=20
=D7=EE=D0=A1=D6=B5=A1=A3=B5=B1<I>q</I>=3D3=CA=B1=A3=AC<I>E</I>=B5=C4=D7=EE=
=B4=F3=D6=B5<I>E</I>_(max)=3D3=A3=AC<I>E</I>=B5=C4=D7=EE=D0=A1=D6=B5<I>E =

</I>_(min)=3D-3/2,=BE=F9=B6=D4=D3=A6=D3=DA=CD=D6=D4=B2=D0=CD=B2=BB=B6=AF=B5=
=E3(elliptic fixed points)=A1=A3<I>E</I>=3D-1=B6=D4=D3=A6=D3=DA=CB=AB=20
=C7=FA=D0=CD=BC=AB=D6=B5=B5=E3=B5=C4=C4=DC=C1=BF=A1=A3=B5=B1<I>E</I>=A1=CA=
(-3/2,-1)=CA=B1=A3=AC=A1=B0=C1=A3=D7=D3=A1=B1=D4=DA=C8=FD=BD=C7=D0=CE=CD=F8=
=B8=F1=C4=DA=D1=D8=CD=AC=20
=D0=C4=CD=F8=BB=B7=D4=CB=B6=AF=A3=BB=B5=B1<I>E</I>=A1=CA(-1=A3=AC3)=CA=B1=
=A3=AC=A1=B0=C1=A3=D7=D3=A1=B1=D4=DA=C1=F9=BD=C7=D0=CE=B8=F1=D7=D3=C4=DA=D1=
=D8=CD=AC=D0=C4=CD=F8=BB=B7=D4=CB=B6=AF=A1=A3</P>
<P><I>E</I>=C8=A1=B2=BB=CD=AC=D6=B5=CA=B1=A3=AC=BB=E1=B5=C3=B5=BD=B8=F7=D6=
=D6=B1=D5=BA=CF=B5=C4=B2=BB=B1=E4=C7=FA=CF=DF=A3=AC=CB=FC=C3=C7=B9=B9=B3=C9=
<I>q</I>=B4=CE=B6=D4=B3=C6=CD=BC=B0=B8=A1=A3=B5=AB=CD=BC=B0=B8=20
=D6=D0=CF=E0=B5=E3=B7=D6=B2=BC=B5=C4=C3=DC=B6=C8=C8=B4=D3=EB<I>E</I>=BA=CD=
<I>q</I>=D3=D0=BA=DC=B4=F3=B9=D8=CF=B5=A1=A3=B5=B1<I>q</I>=AA=FC{1,2,3,4,=
6}=CA=B1=A3=AC<I>=20
E</I>=C8=A1=B2=BB=CD=AC=B5=C4=D6=B5=A3=AC=BB=E1=B5=C3=B5=BD=B7=D6=B2=BC=C3=
=DC=B6=C8=BA=DC=B2=BB=CF=E0=CD=AC=B5=C4=B6=D4=B3=C6=CD=BC=B0=B8=A1=A3</P>=

<P>=BC=C6=CB=E3=B9=FD=B3=CC=D6=D0=A3=AC=C9=A8=C3=E8=C6=BD=C3=E6=C4=B3=D2=BB=
=BE=D8=D0=CE=C7=F8=D3=F2(=B2=BB=CA=A7=D2=BB=B0=E3=D0=D4=A3=AC=BF=C9=D2=D4=
=D1=A1=D4=AD=B5=E3=D6=DC=CE=A7=B5=C4=C7=F8=D3=F2)=A3=AC=B6=D4=C3=BF=D2=BB=
=B5=E3=BC=C6=CB=E3=20
=BA=AF=CA=FD<I>E=3Df</I>(<I>x</I>=A3=AC<I>y</I>)=B5=C4=D6=B5=A3=AC=B8=F9=BE=
=DD<I>E</I>=D6=B5=B5=C4=B4=F3=D0=A1=B1=EA=C9=CF=B2=BB=CD=AC=B5=C4=D1=D5=C9=
=AB=A1=A3=B1=EA=C9=AB=20
=BA=DC=D6=D8=D2=AA=A3=AC=D0=E8=D2=AA=B2=BB=B6=CF=CA=D4=D1=E9=A3=AC=D6=B1=B5=
=BD=C2=FA=D2=E2=CE=AA=D6=B9=A1=A3=BC=C6=CB=E3=B3=CC=D0=F2=C8=E7=CF=C2=A3=BA=
</P>
<P>
<UL><PRE>{Program Five.PAS, Symmetries and Tilings of Map}
{(c)Liu Huajie, Oct.3,1994}
uses graph,crt;
label 20;
const
12345

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