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📄 6.1

📁 分形理论及算法
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Date: Thu, 22 May 2003 10:57:28 +0800
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m">4</A></TD>
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/501.ht=
m">5</A></TD>
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m">6</A></TD>
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m">7</A></TD>
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m">9</A></TD>
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tm">10</A></TD>
    <TD><A=20
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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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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/REF.ht=
m">=B2=CE=BF=BC=CE=C4=CF=D7</A></TD>
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/EE.htm=
">=BA=F3=BC=C7</A></TD>
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tm">=CB=F7=D2=FD</A></TD></TR></TBODY></TABLE></FONT>
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    <TD><A=20
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/601.ht=
m">6.1</A></TD>
    <TD><A=20
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/602.ht=
m">6.2</A></TD>
    <TD><A=20
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/603.ht=
m">6.3</A></TD>
    <TD><A=20
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href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/604.ht=
m">6.4</A></TD>
    <TD><A=20
      =
href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/605.ht=
m">6.5</A></TD>
    <TD><A=20
      =
href=3D"http://www.phil.pku.edu.cn/personal/huajie/fractalart/html/606.ht=
m">6.6</A></TD></TR></TBODY></TABLE></FONT></CENTER>
<HR width=3D"100%">

<H1>=B5=DA=C1=F9=D5=C2 =B8=B4=C6=BD=C3=E6=C9=CF=B5=C4=B5=FC=B4=FA</H1>
<H2>6.1 =
=B8=B4=CA=FD=CB=C4=D4=F2=D4=CB=CB=E3=D3=EB=B5=FC=B4=FA</H2>=B5=CF=CD=F2=C4=
=DA=D4=DA=A1=B6=BB=EC=E3=E7=B6=AF=C1=A6=CF=B5=CD=B3=D2=FD=C2=DB=A1=B7=D6=D0=
=CB=B5=A3=BA=A1=B0=B8=B4=BD=E2=CE=F6=BA=AF=CA=FD=B6=AF=C1=A6=D1=A7=CA=C7=D2=
=BB=B8=F6=B1=C8=BD=CF=D7=A8=C3=C5=B5=C4=BF=CE=CC=E2=A1=A3=A1=AD=A1=AD20=20
=CA=C0=BC=CD20=C4=EA=B4=FA=A3=AC=D5=E2=D2=BB=C1=EC=D3=F2=D4=DA=CA=FD=D1=A7=
=BC=D2=B7=A8=CD=BC=BA=CD=D6=EC=C0=F6=D1=C7=B5=C4=D6=B8=B5=BC=CF=C2=D4=F8=BE=
=AD=BC=AB=B6=C8=B7=B1=C8=D9=A3=AC=A1=AD=A1=AD=B5=AB=D4=DA70=C4=EA=B4=FA=B5=
=C4=D0=C2=B7=B1=C8=D9=CA=B1=C6=DA=D2=D4=C7=B0=D3=D0=D2=BB=B6=CE=D0=DD=C3=DF=
=C6=DA=A1=A3=BA=F3=C0=B4=A3=AC=D6=F7=D2=AA=D3=C9=C3=A2=B5=C2=B2=AA=C2=DE=B5=
=C4=C3=C0=C0=F6=B6=AF=C8=CB=B5=C4=BC=C6=CB=E3=BB=FA=D7=F7=CD=BC=BA=CD=B5=C0=
=B0=A2=B5=DC=A1=A2=B9=FE=B2=AE=B5=C2=BA=CD=C9=B3=C0=FB=CE=C4(D.Sullivan)=B5=
=C8=C8=CB=D2=FD=C8=CB=C8=EB=CA=A4=B5=C4=CA=FD=D1=A7=B9=A4=D7=F7=A3=AC=D3=D6=
=D2=BB=B4=CE=B0=D1=C8=CB=C3=C7=B5=C4=D7=A2=D2=E2=C1=A6=D2=FD=CF=F2=B8=B4=C6=
=BD=C3=E6=B7=E1=B8=BB=B6=E0=B2=CA=B5=C4=B3=F5=B5=C8=D3=B3=C9=E4=B5=C4=B6=AF=
=C1=A6=D1=A7=D0=D0=CE=AA=A1=A3=A1=B1
<P></P>
<P>=B6=D4=D3=DA=B1=BE=CA=E9=D7=F7=D5=DF=BA=CD=B6=C1=D5=DF=B6=F8=D1=D4=A3=AC=
=A1=B0=BD=E2=CE=F6=BA=AF=CA=FD=A1=B1=A1=A2=A1=B0=B8=B4=B1=E4=BA=AF=CA=FD=A1=
=B1=B5=C8=B8=C5=C4=EE=B6=BC=BF=C9=D4=DD=C7=D2=B2=BB=B9=DC=A3=AC=D6=AA=B5=C0=
=D4=DA=B8=B4=C6=BD=C3=E6=C9=CF=B6=D4=BC=F2=B5=A5=B5=C4=B6=E0=CF=EE=CA=BD=BD=
=F8=D0=D0=B5=FC=B4=FA=C4=DC=B9=BB=C9=FA=B3=C9=C3=C0=C3=EE=B5=C4=B7=D6=D0=CE=
=CD=BC=D0=CE=A3=AC=BE=CD=D7=E3=B9=BB=C1=CB=A1=A3=D4=DA=BC=C6=CB=E3=BB=FA=CA=
=AE=B7=D6=C6=D5=BC=B0=D2=D4=C7=B0=A3=AC=D2=AA=D7=F6=D5=E2=D6=D6=C1=B7=CF=B0=
=BC=B8=BA=F5=CA=C7=B2=BB=BF=C9=C4=DC=B5=C4=A1=A3=B5=B1=C4=EA=D6=EC=C0=F6=D1=
=C7=BA=CD=B7=A8=CD=BC=CA=C7=BF=BF=B3=E9=CF=F3=B5=C4=CA=FD=D1=A7=CB=BC=CE=AC=
=A3=AC=BC=E8=C4=D1=B5=D8=D1=D0=BE=BF=B8=B4=B5=FC=B4=FA=B5=C4=A1=A3=BD=F8=C8=
=EB80=C4=EA=B4=FA=A3=AC=BC=C6=CB=E3=BB=FA=B2=FA=D2=B5=B4=F3=B7=A2=D5=B9=A3=
=AC=D5=FD=C7=C9=B7=D6=D0=CE=BC=B8=BA=CE=D1=A7=D3=D6=B5=BD=C0=B4=C1=CB=A3=AC=
=D2=BB=C7=D0=CC=F5=BC=FE=B6=BC=D2=D1=B3=C9=CA=EC=A1=A3=C3=A2=B5=C2=B2=AA=C2=
=DE=D4=DA=B8=C9=B2=F1=C9=CF=B5=E3=C1=CB=D2=BB=B0=D1=BB=F0=A3=AC=B8=B4=B5=FC=
=B4=FA=B8=B4=D0=CB=C1=CB=A3=AC=D5=E2=B0=D1=BB=F0=D2=BB=D6=B1=C9=D5=B5=BD=CF=
=D6=D4=DA=A3=AC=B6=F8=C7=D2=BB=F0=CA=C6=C8=D4=B2=BB=BC=F5=B5=B1=C4=EA=A1=A3=
=20
</P>
<P>=B8=B4=CA=FD=B5=FC=B4=FA=B1=C8=CA=B5=B5=FC=B4=FA(=BC=FB=B5=DA=B0=CB=D5=
=C2)=C9=D4=C9=D4=C2=E9=B7=B3=D2=BB=D0=A9=A3=AC=BD=F8=D0=D0=B8=B4=B5=FC=B4=
=FA=D0=E8=D2=AA=D6=AA=B5=C0=B8=B4=CA=FD=B5=C4=CB=C4=D4=F2=D4=CB=CB=E3=A1=A3=
=CE=D2=C3=C7=CF=C8=B8=B4=CF=B0=D2=BB=CF=C2=B8=DF=D6=D0=D1=A7=B9=FD=B5=C4=C4=
=DA=C8=DD=A1=A3</P>
<P>=C8=CE=D2=E2=B8=B4=CA=FD=BF=C9=D2=D4=D0=B4=B3=C9=C8=FD=D6=D6=D0=CE=CA=BD=
=A3=BA1)=B4=FA=CA=FD=D0=CE=CA=BD=A3=BA<I>z=3Dx</I>+<I>y</I>i=A3=BB2)=C8=FD=
=BD=C7=D0=CE=CA=BD=A3=BA<I>z=3Dr=20
</I>(cos<I>=A6=C8</I>+isin<I>=A6=C8</I>)=A3=BB3)=D6=B8=CA=FD=D0=CE=CA=BD=A3=
=BA<I>z</I>=3D<I>r</I>e^(i<I>=A6=C8</I>)=A1=A3=20
=C6=E4=D6=D0i=3DSQRT(-1)=CA=C7=D0=E9=CA=FD=B5=A5=CE=BB=A3=AC<I>x</I>=3DRe=
(<I>z</I>)=CA=C7=B8=B4=CA=FD=B5=C4=CA=B5=B2=BF=A3=AC<I>y</I>=3DIm(<I>z=20
</I>)=CA=C7=B8=B4=CA=FD=B5=C4=D0=E9=B2=BF,<I>r</I>=3D=A3=FC<I>z</I>=A3=FC=
=3D=A3=FC<I>x+y</I>i=A3=FC=3DSQRT(<I>x</I>^2+<I>y=20
</I>^2)=BD=D0=D7=F6=B8=B4=CA=FD=B5=C4=C4=A3=A3=AC<I>=A6=C8</I>=BD=D0=D7=F6=
=B8=B4=CA=FD=B5=C4=B7=F8=BD=C7=A1=A3=D4=DA=B8=B4=C6=BD=C3=E6=C9=CF=A3=AC=CA=
=B5=B2=BF=D2=BB=B0=E3=D3=C3=BA=E1=D7=F8=B1=EA=B1=ED=CA=BE=A3=AC =
=D0=E9=B2=BF=D2=BB=B0=E3=D3=C3=D7=DD=D7=F8=B1=EA=B1=ED=CA=BE=A1=A3</P>
<P>=C9=E8<I>z</I>_1=A3=AC<I>z</I>_2=A3=AC<I>z</I>_3=B6=BC=CA=C7=B8=B4=CA=FD=
=A3=AC=B8=B4=CA=FD=BB=F9=B1=BE=D4=CB=CB=E3=C8=E7=CF=C2=A3=BA</P>
<UL>=BA=E3=B5=C8=CA=BD=A3=BAe^(i=A6=C8)=3Dcos=A6=C8+isin=A6=C8,<BR>=BC=D3=
=B7=A8=A3=BA<I>z</I>_1+<I>z</I>_2=3D(<I>x</I>_1+<I>x</I>_2)+(<I>y</I>_1+ =

  =
<I>y</I>_2)i,<BR>=BC=F5=B7=A8=A3=BA<I>z</I>_1-<I>z</I>_2=3D(<I>x</I>_1-<I=
>x</I>_2)+(<I>y</I>_1-=20
  =
<I>y</I>_2)i=A3=AC<BR>=B3=CB=B7=A8=A3=BA<I>z</I>_1=A1=A4<I>z</I>_2=3D(<I>=
x</I>_1<I>x</I>_2-=20
  =
<I>y</I>_1<I>y</I>_2)+(<I>x</I>_1<I>y</I>_2+<I>x</I>_2<I>y</I>_1)i=A3=AC<=
BR>=B3=FD=B7=A8=A3=BA<I>z</I>_1/<I>z</I>_2=3D(<I>x</I>_1<I>x</I>_2+<I>y</=
I>_1<I>y</I>_2)/=20
  =
(<I>x</I>^2_2+<I>y</I>^2_2)+(<I>x</I>_2<I>y</I>_1-<I>x</I>_1<I>y</I>_2)/ =

  (<I>x</I>^2_2+<I>y</I>^2_2)i=A3=AC <BR>=D3=E0=CF=D2=A3=BAcos(<I>x</I> =
+ i<I>y</I>)=3D=20
  cos<I>x</I>cosh<I>y</I>-isin<I>x</I> =
sinh<I>y</I>,<BR>=D5=FD=CF=D2=A3=BAsin(<I>x</I> +=20
  i<I>y</I>)=3D sin<I>x</I>cosh<I>y</I>+icos<I>x</I>=20
  sinh<I>y</I>,<BR>=D6=B8=CA=FD=A3=BAe^(<I>x</I> + i<I>y</I>)=3D=20
  e^<I>x</I>cos<I>y</I>+ie^<I>x</I> sin<I>y</I>,</UL>
<P>=C6=E4=D6=D0</P>
<UL>=CB=AB=C7=FA=D3=E0=CF=D2=A3=BAcosh<I>x</I>=3D [e^<I>x</I> + =
e^(-<I>x</I>)]/2,<BR>=CB=AB=C7=FA=D5=FD=CF=D2=A3=BAsinh<I>x</I>=3D=20
12

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