1分形图基本图形以及源程序

分形图基本图形以及源程序

第一部分

本人新手，如有错误请指正。程序完成于2011/6/17晚间到2011/6/18。

很多变量名称采用的是同学的姓名拼音，为的是告诉大家这些都是可以随意命名的变量或函数名，一般大写字母开头的是系统定义的变量不可以随意更改。

一、(*雪花*)

源程序

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i,wuxiaonan=Length[zhe ngguojie],gengping=60Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,e,T={{ca,-sa} ,{sa,ca}}},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*2/3+zhengguojie[[i+1]]/3;

e=zhengguojie[[i]]/3+zhengguojie[[i+1]]*2/3;

d=c+T.(e-c);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,e,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1/2,Sqrt[3]/2},{1,0},{0,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,0]],AspectRatio→Sqrt[3]/2]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,5]],AspectRatio→Sqrt[3]/2]] 基本生成元

二、(*上三角下三角1*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=60Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,g ,f,e,T={{ca,-sa},{sa,ca}},S={{ca,sa},{-sa,ca}}},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*3/4+zhengguojie[[i+1]]/4;

e=zhengguojie[[i]]/2+zhengguojie[[i+1]]/2;

f=zhengguojie[[i]]/4+zhengguojie[[i+1]]*3/4;

d=c+T.(e-c);

g=e+S.(f-e);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,e,g,f,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→Sqrt[3]/2]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,4]],AspectRatio→Sqrt[3]/2]] 基本生成元

(*上三角下三角2*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=60Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,g ,f,e,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*3/4+zhengguojie[[i+1]]/4;

e=zhengguojie[[i]]/2+zhengguojie[[i+1]]/2;

f=zhengguojie[[i]]/4+zhengguojie[[i+1]]*3/4;

d=c+T.(e-c);

S=Transpose[T];

g=e+S.(f-e);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,e,g,f,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→Sqrt[3]/2]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,4]],AspectRatio→Sqrt[3]/2]]图形同上

(*上三角下三角3*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=90Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,d 1,g1,g,f,e,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*3/4+zhengguojie[[i+1]]/4;

e=zhengguojie[[i]]/2+zhengguojie[[i+1]]/2;

f=zhengguojie[[i]]/4+zhengguojie[[i+1]]*3/4;

d=c+T.(e-c);

d1=d+e-c;

S=Transpose[T];

g=e+c-d;

g1=g+f-e;

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,d1,e,g,g1,f,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→1/2]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,4]],AspectRatio→1/2]]

图形同上

三、(*上正方下正方形*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=90Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,d 1,g1,g,f,e,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*3/4+zhengguojie[[i+1]]/4;

e=zhengguojie[[i]]/2+zhengguojie[[i+1]]/2;

f=zhengguojie[[i]]/4+zhengguojie[[i+1]]*3/4;

d=c+T.(e-c);

d1=e+T.(f-e);

S=Transpose[T];

g=e+S.(f-e);

g1=f+S.(f-e);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,d1,e,g,g1,f,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→1/2]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,4]],AspectRatio→1/2]]

基本生成元

分形图

四、(*下正方形上正方形*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=90Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,d 1,g1,g,f,e,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*3/4+zhengguojie[[i+1]]/4;

e=zhengguojie[[i]]/2+zhengguojie[[i+1]]/2;

f=zhengguojie[[i]]/4+zhengguojie[[i+1]]*3/4;

S=Transpose[T];

d=c+S.(e-c);

d1=e+S.(f-e);

g=e+T.(f-e);

g1=f+T.(f-e);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,d1,e,g,g1,f,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→1/2]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,4]],AspectRatio→1/2]]

基本生成元

分形图

五、(*下三角上三角*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=60Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,g ,f,e,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*3/4+zhengguojie[[i+1]]/4;

e=zhengguojie[[i]]/2+zhengguojie[[i+1]]/2;

f=zhengguojie[[i]]/4+zhengguojie[[i+1]]*3/4;

S=Transpose[T];

d=c+S.(e-c);

g=e+T.(f-e);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,e,g,f,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→Sqrt[3]/2]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,5]],AspectRatio→Sqrt[3]/2]] 基本生成元

六、(*单个上正方*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan

=Length[zhengguojie],gengping=90Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,d 1,g1,g,f,e,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*2/3+zhengguojie[[i+1]]/3;

e=zhengguojie[[i]]/3+zhengguojie[[i+1]]*2/3;

S=Transpose[T];

d=c+T.(e-c);

d1=e+T.(e-c);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,d1,e,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,7]],AspectRatio→1/3]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→1/3]]

基本生成元

分形图

七、(*一个正方形向外长大*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=90Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,d 1,g1,g,f,e,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*2/3+zhengguojie[[i+1]]/3;

e=zhengguojie[[i]]/3+zhengguojie[[i+1]]*2/3;

S=Transpose[T];

d=c+T.(e-c);

d1=e+T.(e-c);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,d1,e,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0},{1,-1},{0,-1},{0,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,4]],AspectRatio→1/1]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→1/1]] 基本生成元

分形图

八、(*一个正方形向内长大*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=90Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,d 1,g1,g,f,e,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*2/3+zhengguojie[[i+1]]/3;

e=zhengguojie[[i]]/3+zhengguojie[[i+1]]*2/3;

S=Transpose[T];

d=c+T.(e-c);

d1=e+T.(e-c);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,d1,e,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0},{1,1},{0,1},{0,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,5]],AspectRatio→1/1]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→1/1]]

基本生成元

分形图

九、(*一个M形状图形*)

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=60Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,g ,f,e,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*3/4+zhengguojie[[i+1]]/4;

e=zhengguojie[[i]]/2+zhengguojie[[i+1]]/2;

f=zhengguojie[[i]]/4+zhengguojie[[i+1]]*3/4;

S=Transpose[T];

d=c+T.(e-c);

g=e+T.(f-e);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,e,g,f,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,1]],AspectRatio→Sqrt[3]/8]] Show[Graphics[Line[Nest[lovelyduwangen,dongquanfa,5]],AspectRatio→Sqrt[3]/8]] 基本生成元

十、两个上三角形横线

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=60Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,g ,f,e,e1,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*4/5+zhengguojie[[i+1]]/5;

e=zhengguojie[[i]]*3/5+zhengguojie[[i+1]]*2/5;

e1=zhengguojie[[i]]*2/5+zhengguojie[[i+1]]*3/5;

f=zhengguojie[[i]]/5+zhengguojie[[i+1]]*4/5;

S=Transpose[T];

d=c+T.(e-c);

g=e1+T.(f-e1);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,e,e1,g,f,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show [ Graphics [ Line[Nest[lovelyduwangen,dongquanfa,1]] , AspectRatio→Sqrt[3]/10 ] ]

Show [ Graphics [ Line[Nest[lovelyduwangen,dongquanfa,5]] , AspectRatio→Sqrt[3]/10 ] ]

生成元

分形图

十一、上三角形横线下三角形

lovelyduwangen[zhengguojie_List]:=Block[{weihuayan={},i, wuxiaonan =Length[zhengguojie],gengping=60Degree,sa=Sin[gengping],ca=Cos[gengping],c,d,g ,f,e,e1,T={{ca,-sa},{sa,ca}},S},

For[i=1,i< wuxiaonan,i++,c=zhengguojie[[i]]*4/5+zhengguojie[[i+1]]/5;

e=zhengguojie[[i]]*3/5+zhengguojie[[i+1]]*2/5;

e1=zhengguojie[[i]]*2/5+zhengguojie[[i+1]]*3/5;

f=zhengguojie[[i]]/5+zhengguojie[[i+1]]*4/5;

S=Transpose[T];

d=c+T.(e-c);

g=e1+S.(f-e1);

weihuayan=Join[weihuayan,{zhengguojie[[i]],c,d,e,e1,g,f,zhengguojie[[i+1]]}]];

weihuayan]

dongquanfa={{0,0},{1,0}};

Show [ Graphics [ Line[Nest[lovelyduwangen,dongquanfa,1]] , AspectRatio→Sqrt[3]/5 ] ]

Show [ Graphics [ Line[Nest[lovelyduwangen,dongquanfa,5]] , AspectRatio→Sqrt[3]/5 ] ]

生成元

分形图

分形图基本图形以及源程序

第二部分

该程序写的太复杂的,至少看着程序段太多,在本文档系列第三部分我会给一个简单的程序实现它.

注意,从word直接拷贝到mathematica,箭头会乱码，请自己改一改

如这里的箭头AspectRatio→1/GoldenRatio

一、挖空一个黑色三角形

sierpinski[tris_List]:=Block[{tmp={},i,p=Length[tris]/3,a,b,c,d,e,f},

For[i=0,i

a=tris[[3i+1]];

b=tris[[3i+2]];

c=tris[[3i+3]];

d=(a+b)/2;

e=(a+c)/2;

f=(b+c)/2;

tmp=Join[tmp,{a,d,e,d,b,f,e,f,c}]];

tmp]

Showsierpinski[pts_List]:=Block[{tmp={},i,p=Length[pts]/3},

For[i=0,i

Show[Graphics[tmp],AspectRatio→1/GoldenRatio]]

triangle={{-1,0},{1,0},{0,Sqrt[3]}}

p0=Showsierpinski[Nest[sierpinski,triangle,0]]

p1=Showsierpinski[Nest[sierpinski,triangle,1]]

p2=Showsierpinski[Nest[sierpinski,triangle,2]]

p3=Showsierpinski[Nest[sierpinski,triangle,3]]

p4=Showsierpinski[Nest[sierpinski,triangle,4]]

Show[GraphicsArray[{{p1,p2},{p3,p4}}]];

生成元

分形图

二、挖空一个彩色的三角形

sierpinski[tris_List]:=Block[{tmp={},i,p=Length[tris]/4,a,b,c,d,e,f},

For[i=0,i

a=tris[[4i+1]];

b=tris[[4i+2]];

c=tris[[4i+3]];

d=(a+b)/2;

e=(a+c)/2;

f=(b+c)/2;

tmp=Join[tmp,{a,d,e,a,d,b,f,d,e,f,c,e}]];

tmp]

Showsierpinski[pts_List]:=Block[{tmp={},i,p=Length[pts]/4},

For[i=0,i

AppendTo[tmp,{Thickness[.02],RGBColor[0,0,1],Line[{pts[[4i+1]],pts[[4i+2]],pts[[4 i+3]],pts[[4i+1]]}]}]];

Show[Graphics[tmp]]]

Showsierp[pts_List]:=Block[{tmp={},i,p=Length[pts]/4},

For[i=0,i

Show[Graphics[tmp]]]

triangle={{-1,0},{1,0},{0,Sqrt[3]},{-1,0}}

p0=Showsierpinski[Nest[sierpinski,triangle,2]]

p1=Showsierp[Nest[sierpinski,triangle,2]]

Show[{p0,p1}]

生成元

分形图

三、第一题的逆,填充挖去的部分彩色

swwwierpinski[wtris_List]:=Block[{tmp={},duu={},mm={{},{}},i,j,p=Length[wtris[ [1]]]/4,dd=Length[wtris[[2]]],a,b,c,d,e,f},For[j=1,j

b=wtris[[1]][[4i+2]];

c=wtris[[1]][[4i+3]];

d=(a+b)/2;

e=(a+c)/2;

f=(b+c)/2;

mm[[1]]=Join[mm[[1]],{a,d,e,a,d,b,f,d,e,f,c,e}];

mm[[2]]=Join[mm[[2]],{d,e,f,d}]];

mm]

Shwwowsierp[pts_List]:=Block[{tmp={},i,p=Length[pts[[2]]]/4},For[i=0,i

Show[Graphics[tmp]]]

triangle={{{-1,0},{1,0},{0,Sqrt[3]},{-1,0}},{}};

p9=Shwwowsierp[Nest[swwwierpinski,triangle,4]]

p22=Shwwowsierp[Nest[swwwierpinski,triangle,4]]

生成元

分形图

四、第一题的逆,填充挖去的部分黑白

swwwierpinski[wtris_List]:=Block[{tmp={},duu={},mm={{},{}},i,j,p=Length[wtris[ [1]]]/4,dd=Length[wtris[[2]]],a,b,c,d,e,f},For[j=1,j

b=wtris[[1]][[4i+2]];

c=wtris[[1]][[4i+3]];

d=(a+b)/2;

e=(a+c)/2;

f=(b+c)/2;

mm[[1]]=Join[mm[[1]],{a,d,e,a,d,b,f,d,e,f,c,e}];

mm[[2]]=Join[mm[[2]],{d,e,f,d}]];

mm]

Shwwowsierp[pts_List]:=Block[{tmp={},i,p=Length[pts[[2]]]/4},For[i=0,i

Show[Graphics[tmp]]]

triangle={{{-1,0},{1,0},{0,Sqrt[3]},{-1,0}},{}};

p9=Shwwowsierp[Nest[swwwierpinski,triangle,5]]

生成元

除了颜色之外其他同上

分形图