1分形图基本图形以及源程序.doc

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lovelyduwangenzhengguojie_List:=Blockweihuayan=,i,wuxiaonan=Lengthzhengguojie,gengping=60Degree,sa=Singengping,ca=Cosgengping,c,d,e,T=ca,-sa,sa,ca, Fori=1,i wuxiaonan,i+,c=zhengguojiei*2/3+zhengguojiei+1/3; e=zhengguojiei/3+zhengguojiei+1*2/3; d=c+T.(e-c); weihuayan=Joinweihuayan,zhengguojiei,c,d,e,zhengguojiei+1; weihuayandongquanfa=0,0,1/2,Sqrt3/2,1,0,0,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,0,AspectRatioSqrt3/2ShowGraphicsLineNestlovelyduwangen,dongquanfa,5,AspectRatioSqrt3/2基本生成元分形图二、 (*上三角下三角1*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=60Degree,sa=Singengping,ca=Cosgengping,c,d,g,f,e,T=ca,-sa,sa,ca,S=ca,sa,-sa,ca, Fori=1,i wuxiaonan,i+,c=zhengguojiei*3/4+zhengguojiei+1/4; e=zhengguojiei/2+zhengguojiei+1/2; f=zhengguojiei/4+zhengguojiei+1*3/4; d=c+T.(e-c); g=e+S.(f-e); weihuayan=Joinweihuayan,zhengguojiei,c,d,e,g,f,zhengguojiei+1; weihuayandongquanfa=0,0,1,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatioSqrt3/2ShowGraphicsLineNestlovelyduwangen,dongquanfa,4,AspectRatioSqrt3/2基本生成元分形图(*上三角下三角2*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=60Degree,sa=Singengping,ca=Cosgengping,c,d,g,f,e,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*3/4+zhengguojiei+1/4; e=zhengguojiei/2+zhengguojiei+1/2; f=zhengguojiei/4+zhengguojiei+1*3/4; d=c+T.(e-c); S=TransposeT; g=e+S.(f-e); weihuayan=Joinweihuayan,zhengguojiei,c,d,e,g,f,zhengguojiei+1; weihuayandongquanfa=0,0,1,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatioSqrt3/2ShowGraphicsLineNestlovelyduwangen,dongquanfa,4,AspectRatioSqrt3/2图形同上(*上三角下三角3*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=90Degree,sa=Singengping,ca=Cosgengping,c,d,d1,g1,g,f,e,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*3/4+zhengguojiei+1/4; e=zhengguojiei/2+zhengguojiei+1/2; f=zhengguojiei/4+zhengguojiei+1*3/4; d=c+T.(e-c); d1=d+e-c; S=TransposeT; g=e+c-d; g1=g+f-e; weihuayan=Joinweihuayan,zhengguojiei,c,d,d1,e,g,g1,f,zhengguojiei+1; weihuayandongquanfa=0,0,1,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatio1/2ShowGraphicsLineNestlovelyduwangen,dongquanfa,4,AspectRatio1/2图形同上三、 (*上正方下正方形*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=90Degree,sa=Singengping,ca=Cosgengping,c,d,d1,g1,g,f,e,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*3/4+zhengguojiei+1/4; e=zhengguojiei/2+zhengguojiei+1/2; f=zhengguojiei/4+zhengguojiei+1*3/4; d=c+T.(e-c); d1=e+T.(f-e); S=TransposeT; g=e+S.(f-e); g1=f+S.(f-e); weihuayan=Joinweihuayan,zhengguojiei,c,d,d1,e,g,g1,f,zhengguojiei+1; weihuayandongquanfa=0,0,1,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatio1/2ShowGraphicsLineNestlovelyduwangen,dongquanfa,4,AspectRatio1/2基本生成元分形图四、 (*下正方形上正方形*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=90Degree,sa=Singengping,ca=Cosgengping,c,d,d1,g1,g,f,e,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*3/4+zhengguojiei+1/4; e=zhengguojiei/2+zhengguojiei+1/2; f=zhengguojiei/4+zhengguojiei+1*3/4; S=TransposeT; d=c+S.(e-c); d1=e+S.(f-e); g=e+T.(f-e); g1=f+T.(f-e); weihuayan=Joinweihuayan,zhengguojiei,c,d,d1,e,g,g1,f,zhengguojiei+1; weihuayandongquanfa=0,0,1,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatio1/2ShowGraphicsLineNestlovelyduwangen,dongquanfa,4,AspectRatio1/2基本生成元分形图五、 (*下三角上三角*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=60Degree,sa=Singengping,ca=Cosgengping,c,d,g,f,e,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*3/4+zhengguojiei+1/4; e=zhengguojiei/2+zhengguojiei+1/2; f=zhengguojiei/4+zhengguojiei+1*3/4; S=TransposeT; d=c+S.(e-c); g=e+T.(f-e); weihuayan=Joinweihuayan,zhengguojiei,c,d,e,g,f,zhengguojiei+1; weihuayandongquanfa=0,0,1,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatioSqrt3/2ShowGraphicsLineNestlovelyduwangen,dongquanfa,5,AspectRatioSqrt3/2基本生成元分形图六、 (*单个上正方*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=90Degree,sa=Singengping,ca=Cosgengping,c,d,d1,g1,g,f,e,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*2/3+zhengguojiei+1/3; e=zhengguojiei/3+zhengguojiei+1*2/3; S=TransposeT; d=c+T.(e-c); d1=e+T.(e-c); weihuayan=Joinweihuayan,zhengguojiei,c,d,d1,e,zhengguojiei+1; weihuayandongquanfa=0,0,1,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,7,AspectRatio1/3ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatio1/3基本生成元分形图七、 (*一个正方形向外长大*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=90Degree,sa=Singengping,ca=Cosgengping,c,d,d1,g1,g,f,e,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*2/3+zhengguojiei+1/3; e=zhengguojiei/3+zhengguojiei+1*2/3; S=TransposeT; d=c+T.(e-c); d1=e+T.(e-c); weihuayan=Joinweihuayan,zhengguojiei,c,d,d1,e,zhengguojiei+1; weihuayandongquanfa=0,0,1,0,1,-1,0,-1,0,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,4,AspectRatio1/1ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatio1/1基本生成元分形图八、 (*一个正方形向内长大*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=90Degree,sa=Singengping,ca=Cosgengping,c,d,d1,g1,g,f,e,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*2/3+zhengguojiei+1/3; e=zhengguojiei/3+zhengguojiei+1*2/3; S=TransposeT; d=c+T.(e-c); d1=e+T.(e-c); weihuayan=Joinweihuayan,zhengguojiei,c,d,d1,e,zhengguojiei+1; weihuayandongquanfa=0,0,1,0,1,1,0,1,0,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,5,AspectRatio1/1ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatio1/1基本生成元分形图九、 (*一个M形状图形*)lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=60Degree,sa=Singengping,ca=Cosgengping,c,d,g,f,e,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*3/4+zhengguojiei+1/4; e=zhengguojiei/2+zhengguojiei+1/2; f=zhengguojiei/4+zhengguojiei+1*3/4; S=TransposeT; d=c+T.(e-c); g=e+T.(f-e); weihuayan=Joinweihuayan,zhengguojiei,c,d,e,g,f,zhengguojiei+1; weihuayandongquanfa=0,0,1,0;ShowGraphicsLineNestlovelyduwangen,dongquanfa,1,AspectRatioSqrt3/8ShowGraphicsLineNestlovelyduwangen,dongquanfa,5,AspectRatioSqrt3/8基本生成元分形图十、 两个上三角形 横线lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=60Degree,sa=Singengping,ca=Cosgengping,c,d,g,f,e,e1,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*4/5+zhengguojiei+1/5; e=zhengguojiei*3/5+zhengguojiei+1*2/5; e1=zhengguojiei*2/5+zhengguojiei+1*3/5; f=zhengguojiei/5+zhengguojiei+1*4/5; S=TransposeT; d=c+T.(e-c); g=e1+T.(f-e1); weihuayan=Joinweihuayan,zhengguojiei,c,d,e,e1,g,f,zhengguojiei+1; weihuayan dongquanfa=0,0,1,0; Show Graphics LineNestlovelyduwangen,dongquanfa,1 , AspectRatio Sqrt3/10 Show Graphics LineNestlovelyduwangen,dongquanfa,5 , AspectRatio Sqrt3/10 生成元分形图十一、 上三角形 横线 下三角形 lovelyduwangenzhengguojie_List:=Blockweihuayan=,i, wuxiaonan =Lengthzhengguojie,gengping=60Degree,sa=Singengping,ca=Cosgengping,c,d,g,f,e,e1,T=ca,-sa,sa,ca,S, Fori=1,i wuxiaonan,i+,c=zhengguojiei*4/5+zhengguojiei+1/5; e=zhengguojiei*3/5+zhengguojiei+1*2/5; e1=zhengguojiei*2/5+zhengguojiei+1*3/5; f=zhengguojiei/5+zhengguojiei+1*4/5; S=TransposeT; d=c+T.(e-c); g=e1+S.(f-e1); weihuayan=Joinweihuayan,zhengguojiei,c,d,e,e1,g,f,zhengguojiei+1; weihuayan dongquanfa=0,0,1,0; Show Graphics LineNestlovelyduwangen,dongquanfa,1 , AspectRatio Sqrt3/5 Show Graphics LineNestlovelyduwangen,dongquanfa,5 , AspectRatio Sqrt3/5 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AspectRatio1/GoldenRatio一、 挖空一个黑色三角形sierpinskitris_List:=Blocktmp=,i,p=Lengthtris/3,a,b,c,d,e,f, Fori=0,ip,i=i+1, a=tris3i+1; b=tris3i+2; c=tris3i+3; d=(a+b)/2; e=(a+c)/2; f=(b+c)/2; tmp=Jointmp,a,d,e,d,b,f,e,f,c; tmpShowsierpinskipts_List:=Blocktmp=,i,p=Lengthpts/3, Fori=0,ip,i=i+1,AppendTotmp,Polygonpts3i+1,pts3i+2,pts3i+3; ShowGraphicstmp,AspectRatio1/GoldenRatiotriangle=-1,0,1,0,0,Sqrt3p0=ShowsierpinskiNestsierpinski,triangle,0p1=ShowsierpinskiNestsierpinski,triangle,1p2=ShowsierpinskiNestsierpinski,triangle,2p3=ShowsierpinskiNestsierpinski,triangle,3p4=ShowsierpinskiNestsierpinski,triangle,4ShowGraphicsArrayp1,p2,p3,p4;生成元分形图二、 挖空一个彩色的三角形sierpinskitris_List:=Blocktmp=,i,p=Lengthtris/4,a,b,c,d,e,f, Fori=0,ip,i=i+1, a=tris4i+1; b=tris4i+2; c=tris4i+3; d=(a+b)/2; e=(a+c)/2; f=(b+c)/2; tmp=Jointmp,a,d,e,a,d,b,f,d,e,f,c,e; tmpShowsierpinskipts_List:=Blocktmp=,i,p=Lengthpts/4, Fori=0,ip,i=i+1,(*AppendTotmp,RGBColor1,0,0,Polygonpts4i+1,pts4i+2,pts4i+3,*) AppendTotmp,Thickness.02,RGBColor0,0,1,Linepts4i+1,pts4i+2,pts4i+3,pts4i+1; ShowGraphicstmpShowsierppts_List:=Blocktmp=,i,p=Lengthpts/4, Fori=0,ip,i=i+1,AppendTotmp,RGBColor1,0,0,Polygonpts4i+1,pts4i+2,pts4i+3,pts4i+1; ShowGraphicstmptriangle=-1,0,1,0,0,Sqrt3,-1,0p0=ShowsierpinskiNestsierpinski,triangle,2p1=ShowsierpNestsierpinski,triangle,2Showp0,p1生成元 分形图三、 第一题的逆,填充挖去的部分 彩色swwwierpinskiwtris_List:=Blocktmp=,duu=,mm=,i,j,p=Lengthwtris1/4,dd=