1、科赫雪花曲線的 MATLAB編程 實現作者: 日期:科赫雪花曲線的 MA TL AB編程實現2 .1經一次迭代的科赫曲線M A T LAB實現程序如下：x1 = 1 2 2.5 3 4 ;y1=00 0 0 0;h1= pl ot(X 1,y1,/ l i new idt h，, 2, ' eras emode，, 'xor，); axis eq uala x i s offfor g = li ns pac e (0, 1,40)*s i n(p i / 3);yi( 3)=g；se t( h 1,， ydata ',y 1);draw now;end一次迭代所得科赫

2、曲線如圖一：圖一:勺口 d I軒®辺必T s a二2.2經二次迭代的科赫曲線MA T LA B實現程序如下：x2=x 1 (1);y2=yl( 1);f o r k=2:len g th(x 1 );t= li ns pac e(x1 (k-1),x1(k), 4 );tt=t(2) ,m ean(t),t(3:4);x 2 =x2,t t ;t=li n spac e(y 1(k-1),y 1 (k), 4);tt = t(2) ,mea n(t) ,t (3:4);y 2=y 2 ,t t ;e ndA=an g le (y2 (4 : 4 : e n d )y 2(2:4: e

3、n d)*i+ (x2( 4 :4: e nd)- x 2(2: 4: en d);for g = li n space (0 ,1,4 0) *si n (pi/ 3 )/3;y2( 3: 4:en d )=(y2(4: 4 : end )+y2 (2 :4: e nd ) /2 +im a g (g*ex p ( i *( A + P i/2);x2(3:4: end)= (x2(4:4:end)+x2(2:4 :en d)/2+real (g* exp (i*( A +p i /2);s et (h1, ' y data ', y2, ' x da t a'

4、;,x2);draw now;en d二次迭代后所得科赫曲線如圖二：2.3經三次迭代的科赫曲線MATLA B實現程序如下x3= x2(l);y3=y2( i);fo r k = 2: le ngth (x2);t=l i n sp ac e (x2( k -1),x2(k),4);tt= t(2),mean (t ),t(3: 4 );x 3=x3 , t t;t= lins p ace (y2(k-1) , y 2( k ),4);11 = t(2 ),mea n( t), t (3 :4); y3=y 3,tt;endA =an gle(y3(4:4:e nd) y 3 (2:4:e nd

5、)* i+( x3 (4: 4:e nd)-x3(2: 4: e nd); for g =li nsp ac e(0,1,40)*si n ( p i/3) /9;y 3(3 :4:end)=(y3 (4: 4 :en d) +y 3 (2:4:end)/2+imag (g * ex p(i* (A+ pi/2); x3(3:4:e nd) =(x 3 (4: 4:e nd)+x3 (2: 4:e nd) )/2+re a l(g* ex p (i*(A+pi/ 2 );s et (h1,/ yd a ta', y3,' x data ',x3);d raw now;e

6、 nd三次迭代后所得科赫曲線如圖三:圖三 Figure 1Ale Edit View Insert Tools Desktop Uindow Helpn 已 Q hs I ''s 沙 ® 遲 s 因 I p E Note new toolbar button?:日ata bnjwh ng & linkeJ plots 二凰 Pl彎忻日芒。2.4經四次迭代的科赫曲線MATLAB實現程序如下x4 = x3(1);y4 =y3( 1 )；for k= 2 :leng t h( x 3);t=linspace (x3( k 1),x3(k), 4);t t=t(2),

7、mean(t), t(3:4);x4=x4, tt;t=l i nspace (y 3 (k - 1 ) ,y 3(k),4);tt = t (2) ,me an(t), t (3: 4);y4 = y 4,11;e ndA=angl e (y 4 (4:4:end)-y4(2:4:end)*i +(x4(4: 4 :end) - x 4 (2: 4 :end);f or g= 1 inspac e(0,1, 40)* s i n (p”3)/27;y 4(3:4:end)=(y 4( 4 :4: e nd)+y 4(2 :4: e nd)/2 + imag(g*e x p (i*(A+pi/

8、2); x4(3:4:en d)=( x 4(4:4:en d) + x4(2:4:end)/2 + r eal( g * e xp( i* (A+pi/2); se t(h 1, 'y d at a，,y4,' x da t a',x4);d r awn ow;end四次迭代后所得科赫曲線如圖四:2.5經五次迭代的科赫曲線M ATL AB實現程序如下X 5=x4(1);y5=y 4(1);f or k =2:1 e ng t h(x 4 );t=li ns pa ce(x4 (k-1), x4(k), 4);t t=t(2) ,mean (t) , t(3 :4);x

9、5=x5, tt;t=li ns pace(y4( k-1) ,y4 (k), 4);t t=t(2),m e an(t),t(3:4);y 5=y 5,t t;endA=angl e (y5( 4 : 4 : e nd)-y5(2:4: en d)* i+(x 5 (4:4: e nd)-x5 (2:4: en d); for g=l i nspace(0 ,1,4 0 )*si n (p i/ 3)/81;y5 (3: 4:end) =(y5 (4:4: e nd)+ y 5(2:4:en d) )/ 2 + i mag(g * ex p (i* (A + pi/2);x5(3: 4 :end)= (x 5 (4: 4 : e nd) +