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matlab绘制peano(皮亚诺)曲线和koch(科赫曲线,雪花曲线)分形曲线
koch曲线
matlab plot函数绘制koch曲线程序,程序还是比较简单的,这里只绘制出了雪花的三分之一
- function koch_curve(number)%number代表koch的阶数,范围为大于等于2
- figure
- set(gcf,'position',[0,0,1920,1080]);%设置窗口分辨率,[0,0]和[1920,1080]分别为窗口左上角和右下角坐标可根据自己的屏幕分辨率调整,注释掉这句则使用matlab默认窗口分辨率
- n=2;
- koch1=[0,0;1,0];
- for i=1:number
- koch2=zeros(4*n-3,2);
- k=2;
- for j=2:n
- koch2(k,:)=[(koch1(j-1,1)*2+koch1(j,1))/3,(koch1(j-1,2)*2+koch1(j,2))/3];
- koch2(k+1,:)=[(koch1(j-1,1)+koch1(j,1)+sqrt(3)*(koch1(j-1,2)-koch1(j,2))/3)/2,(koch1(j-1,2)+koch1(j,2)-sqrt(3)*(koch1(j-1,1)-koch1(j,1))/3)/2];
- koch2(k+2,:)=[(koch1(j,1)*2+koch1(j-1,1))/3,(koch1(j,2)*2+koch1(j-1,2))/3];
- koch2(k+3,:)=koch1(j,:);
- k=k+4;
- end
- n=4*n-3;
- x=koch2(:,1);
- y=koch2(:,2);
- plot(x,y)
- axis equal
- koch1=koch2;
- pause(1);
- end
- end
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matlab 绘制皮亚诺曲线
- function peano_curve(n)
- peano_old=[0,0;0,1;0.5,1;0.5,0;1,0;1,1];
- x=peano_old(:,1);
- y=peano_old(:,2);
- figure
- set(gcf,'position',[0,0,1920,1080]);
- plot(x,y)
- axis equal
- for i=1:n-1
- p1=[peano_old(:,1),2+1/(3^i-1)-peano_old(:,2)];
- p1=p1(length(p1):-1:1,:);
- p2=[p1(:,1),4+3/(3^i-1)-p1(:,2)];
- p2=p2(length(p2):-1:1,:);
- peano_new=[peano_old;p1;p2];
- p1=[2+1/(3^i-1)-peano_new(:,1),peano_new(:,2)];
- p1=p1(length(p1):-1:1,:);
- p2=[4+3/(3^i-1)-p1(:,1),p1(:,2)];
- p2=p2(length(p2):-1:1,:);
- peano_new=[peano_new;p1;p2];
- peano_old=peano_new/(3+2/(3^i-1));
- x=peano_old(:,1);
- y=peano_old(:,2);
- plot(x,y)
- axis equal
- pause(1)
- end
- end
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