matlab繪製peano（皮亞諾）曲線和koch（科赫曲線，雪花曲線）分形曲線

koch曲線

matlab plot函數繪製koch曲線程序，程序仍是比較簡單的，這裏只繪製出了雪花的三分之一

function koch_curve(number)%number表明koch的階數，範圍爲大於等於2  
figure  
set(gcf,'position',[0,0,1920,1080]);%設置窗口分辨率，[0,0]和[1920,1080]分別爲窗口左上角和右下角座標可根據本身的屏幕分辨率調整，註釋掉這句則使用matlab默認窗口分辨率  
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

matlab 繪製皮亞諾曲線

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