相互垂直的同频和不同频（李萨如图）简谐振动合成程序[转]

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注：混沌吸引子的相图就是李萨如图。DNA双链纵投影也构成某种二维李萨如图。
%相互垂直的同频和不同频（李萨如图形)简谐振动合成begin
%骆遥 编写 [e-mail]
A1=3;
A2=8;
t=0:0.00001:0.04;
%1
T1_T2=1;
alpha1_alpha2=0;
f1=1000;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,1);
plot(x,y);
title('φ1-φ2=0');
ylabel('T1:T2=1:1');
%2
T1_T2=1;
alpha1_alpha2=pi/4;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,2);
plot(x,y);

title('π/4')
%3
T1_T2=1;
alpha1_alpha2=pi/2;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,3);
plot(x,y);
title('π/2');
%4
T1_T2=1;
alpha1_alpha2=pi*3/4;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,4);
plot(x,y);
title('3/4*π');
%5
T1_T2=1;
alpha1_alpha2=pi;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,5);
plot(x,y);
title('π');
%6
T1_T2=1/2;
alpha1_alpha2=0;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,6);
plot(x,y);
ylabel('T1:T2=1:2');
%7
T1_T2=1/2;
alpha1_alpha2=pi/4;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,7);
plot(x,y);
%8
T1_T2=1/2;
alpha1_alpha2=pi/2;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,8);
plot(x,y);
%9
T1_T2=1/2;
alpha1_alpha2=pi*3/4;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,9);
plot(x,y);
T1_T2=1/2;
alpha1_alpha2=pi;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,10);
plot(x,y);
T1_T2=1/3;
alpha1_alpha2=0;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,11);
plot(x,y);
ylabel('T1:T2=1:3');
T1_T2=1/3;
alpha1_alpha2=pi/4;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,12);
plot(x,y);
T1_T2=1/3;
alpha1_alpha2=pi/2;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,13);
plot(x,y);
T1_T2=1/3;
alpha1_alpha2=pi*3/4;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,14);
plot(x,y);
T1_T2=1/3;
alpha1_alpha2=pi;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,15);
plot(x,y);
T1_T2=2/3;
alpha1_alpha2=0;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,16);
plot(x,y);
ylabel('T1:T2=2:3');
title('φ1-φ2=0');
T1_T2=2/3;
alpha1_alpha2=pi/8;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,17);
plot(x,y);
title('π/8');
T1_T2=2/3;
alpha1_alpha2=pi/4;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,18);
plot(x,y);
title('π/4');
xlabel('李萨如图形(骆遥 绘制)');
T1_T2=2/3;
alpha1_alpha2=pi*3/8;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,19);
plot(x,y);
title('3/8*π');
T1_T2=2/3;
alpha1_alpha2=pi/2;
f1=100;
f2=f1*T1_T2;
alpha2=0;
alpha1=alpha2+alpha1_alpha2;
x=A1*cos(2*pi*f1*t+alpha1);
y=A2*cos(2*pi*f2*t+alpha2);
subplot(4,5,20);
plot(x,y);
title('π/2');
xlabel('注：所有φ2=0')
%end