pickover3.m

分形计算的几个程序原码

%三维国王映射的特点是有三个迭代方程，描点时z可用也可不用 。映射的具体形式为： 

%x_(n+1)=sin(ay_n)-zcos(bx_n), 
%y_(n+1)=zsin(cx_n)-cos(dy_n), 
%z_(n+1)=esinx_n. 

function Pickover3 
% 三维国王映射 
% 迭代形式: 
% x_(n+1)=sin(by_n)-zcos(bx_n), 
% y_(n+1)=sin(cx_n)-cos(dy_n), 
% z_(n+1)=fsinx_n. 
x=0.1; 
y=0.1; 
z=0.1; 
a=2.24; 
b=0.43; 
c=-0.65; 
d=-2.43; 
f=0.7;     %f的取值可在0.5至1.0之间改变 
for k=1:10000;        % 10000次迭代 
   x(k+1)=sin(b*y(k))-z(k)*cos(b*x(k)); 
   y(k+1)=sin(a*x(k))-cos(d*y(k)); 
   z(k+1)=f*sin(x(k)); 
end 
figure; 
plot(x,y,'.') 
figure; 
plot3(x,y,z)