number of iteration

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samia 2011-5-2

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/6619-number-of-iteration

I want to determine the number of iterations needed for the matrix its original state if a pixel is rotated according to a rule. for example to make the rotation I build this function:

%%%%%%%%%%%%%%

function nv_vect=catmap(N,a,b)
A=[1 a; b a*b+1];
nv_vect=zeros(2,N*N);
c=1;
for i=0:N-1
    for j=0:N-1
        nv_vect(:,c)=mod(A*[i j]',N);
        c=c+1;
      end
  end
nv_vect=uint8(nv_vect+1);

%%%%%%%%%%%%%%%%

   to construct the matrix I use this function:
function J=consruct_imag(I,nv_vect,N)
c=1;
for i=1:N
    for j=1:N
        J(i,j)=I(nv_vect(1,c),nv_vect(2,c));
        c=c+1;
    end
 end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

now I will use the number of iteration to return the original image:

%%%%%%%%%%%%%%%%%%%%%%%%%

function J=cat_k_fois(I,N,a,b,k)
for g=1:k
nv_vect=catmap(N,a,b);
J=consruct_imag(I,nv_vect,N);
I=J;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

I try to implement a function that allows me to determine the period T necessary to rebuild the image:

%%%%%%%%%%%%%%

function T=rech_k(I)
N=length(I);
a=1;k=1;k=1;
for(b=1:N-2)
    while(k<=3*N)
       K=cat_k_fois(I,N,a,b,k);
         if(K==I)
          T=k;break
         else
             k=k+1;
         end
      end
  end
   T;