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;

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

the problem is that the execution is very very slow, why??

[Oleg Komarov]

Format the code properly and supply example inputs.

Use the profile and *preallocate*.

[samia]

if I understood you: my example is an image, I want to determine the period T if I change the image size; ie the main program is:

I=imread('image');

%% size(I)=N*N

T= rech_k(I);