function torus_map(kmx)

 t1 = 2*pi*(0:199)/199;
 t2 = 2*pi*(0:319)/319;
 r = 2;

 [P,Q] = meshgrid(t2,t1);
 Z = sin(Q);
 YY = sqrt(r^2 + 1 - 2*r*cos(Q)).*sin(P);
 XX = sqrt(r^2 + 1 - 2*r*cos(Q)).*cos(P);
 
 Cdat = Z;
 
 figure(1);
 clf;
 surface(XX,YY,Z,Cdat,'EdgeColor','none')
 axis equal;
 colormap('default');
 view(8,45);
 
 M = [ 2 1; 1 1];
 
 [n1,n2] = size(Z);
 
 Mt = M^kmx;
 
 for i = 1:n1
     for j = 1:n2
         x1 = [(i-1)/(n1-1) (j-1)/(n2-1)]*Mt(:,1);
         x2 = [(i-1)/(n1-1) (j-1)/(n2-1)]*Mt(:,2);
         k1 = floor(n1*mod(x1,1))+1;
         k2 = floor(n2*mod(x2,1))+1;
         tmp(i,j) = Cdat(k1,k2);
     end
 end
 Cdat = tmp;

 figure(2);
 clf;
 
 surface(XX,YY,Z,Cdat,'EdgeColor','none')
 axis equal;
 view(8,45);