Consider the example:
% generate test images
% this part uses MIMT from FEX, but it's otherwise not needed
inpict = imread('cameraman.tif'); % raw single-channel source
A = uint8(repmat(double(inpict),[1 1 3]).*permute([1 0.3 0.8],[1 3 2]));
B = imtweak(A,'lchab',[1 1 0.25]);
C = imtweak(A,'lchab',[1 1 0.50]);
D = imtweak(A,'lchab',[1 1 0.75]);
% make mask
sout = size(inpict);
squaresize = [32 32];
xx = mod(0:(sout(2)-1),squaresize(2)*2)<squaresize(2);
yy = mod(0:(sout(1)-1),squaresize(1)*2)<squaresize(1);
m = uint8(xx & yy');
% combine images
outpict = A.*m + B.*circshift(m,squaresize.*[1 0]) ...
+ C.*circshift(m,squaresize.*[0 1]) ...
+ D.*circshift(m,squaresize.*[1 1]);
