Loop for concentric squares

I want to try and make a loop that makes concentric square matricies. Just as an example, I have my sample code here:

A = zeros(20)
%difference = 2
A(3:18,3:18) = 1
A(5:16,5:16) = 0
A(7:14, 7:14) = 1
A(9:12, 8:12) = 0

So I start with a matrix of height H and there's a height difference 'difference' between each matrix (in my example, it's 2). I'm not sure how I could use a 'for' loop to automatically do this since I'm not sure how to assign a name to each subsequent matrix in my code. Any help is appreciated.

Answer 1

[Adam Danz]

Vectorized version,

sz = 20;         % matrix size, square, positive integer
difference = 2;  % width of bands, positive integer 1 <= x <= (sz/2)-1

% Create matrix
nestedMat = (sz-difference*2):-difference*2:0;
layers = arrayfun(@(m){padarray(ones(m),(sz-m)*[.5,.5])},nestedMat);
A = mod(sum(cat(3,layers{:}),3),2);

% Plot it
imagesc(A)
axis equal

Loop version,

sz = 20;         % matrix size, square, positive integer
difference = 2;  % width of bands, positive integer 1 <= x <= (sz/2)-1

% Create matrix
nestedMat = (sz-difference*2):-difference*2:0;
layers = zeros(sz);
for i = 1:numel(nestedMat)
    layers = layers + padarray(ones(nestedMat(i)), (sz-nestedMat(i))*[.5,.5]);
end
A = mod(layers,2);

% Plot it
imagesc(A)
axis equal