Alternative to for loop i.e. recursion

My code like this but what should I do to change the code so that it automatically calcultes the matrix for p=4 without using for loops. I want to convert this function into a recursive function.

function M=FakLoop3
    p=3;
    v=0;
    indis=zeros(1,p);
    M=zeros(2^p,p)
    for i=0:1
        indis(1)=i;
        for j=0:1
            indis(2)=j;
            for k=0:1
                indis(3)=k;
                v=v+1;
                M(v,:)=indis;
            end
        end
    end
end

[Torsten]

https://www.researchgate.net/post/How_can_I_generate_all_combinations_of_0_1_in_MATLAB

[Jan]

A recursive function will not be efficient in Matlab. Therefore I assume that this is a homework. Then posting a working solution would not be useful. So please post, what you have tried so far and ask a specific question.

Efficient would be an inlined dec2bin:

M = rem(floor((0:2^p-1).' .* 2 .^ (1-p:0)), 2)

[Maaz ul mosaid]

This is not a homework. I am trying to replace the for loops so that it can vary with p, I think recursive is the solution to this problem. Please post the solution if you can.

[Jan]

I've posted an efficient solution already. I repeat it in an answer. Of course you can solve this by recursion, but the shown method is much more efficient.

Answer 1

[Jan]

Inlined dec2bin(0:2^p-1):

M = rem(floor((0:2^p-1).' .* 2 .^ (1-p:0)), 2)

Another solution:

M  = zeros(2^p, p, 'uint8');
n1 = 1;
n2 = 2^(p-1);
v  = uint8([0;1]);
for k = 1:p
    M(:, k) = repmat(repelem(v, n2, 1), n1, 1);
    n1 = n1 * 2;
    n2 = n2 / 2;
end

Or:

M  = zeros(2^p, p, 'uint8');
v  = uint8(0:2^p-1).';
for k = p:-1:1
    M(:, k) = bitget(v, 1);
    v       = bitshift(v, -1);
end

With doubles instead:

M  = zeros(2^p, p, 'uint8');
v  = (0:2^p-1).';
for k = p:-1:1
    M(:, k) = rem(v, 2);
    v       = floor(v / 2);
end