How do I change values in an array based upon its previous value?

Hi all! I'm new to MATLAB.

So basically I have a 2D array and a spreading pattern/fractal that I wish to execute, I can make the pattern happen when turning zeros to ones but then it get's messy after that. the image is a basic rundown of what I want to happen for each iteration of the pattern.

Thank you, Michael.

[Guillaume]

Why isn't the pattern spread around the 1s in step 2? I.e. why isn't that last matrix:

0 0 1 0 0
0 1 2 1 0
1 2 3 2 1
0 1 2 1 0
0 0 1 0 0

Answer 1

[Guillaume]

Assuming you've made a mistake in your second step (see comment), this is trivially achieved with imdilate (requires image processing toolbox

A = [0 0 0 0 0; 0 0 0 0 0;0 0 1 0 0; 0 0 0 0 0; 0 0 0 0 0]
nstep = 5;
for step = 1:nstep
    A = imdilate(A > 0, [0 1 0; 1 1 1;0 1 0]) + A
end

[Michael Rowlinson]

I should've probably added that the pattern won't spread to a zero if it has two or more occupied spaces around it such as having a 1 or 2 and another 1 or 2 adjacent to it.

so the next step after the third would be something like this but I don't think this would be the case because it's being demonstrated on a 5x5 array and would be exceeding the boundary?

0 1 2 1 0
1 0 3 0 1
2 3 4 3 2
1 0 3 0 1
0 1 2 1 0

[Guillaume]

Ah, ok. You can use a simple 2d convolution to find the number of neighbours a value. Then it's a simple matter of a bit of arithmetic:

A = [0 0 0 0 0; 0 0 0 0 0;0 0 1 0 0; 0 0 0 0 0; 0 0 0 0 0]
nstep = 5;
for step = 1:nstep
    A(A > 0) = A(A > 0) + 1; %increase existing values by 1
    A = A + (conv2(A > 0, [0 1 0;1 0 1;0 1 0], 'same') == 1) .* ~A  %find zeros with just one neighbour, set them to 1
end

[Michael Rowlinson]

That looks about right, I can't check if it'll work for me right now but I'll get back to this soon, thank you!