MATLAB: Help needed adding features to this script.

data matriximages

I have a script (shown below) that will generate a 12×12 matrix of all 0's and a single 1, which will replicate in a randomised order 7200 times. There are three features I want to add to this script but don't know how:
  1. Instead of generating a matrix in a complete random order I want digits to move either one place up, down, left or right from their position in the previous matrix.
  2. A shortcut that will create an imagesc() for all 7200 matrix's (like the image below).
Any help would be greatly appreciated.
Thanks,
Joe
count=0;
m=zeros(144,1);
rand_int=datasample(1:144,1);
m(rand_int)=1;
old_matrix=reshape(m,[12 12]);
for i=1:7200
    m=zeros(144,1);
    rand_int=datasample(1:144,1);
    m(rand_int)=1;
    new_matrix=reshape(m,[12 12]);
    if sum(abs(old_matrix-new_matrix),'All')>0
        count=count+1;
    end
    old_matrix=new_matrix
end

Best Answer

Here is one way:
m = zeros(12, 12);
numIterations = 7200;
row = ones(1, numIterations);
col = ones(1, numIterations);
m(row(1), col(1)) = 1;
imagesc(m);
axis('on', 'image');
for k = 2 : numIterations
	row(k) = row(k-1) + randi([-1,1], 1);
	while row(k) <= 0 || row(k) > size(m, 1)
		row(k) = row(k-1) + randi([-1,1], 1);
	end
	col(k) = col(k-1) + randi([-1,1], 1);
	while col(k) <= 0 || col(k) > size(m, 2)
		col(k) = col(k-1) + randi([-1,1], 1);
	end
	m(row(k), col(k)) = 1;	% Set new location
	m(row(k-1), col(k-1)) = 0; % Clear old location
	imagesc(m);
	drawnow;
end
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