Although you are setting all the elements to the same value in this particular case, it would only take a trivial modification of your code to arrive at a situation in which the values were not all the same. Then because parfor is allowed to execute the iterations in any order, relying on the sequential increment of "a" is not going to work: for example iterations i=1, i=5, and i=14 might all be running simultaneously in the "first round" at the time that a is 0, so depending on exact timing and internal implementation, you could end up writing into aa_array(1,1) three times or aa_array(3,1) three times, or (1,1) twice and (2,1) once, or any combination. Likewise, "a" could end up as 1 or 2 or 3 depending on how the three iterations "race" each other.
aa_array = cell(20,1);
parfor i = 1 : 20
if 1 == 1
aa_array(i,1) = {'done'};
end
end
