Generating the Ulam Spiral

This short spiral(n) function is supposed to generate a number spiral centered at one. For the most part, I understand the code but I can't seem to grasp why the polynomial m^2-m+1 is used.

function S = spiral(n)
%SPIRAL SPIRAL(n) is an n-by-n matrix with elements
%   1:n^2 arranged in a rectangular spiral pattern.

S = [];
for m = 1:n
   S = rot90(S,2);
   S(m,m) = 0;
   p = m^2-m+1;
   v = (m-1:-1:0);
   S(:,m) = p-v';
   S(m,:) = p+v;
end
if mod(n,2)==1
   S = rot90(S,2);
end

Any ideas?

Answer 1

[Prince]

Figured it out... the quadratic designates the values along the main diagonal.

 For any future searchers