The Ulam spiral is simple to describe. On a gridded piece of paper, write down the number 1. Then write successive integers as you spiral out in a counter-clockwise fashion. For example:

 17    16    15    14    13
 18     5     4     3    12
 19     6     1     2    11
 20     7     8     9    10
 21    22    23    24    25

Although you can stop writing numbers at any time, for the purpose of this problem let's assume you want to fill an N x N square matrix with numbers from 1 to N^2.