I am shamelessly ripping off fletch's work here, but the following (hexagonal) grid:

 -8        . . . - -             -8
 -7       . . . . - ^            -7
 -6    . . . . - - - -           -6
 -5   . . - . a a - ^ ? ? -      -5
 -4  . . . . k o ! - ^ ? ? ?     -4
 -3 . - . a h j a ^ ^ ^ ^ ^ -    -3
 -2  . . - . a a a ^ a a - - -   -2
 -1   . . . a a a b + + ^ ^ -    -1
  0  . . . m c u a a - ^ - ^     0
  1   . - . a a . a a - - ^      1
  2    - ^ ^ a a a ^ a - - ^     2
  3     - - - - - - - . . -      3
  4      ^ - - - - - ^ - -       4
  5       - ^ - - ^ - - -        5
[download]

Is actually the same grid as this rectangular grid:

 -8    ...--      -8
 -7   ....-^      -7
 -6  ....----     -6
 -5 ..-.aa-^??-   -5
 -4 ....ko!-^???  -4
 -3.-.ahja^^^^^-  -3
 -2 ..-.aaa^aa--- -2
 -1 ...aaab++^^-  -1
  0 ...mcuaa-^-^  0
  1 .-.aa.aa--^   1
  2  -^^aaa^a--^  2
  3  -------..-   3
  4   ^-----^--   4
  5   -^--^---    5
[download]

It is just a question of

1. How the grid is rendered.
2. how a cell's neighboring cells are determined.

Once the data structure is reduced to rectangular, the mystery of the hexagon disappears. It is this kind of thinking that reduces a checkerboard to an 8 x 4 board, for certain games.