 This correspondence between states is due to Andrew Lenard and is given as follows.If a square has color "i" = 0, 1, or 2, then the arrow
on the edge to an adjacent square goes left or right (according to an observer in the square) depending on whether the color in the adjacent square is "i"+1 or "i"−1 mod 3.There are 3 possible ways to color a fixed initial square, and once this initial color is chosen this gives a 1