Interesting pattern.

This comes from very simple rules

Initial
End
Rules	: 3x3
Move 1	: (1, 1)
Move 2	: (2, 2)
Move 3	: (3, 3)
Move 4	: (4, 4)
Move 5	: (5, 5)
Move 6	: (2, 5)
Move 7	: (3, 5)
Move 8	: (5, 2)
Move 9	: (5, 3)

Courtesy of T-Lights