Cellular Automata - nearest neighbors
The boundary conditions are periodic in both directions: the top row and bottom rows are adjacent as are the left and right columns.
Choose the rules for when changes from occupied to empty (1 -> 0) or empty to occupied (0 -> 1). The adjacent cells are the four cells above, below, left, and right of any cell. That is, cells must share a line - rather than a point - in order to be nearest neighbors.