Rules of Conway's Game of Life

Wikipedia gives a great description of the rules of Conway's Game ofLife:

Consider the following initial universe:

We can calculate the next generation by considering each cell. The top left cellis dead. Rule (4) is the only transition rule that applies to deadcells. However, because the top left cell does not have exactly three liveneighbors, the transition rule does not apply, and it remains dead in the nextgeneration. The same goes for every other cell in the first row as well.

Things get interesting when we consider the top live cell, in the second row,third column. For live cells, any of the first three rules potentiallyapplies. In this cell's case, it has only one live neighbor, and therefore rule(1) applies: this cell will die in the next generation. The same fate awaits thebottom live cell.

The middle live cell has two live neighbors: the top and bottom live cells. Thismeans that rule (2) applies, and it remains live in the next generation.

The final interesting cases are the dead cells just to the left and right of themiddle live cell. The three live cells are all neighbors both of these cells,which means that rule (4) applies, and these cells will become alive in the nextgeneration.

From these simple, deterministic rules, strange and exciting behavior emerges:

Answer

It should be the initial state of the example universe:

This pattern is periodic: it returns to the initial state after every twoticks.

• Can you find an initial universe that is stable? That is, a universe in whichevery generation is always the same.

There are an infinite number of stable universes! The trivially stableuniverse is the empty universe. A two-by-two square of live cells is also astable universe.