# Still Life Theory

People familiar with Conway's Game of Life often talk about "still-lifes": patterns with period 1, also known as stable patterns.
These can be organized into the following categories:

Stable Pattern |
Any arrangement of on and off cells that stays the same from generation to generation |
honey farm |

Cluster |
Any stable pattern in which every pair of live cells is connected by a path of cells (using horizontal, vertical, or diagonal steps) that does not have two consecutive empty cells. |
di-block by hive |

General Still-Life |
Any stable pattern in which every pair of live cells is connected by a path of live or overcrowded cells. |
switch |

Pseudo-Still-Life |
A general still-life whose islands can be partitioned into two subsets so that each subset is stable on its own. |
tri-block |

Strict Still-Life |
A general still-life whose islands cannot be partitioned into two subsets so that each subset is stable on its own. |
dead spark coil on table |

Island |
Any pattern in which every pair of live cells is connected by a path of live cells. |
sphinx |

<<insert examples here>>

#### Alternate Strict Still-Life Definitions

The standard definitions for pseudo-still-lifes and strict still-lifes talk about partitioning into exactly two proper subsets. But other definitions are plausible --
in particular, it would be reasonable to allow any number of proper subsets.
First of all, we note the surprising result that any pattern whose islands can be partitioned into 5 or more stable proper subsets can also have them partitioned into 4 or fewer such subsets. (proof)

So we can consider the following definitions:

difficulty in
distinguishing
pseudo from strict
exactly two subsets (the standard definition) O(n^2)
two or three subsets NP-complete
two or three or four subsets (i.e. any number of subsets) [open problem]