Conway's Game of Life is a mathematical toy which describes a transition of a grid-world over time. As one can read on the Wikipedia article, there are certain structures which are either stable or form short cycles. I wanted to see whether these structures could be found in a systematic way.
So I have just tried a brute-force way to generate states, and see how they evolve. This builds a graph, and that graph can be decomposed into subgraphs. The subgraph that is connected to the empty world is the not very interesting. So I show some of the ones which are not connected to the empty world.
The simplest subgraph is one with only a single node, which is stable: