u/Freact

The graph shows all state transitions for the Game of Life on a 4x4 toroidal grid (edge-wrapping).

With 16 cells, there are 2^{16} = 65,536 total states. By quotienting out spatial symmetries (translation, rotation, and reflection) the entire state space collapses into 805 canonical representatives.

• Red Central Node: The empty/extinction state (State 0), drawing in the vast majority of transient trees.
• 14 Blue Nodes: "Fixed states" in this quotient graph (self-loops). These include true still lifes as well as oscillators whose next phase is a rotated or translated version of the same canonical state. (Breakdown: 5 still lifes, 8 period-2, 1 period-4).
• Green Node Clusters: Two 4-state cycles. While they form a period-4 loop in this canonical graph, accounting for their rotational/translational shifts at each step gives them a true period of 8 on the actual grid.