This document details the operational principles of a zero-player game, a cellular automaton developed by mathematician John Conway. It specifies how a grid of cells, each in one of two states (alive or dead), evolves over discrete time steps based on a set of predefined conditions. As an illustration, a dead cell with exactly three living neighbors becomes alive in the next generation, while a living cell with fewer than two living neighbors dies (underpopulation).
Understanding the formal description of this game is crucial for simulating, analyzing, and extending its behavior. The succinctness of the rules allows for emergent complexity, demonstrating how simple initial conditions can lead to intricate and unpredictable patterns. These patterns have implications for understanding self-organization in natural systems and have served as inspiration in fields ranging from computer science to biology.
