Conway's Game of Life

A zero-player cellular automaton on a grid where each cell lives or dies according to its neighbors. Simple local rules produce patterns that evolve without further input.

Cellular automaton: A discrete system whose cells update in steps according to local rules. The Game of Life is a cellular automaton with binary states and a fixed neighborhood.
Grid graph: A graph whose vertices form a regular lattice and connect to nearby vertices. Life's cells occupy lattice positions, with adjacency defining local interaction.
Turing completeness: The ability of a computational system to simulate any Turing machine. Life can implement universal computation using carefully arranged patterns.
John Horton Conway: British mathematician known for work in group theory, combinatorics, and recreational mathematics. Conway devised the cellular automaton and its rules in the late 1960s.
Emergence: The appearance of system-level patterns or properties from interactions among simpler components. Life is a vivid example of large-scale order arising from local cell updates.
Moore neighborhood: The eight cells surrounding a grid cell, including diagonal neighbors. Each cell's next state depends on these eight surrounding cells.
Discrete time: A model of time represented as a sequence of separate steps. Life updates all cells simultaneously from one generation to the next.
Conway's Game of Life glider gun: A repeating Life pattern that emits a glider at regular intervals. Glider guns supply moving signals for computational constructions.
Martin Gardner: American writer whose Scientific American column popularized recreational mathematics. Gardner's 1970 column introduced the Game of Life to a broad audience.
Complex systems: Systems whose interacting components produce behavior not easily inferred from components alone. Life became a compact model for exploring complexity through simple interactions.

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