Conway's Game of Life
A zero-player cellular automaton where cell evolution is determined entirely by its initial state. Read more on Wikipedia.
The Mathematics & Rules of Life
Invented in 1970, Conway's Game of Life is one of the most famous models of cellular computation, illustrating how astonishing complexity and lifelike behavior emerge spontaneously from pure determinism.
Zero-Player Automaton
Conceived by mathematician John Horton Conway at Cambridge University and popularized in Martin Gardner's Scientific American column. It is classified as a "zero-player game": its entire progression is determined by its initial configuration without needing ongoing user intervention.
Neighborhood Transitions
- Underpopulation:Live cells with fewer than 2 live neighbors die.
- Survival:Live cells with 2 or 3 live neighbors live on to the next generation.
- Overpopulation:Live cells with more than 3 live neighbors die.
- Reproduction:Dead cells with exactly 3 live neighbors become live cells.
Turing Completeness
Local interactions produce complex macroscopic phenomena: static Still Lifes, repeating Oscillators, and self-propagating Spaceships (such as Gliders). The Game of Life is Turing complete—given sufficient space and time, it can simulate any digital computer or even an entire copy of itself.