Game of Life

Conway’s Game of Life — Technical Overview

Definition
Conway’s Game of Life is a two-dimensional cellular automaton introduced by mathematician John H. Conway in 1970. It is a zero-player game: once the initial state is set, the board evolves deterministically with no further input.

Core Concepts

Item	Details
Universe	Infinite orthogonal grid of square cells (practically, finite with wrap or hard edges).
Cell State	Each cell is either alive (1) or dead (0).
Neighbourhood	The eight orthogonally and diagonally adjacent cells (Moore neighbourhood).
Generation	One simultaneous update of every cell based on the rules below.

Transition Rules (per generation)

1. Under-population Any live cell with fewer than two live neighbours dies.

2. Survival Any live cell with two or three live neighbours lives on.

3. Over-population Any live cell with more than three live neighbours dies.

4. Reproduction Any dead cell with exactly three live neighbours becomes a live cell.

All updates are applied simultaneously, producing the next generation.

Behavioural Classes

• Still lifes – static patterns (e.g., Block, Beehive).

• Oscillators – repeat after n generations (e.g., Blinker, Toad, Pulsar).

• Spaceships – translate across the grid while repeating (e.g., Glider, Light-weight spaceship).

• Methuselahs – small seeds that generate long, chaotic evolutions before stabilising (e.g., R-pentomino).

• Guns – emit an endless stream of spaceships (e.g., Gosper Glider Gun).

Computational Significance

• Proven Turing-complete – can emulate any Turing machine given a suitable pattern arrangement.

• Demonstrates how complexity can emerge from extremely simple rules.

• Widely used in theoretical computer science, complexity studies, and algorithm education.

Common Implementation Notes

Aspect	Recommendation
Data structure	2-D array / bit-array (+ double buffer) or sparse hash-set for large sparse worlds.
Boundary handling	Wrap-around (toroidal), fixed dead border, or dynamic expansion.
Rendering	Direct pixel/rect draw, texture blitting, or shader-based visualization for speed.
Interactivity	Step, run/pause, reset, pattern insertion, speed and zoom controls.