Cellular AutomatonA discrete computational model consisting of a regular grid of cells, each in one of a finite number of states, that evolves through discrete time steps according to rules based on neighboring cell states.
Moore NeighborhoodThe eight cells surrounding a central cell in a 2D grid (including diagonals), named after Edward F. Moore who proved the Garden of Eden theorem in 1962.
Von Neumann NeighborhoodThe four orthogonally adjacent cells (up, down, left, right) surrounding a central cell, named after John von Neumann's original cellular automaton design.
Game of LifeA two-dimensional cellular automaton created by John Conway in 1970 with simple birth/survival/death rules that can produce complex emergent behavior, proven to be Turing-complete.
GliderA small pattern in Conway's Game of Life that translates itself across the grid over a 4-step cycle, one of the most iconic structures in cellular automata.
Elementary Cellular AutomatonA one-dimensional CA with two states and nearest-neighbor rules, systematically classified by Stephen Wolfram into 256 rules (Rule 0 through Rule 255).
Rule 110An elementary cellular automaton proven to be Turing-complete by Matthew Cook in 2004, demonstrating that even the simplest CA can perform any computation.
Rule 30An elementary CA discovered by Wolfram that generates apparently random behavior from a single initial cell, used in Mathematica's random number generator.
Wolfram ClassesStephen Wolfram's four-class taxonomy of cellular automata behavior: Class 1 (uniform), Class 2 (periodic), Class 3 (chaotic), Class 4 (complex/edge of chaos).
Garden of EdenA configuration in a cellular automaton that can only appear as an initial condition and cannot be reached from any other state, proven to exist by Moore (1962) and Myhill (1963).
Self-ReplicationThe ability of a pattern within a CA to create copies of itself, the original motivation for von Neumann's work, inspired by biological cell reproduction.
Totalistic RuleA CA rule where a cell's next state depends only on the sum (or average) of the values of cells in its neighborhood, simplifying the rule space.
Langton's AntA simple 2D cellular automaton where an 'ant' moves on a grid, flipping cell colors, producing initially chaotic behavior that eventually forms a highway pattern.
Reversible CAA cellular automaton where every configuration has a unique predecessor, studied by Tommaso Toffoli (1977) for modeling physical laws that obey time-reversal symmetry.
Lattice Gas AutomatonA CA-based model for simulating fluid dynamics, where particles move and collide on a lattice grid, pioneered in the 1980s.
WireworldA cellular automaton designed by Brian Silverman in 1987 to simulate electronic logic circuits, using four states to model signal propagation.
HashlifeAn algorithm invented by Bill Gosper for extremely fast computation of Life patterns by exploiting the repetitive nature of CA evolution through memoization.
SpaceshipAny pattern in a CA that translates itself across the grid while maintaining its structure, generalizing the concept of gliders.
OscillatorA pattern in a CA that returns to its initial state after a fixed number of time steps, cycling between a finite set of configurations.
Still LifeA pattern in a CA that remains unchanged from one generation to the next, representing a stable equilibrium.