Cellular automaton

A discrete computational model in which cells on a grid update their states synchronously according to local rules. Simple rules can produce complex spatial and temporal patterns.

Cellular automaton rule: A specification mapping a cell’s current state and neighborhood configuration to its next state. The rule determines every transition in a cellular automaton.
Conway's Game of Life: A two-dimensional binary cellular automaton introduced by mathematician John Conway. Its four local rules produce moving patterns, stable structures, and computation.
Cellular automaton machine: A parallel computational architecture that performs operations through local state updates on a grid. The model’s local, uniform rules can be implemented directly in parallel hardware.
John von Neumann: A mathematician who made foundational contributions to computing, game theory, and cellular automata. His self-reproducing automaton helped establish cellular automata as a formal model.
Continuous cellular automaton: A grid-based system whose cell values or update rules use continuous rather than discrete quantities. It relaxes the discrete-state assumption central to the standard model.
Neighborhood (cellular automaton): The set of cells whose states influence a given cell’s update. Neighborhood choice determines which local information each update can use.
Elementary cellular automaton: A one-dimensional binary cellular automaton whose updates depend on a cell and its two neighbors. Its 256 possible rules provide a compact catalog of cellular-automaton behavior.
Lattice gas automaton: A cellular automaton that models fluid flow using particles moving and colliding on a lattice. It applies local grid updates to simulate macroscopic fluid behavior.
Stanislaw Ulam: A mathematician whose work with grid-based simulations helped shape cellular automata. His suggestions helped von Neumann study self-reproduction on a discrete lattice.
Asynchronous cellular automaton: A cellular automaton in which cells update at different times or in an order not fixed to one shared step. It contrasts with the synchronized updates characteristic of the standard definition.

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