# Category: Cellular automaton rules

Biham–Middleton–Levine traffic model
The Biham–Middleton–Levine traffic model is a self-organizing cellular automaton traffic flow model. It consists of a number of cars represented by points on a lattice with a random starting position,
Rule 90
In the mathematical study of cellular automata, Rule 90 is an elementary cellular automaton based on the exclusive or function. It consists of a one-dimensional array of cells, each of which can hold
Cyclic cellular automaton
A cyclic cellular automaton is a kind of cellular automaton rule developed by and studied by several other cellular automaton researchers. In this system, each cell remains unchanged until some neighb
Wireworld
Wireworld is a cellular automaton first proposed by Brian Silverman in 1987, as part of his program Phantom Fish Tank. It subsequently became more widely known as a result of an article in the "Comput
Day and Night (cellular automaton)
Day and Night is a cellular automaton rule in the same family as Game of Life. It is defined by rule notation B3678/S34678, meaning that a dead cell becomes live (is born) if it has 3, 6, 7, or 8 live
Von Neumann cellular automaton
Von Neumann cellular automata are the original expression of cellular automata, the development of which was prompted by suggestions made to John von Neumann by his close friend and fellow mathematici
Lenia
Lenia is a family of cellular automata created by Bert Wang-Chak Chan. It is intended to be a continuous generalization of Conway's Game of Life. As a consequence of its continuous, high-resolution do
Life without Death
Life without Death is a cellular automaton, similar to Conway's Game of Life and other Life-like cellular automaton rules. In this cellular automaton, an initial seed pattern grows according to the sa
CoDi
CoDi is a cellular automaton (CA) model for spiking neural networks (SNNs). CoDi is an acronym for Collect and Distribute, referring to the signals and spikes in a neural network. CoDi uses a von Neum
Turmite
In computer science, a turmite is a Turing machine which has an orientation in addition to a current state and a "tape" that consists of an infinite two-dimensional grid of cells. The terms ant and va
Brian's Brain
Brian's Brain is a cellular automaton devised by Brian Silverman, which is very similar to his Seeds rule.
Life-like cellular automaton
A cellular automaton (CA) is Life-like (in the sense of being similar to Conway's Game of Life) if it meets the following criteria: * The array of cells of the automaton has two dimensions. * Each c
Conway's Game of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined
3D Life
3D Life is a cellular automaton. It is a three-dimensional extension of Game of Life, investigated by Carter Bays. A number of different semitotalistic rules for the 3D rectangular Moore neighborhood
Rule 110
The Rule 110 cellular automaton (often called simply Rule 110) is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos. In this respect, it is similar
Langton's ant
Langton's ant is a two-dimensional universal Turing machine with a very simple set of rules but complex emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of blac
Codd's cellular automaton
Codd's cellular automaton is a cellular automaton (CA) devised by the British computer scientist Edgar F. Codd in 1968. It was designed to recreate the computation- and construction-universality of vo
Nobili cellular automata
Nobili cellular automata (NCA) are a variation of von Neumann cellular automata (vNCA), in which additional states provide means of memory and the interference-free crossing of signal. Nobili cellular
Critters (cellular automaton)
Critters is a reversible block cellular automaton with similar dynamics to Conway's Game of Life, first described by Tommaso Toffoli and Norman Margolus in 1987.
Rule 184
Rule 184 is a one-dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particl
Highlife (cellular automaton)
Highlife is a cellular automaton similar to Conway's Game of Life. It was devised in 1994 by Nathan Thompson. It is a two-dimensional, two-state cellular automaton in the "Life family" and is describe
Toom's rule
Toom's rule is a 2-dimensional cellular automaton model created by Andrei Toom in 1978. This model is both more robust and simpler than the 2-dimensional majority vote rule. Toom's rule is a cellular
Greenberg–Hastings cellular automaton
The Greenberg–Hastings Cellular Automaton (abbrev. GH model) is a three state two dimensional cellular automaton (abbrev CA) named after James M. Greenberg and Stuart Hastings, designed to model excit
Wa-Tor
Wa-Tor is a population dynamics simulation devised by A. K. Dewdney and presented in the December 1984 issue of Scientific American in a five-page article entitled "Computer Recreations: Sharks and fi
Seeds (cellular automaton)
Seeds is a cellular automaton in the same family as the Game of Life, initially investigated by Brian Silverman and named by Mirek Wójtowicz. It consists of an infinite two-dimensional grid of cells,
Byl's loop
The Byl's loop is an artificial lifeform similar in concept to Langton's loop. It is a two-dimensional, 5-neighbor cellular automaton with 6 states per cell, and was developed in 1989 by John Byl, fro
Ulam–Warburton automaton
The Ulam–Warburton cellular automaton (UWCA) is a 2-dimensional fractal pattern that grows on a regular grid of cells consisting of squares. Starting with one square initially ON and all others OFF, s
Abelian sandpile model
The Abelian sandpile model (ASM) is the more popular name of the original Bak–Tang–Wiesenfeld model (BTW). BTW model was the first discovered example of a dynamical system displaying self-organized cr
Paterson's worms
Paterson's worms are a family of cellular automata devised in 1971 by Mike Paterson and John Horton Conway to model the behaviour and feeding patterns of certain prehistoric worms. In the model, a wor
Sugarscape
Sugarscape is a model for artificially intelligent agent-based social simulation following some or all rules presented by Joshua M. Epstein & Robert Axtell in their book Growing Artificial Societies.
Rule 30
Rule 30 is an elementary cellular automaton introduced by Stephen Wolfram in 1983. Using Wolfram's classification scheme, Rule 30 is a Class III rule, displaying aperiodic, chaotic behaviour. This rul
Nagel–Schreckenberg model
The Nagel–Schreckenberg model is a theoretical model for the simulation of freeway traffic. The model was developed in the early 1990s by the German physicists Kai Nagel and Michael Schreckenberg. It
Langton's loops
Langton's loops are a particular "species" of artificial life in a cellular automaton created in 1984 by Christopher Langton. They consist of a loop of cells containing genetic information, which flow