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Discrete model of computation
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called
Cellular_automaton
Mathematics concept
mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0
Elementary_cellular_automaton
Cellular automaton that can be run backwards
A reversible cellular automaton is a cellular automaton in which every configuration has a unique predecessor. That is, it is a regular grid of cells,
Reversible_cellular_automaton
Abstract model of quantum computation
A quantum cellular automaton (QCA) is an abstract model of quantum computation, devised in analogy to conventional models of cellular automata introduced
Quantum_cellular_automaton
Kind of cellular automaton
A block cellular automaton or partitioning cellular automaton is a special kind of cellular automaton in which the lattice of cells is divided into non-overlapping
Block_cellular_automaton
Cellular automaton pattern that emits spaceships
In a cellular automaton, a gun is a pattern with a main part that repeats periodically, like an oscillator, and that also periodically emits spaceships
Gun_(cellular_automaton)
2D cellular automaton similar to Conway's Game of Life
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
Seeds_(cellular_automaton)
Cellular automaton with probabilistic rules
A stochastic cellular automaton (SCA), also known as a probabilistic cellular automaton (PCA), is a type of computational model. It consists of a grid
Stochastic_cellular_automaton
Pattern that has no predecessors
In a cellular automaton, a Garden of Eden is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot
Garden of Eden (cellular automaton)
Garden_of_Eden_(cellular_automaton)
2D cellular automaton devised by Edgar F. Codd in 1968
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
Codd's_cellular_automaton
Type of cellular automaton with similarities to Conway's Game of Life
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
Life-like_cellular_automaton
Reversible block 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
Critters_(cellular_automaton)
Type of moving pattern which periodically produces spaceships
A rake, in the lexicon of cellular automata, is a type of puffer train, which is an automaton that leaves behind a trail of debris. In the case of a rake
Rake_(cellular_automaton)
Method in computational solid mechanics based on the discrete concept
The movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept. It provides advantages both of
Movable_cellular_automaton
2D cellular automaton similar to Conway's Game of Life
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
Highlife_(cellular_automaton)
Type of pattern that returns to its original configuration after a number of steps
In a cellular automaton, an oscillator is a pattern that returns to its original state, in the same orientation and position, after a finite number of
Oscillator (cellular automaton)
Oscillator_(cellular_automaton)
Two-dimensional cellular automaton
Game of Life (sometimes abbreviated as CGoL) or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It
Conway's_Game_of_Life
Type of pattern whose population grows without bound but does not tend to infinity
In a cellular automaton, a finite pattern is called a sawtooth if its population grows without bound but does not tend to infinity. In other words, a sawtooth
Sawtooth_(cellular_automaton)
Elementary cellular automaton
The Rule 110 cellular automaton (often called simply Rule 110) is an elementary cellular automaton with interesting behavior on the boundary between stability
Rule_110
Type of pattern that periodically changes position
In a cellular automaton, a finite pattern is called a spaceship if it reappears after a certain number of generations in the same orientation but in a
Spaceship (cellular automaton)
Spaceship_(cellular_automaton)
Automated methods for the creation of mazes
corridors compared with Maze, with the rule B3/S12345. Since these cellular automaton rules are deterministic, each maze generated is uniquely determined
Maze_generation_algorithm
Type of pattern that infinitely produces copies of itself
In cellular automata, a replicator is a pattern that produces copies of itself. In the one-dimensional Rule 90 cellular automaton, every pattern is a replicator
Replicator (cellular automaton)
Replicator_(cellular_automaton)
Type of cellular automaton
making it extremely practical to perform computing with them. A cellular automaton (CA) is a discrete dynamical system consisting of a uniform (finite
Quantum dot cellular automaton
Quantum_dot_cellular_automaton
Type of pattern that grows quadratically
In cellular automata such as Conway's Game of Life, a breeder is a pattern that exhibits quadratic growth, by generating multiple copies of a secondary
Breeder_(cellular_automaton)
Type of reversible cellular automaton
A second-order cellular automaton is a type of reversible cellular automaton (CA) invented by Edward Fredkin where the state of a cell at time t depends
Second-order cellular automaton
Second-order_cellular_automaton
Cellular automaton used to model universal construction
Neumann's universal constructor. Nobili cellular automaton is a variation of von Neumann's cellular automaton, augmented with the ability for confluent
Von Neumann cellular automaton
Von_Neumann_cellular_automaton
Type of pattern that takes many generations to stabilize
In cellular automata, a methuselah is a small "seed" pattern of initial live cells that take a large number of generations in order to stabilize. More
Methuselah (cellular automaton)
Methuselah_(cellular_automaton)
A cyclic cellular automaton is a kind of cellular automaton rule developed by David Griffeath and studied by several other cellular automaton researchers
Cyclic_cellular_automaton
2D cellular automaton with black/white reversal symmetry
Day and Night is a two-dimensional Life-like cellular automaton rule related to Game of Life. It is defined by the rule notation B3678/S34678: a dead cell
Day and Night (cellular automaton)
Day_and_Night_(cellular_automaton)
Type of pattern that does not change from one generation to the next
In cellular automata, a still life is a pattern that does not change from one generation to the next. The term comes from the art world where a still life
Still life (cellular automaton)
Still_life_(cellular_automaton)
Type of pattern which temporarily appears at the edge of a larger pattern
In Conway's Game of Life and similar cellular automaton rules, a spark is a small collection of live cells that appears at the edge of some larger pattern
Spark_(cellular_automaton)
Independently updating cells
the new states influence other cells. In contrast, an asynchronous cellular automaton is able to update individual cells independently, in such a way that
Asynchronous cellular automaton
Asynchronous_cellular_automaton
Type of pattern that can redirect a stream of incoming spaceships
In cellular automata such as Conway's Game of Life, a reflector is a pattern that can interact with a spaceship to change its direction of motion, without
Reflector (cellular automaton)
Reflector_(cellular_automaton)
Continuous generalization of cellular automata
that any cellular automaton could be represented as a convolutional neural network, and trained neural networks to reproduce existing cellular automata
Lenia
density classification task, is the problem of finding one-dimensional cellular automaton rules that accurately perform majority voting. Using local transition
Majority_problem
Elementary cellular automaton
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,
Rule_30
Encoding of 1D cellular automaton rules
Wolfram code is a widely used numbering system for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper and popularized
Wolfram_code
Postulate in particle physics
formulation Parton model Sticky bead argument One-electron universe Quantum cellular automaton Rogers Commission Report Feynman checkerboard Feynman sprinkler Works
One-electron_universe
Self-replicating cellular automaton
Neumann's universal constructor is a self-replicating machine in a cellular automaton (CA) environment. It was designed in the 1940s, without the use of
Von Neumann universal constructor
Von_Neumann_universal_constructor
to itself represents the transition function of a one-dimensional cellular automaton if and only if it is continuous (with respect to the Cantor topology)
Curtis–Hedlund–Lyndon_theorem
Self-operating machine
An automaton (/ɑːˈtɑːmətɑːn/ ; pl.: automata or automatons) is a relatively self-operating machine or control mechanism designed to automatically follow
Automaton
Self-reproducing cellular automaton patterns
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
Langton's_loops
Two-dimensional Turing machine with emergent behavior
square, move forward one unit Langton's ant can also be described as a cellular automaton, where the grid is colored black or white and the "ant" square has
Langton's_ant
Topics referred to by the same term
of documents Rule 34, the Wolfram code for a particular elementary cellular automaton The 34th Rule, a 1999 Star Trek: Deep Space Nine novel This disambiguation
Rule_34_(disambiguation)
Fractal composed of triangles
certain cellular automata (such as Rule 90), including those relating to Conway's Game of Life. For instance, the Life-like cellular automaton B1/S12 when
Sierpiński_triangle
Maximum rate at which information propagates in a cellular automaton grid
In Conway's Game of Life (and related cellular automata), the speed of light is a propagation rate across the grid of exactly one step (either horizontally
Speed of light (cellular automaton)
Speed_of_light_(cellular_automaton)
Rakha-Pasumarthy-Adjerid model (RPA model) Fadhloun-Rakha model (FR model) Cellular automaton (CA) models use integer variables to describe the dynamical properties
Microscopic traffic flow model
Microscopic_traffic_flow_model
Topics referred to by the same term
Tamayo Still life photography Still life (cellular automaton), an unchanging pattern in a cellular automaton Still Life (video game), a 2005 video game
Still_Life_(disambiguation)
Elementary cellular automaton
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
Rule_90
Topics referred to by the same term
Look up cellular in Wiktionary, the free dictionary. Cellular may refer to: Cellular automaton, a model in discrete mathematics Cell biology, the evaluation
Cellular
2D cellular automaton similar to Conway's Game of Life
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
Life_without_Death
Type of cellular automaton
Lattice gas automata (LGCA), or lattice gas cellular automata, are a type of cellular automaton used to simulate fluid flows, pioneered by Hardy–Pomeau–de
Lattice_gas_automaton
Topics referred to by the same term
especially those who have many children Breeder (cellular automaton), a pattern in a cellular automaton which grows quadratically Breeder (film), a 2026
Breeder_(disambiguation)
Excitable cellular automaton
The Greenberg–Hastings Cellular Automaton (abbrev. GH model) is a two dimensional cellular automaton (abbrev. CA) named after James M. Greenberg and Stuart
Greenberg–Hastings cellular automaton
Greenberg–Hastings_cellular_automaton
Idea that the universe is fundamentally computational or informational
emergent from the automaton's processing. Zuse, Fredkin, Toffoli and Margolus all worked within this frame. 'T Hooft's cellular automaton interpretation
Digital_physics
2D cellular automaton devised by Brian Silverman in 1987
Wireworld, alternatively WireWorld, is a cellular automaton first proposed by Brian Silverman in 1987, as part of his program Phantom Fish Tank. It subsequently
Wireworld
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
Ulam–Warburton_automaton
Cellular automaton pattern
In a cellular automaton, a puffer train, or simply puffer, is a finite pattern that moves itself across the "universe", leaving debris ("ash") behind.
Puffer_train
Moving pattern in Conway's Game of Life
synthesis in Conway's Game of Life and other cellular automata". In Adamatzky, Andrew (ed.). Game of Life Cellular Automata. Springer-Verlag. pp. 115–134.
Glider (Conway's Game of Life)
Glider_(Conway's_Game_of_Life)
Elementary cellular automaton
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
Rule_184
Topics referred to by the same term
to in vacuum Speed of light (cellular automaton), the greatest rate of information propagation in a cellular automaton "Speed of Light", a song by the
Speed of light (disambiguation)
Speed_of_light_(disambiguation)
Ability of a computing system to simulate Turing machines
computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it
Turing_completeness
Mathematical model of the time dependence of a point in space
integers the system is called a semi-cascade.[clarification needed] A cellular automaton is a tuple (T, M, Φ), with T a lattice such as the integers or a higher-dimensional
Dynamical_system
Cellular automaton neighborhood consisting of four adjacent cells
named after John von Neumann, who used it to define the von Neumann cellular automaton and the von Neumann universal constructor within it. It is one of
Von_Neumann_neighborhood
Type of cellular automaton
configuration of von Neumann cellular automata, and the computational throughput is increased. In von Neumann's original cellular automaton, the crossing of signals
Nobili_cellular_automata
Toom's rule is a 2-dimensional cellular automaton model created by Andrei Toom in 1978. It is a modification of the 2-dimensional majority vote rule and
Toom's_rule
2D cellular automaton devised by Brian Silverman
Brian's Brain is a cellular automaton devised by Brian Silverman, which is very similar to his Seeds rule. Brian's Brain consists of an infinite two-dimensional
Brian's_Brain
Concept in computer science
uses quantum mechanics Quantum dot cellular automaton – Type of cellular automaton, a variant of reversible cellular automata Toffoli gate – Universal
Reversible_computing
Traffic simulation model
physicists Kai Nagel and Michael Schreckenberg. It is essentially a simple cellular automaton model for road traffic flow that can reproduce traffic jams, i.e.
Nagel–Schreckenberg_model
Canadian-American physicist and computer scientist
inventing the block cellular automaton and the Margolus neighborhood for block cellular automata, which he used to develop cellular automaton simulations of
Norman_Margolus
American mathematician
computer scientist who is best known for having proved that the Rule 110 cellular automaton is Turing-complete. Cook was born in Morgantown, West Virginia and
Matthew_Cook
Methods that imitate, replicate or use natural processes
dating back to the 1960s, states that the entire universe is a huge cellular automaton which continuously updates its rules. Recently it has been suggested
Natural_computing
mathematics, a surjunctive group is a group such that every injective cellular automaton with the group elements as its cells is also surjective. Surjunctive
Surjunctive_group
Book by Stephen Wolfram
universe is a rewriting network, not a cellular automaton, as Wolfram himself has suggested a cellular automaton cannot account for relativistic features
A_New_Kind_of_Science
English mathematician (1937–2020)
branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent
John_Horton_Conway
Topics referred to by the same term
Life also often refers to: Conway's Game of Life, in mathematics, a cellular automaton Game of Life or The Game of Life may also refer to: Life Game, the
The Game of Life (disambiguation)
The_Game_of_Life_(disambiguation)
Cellular automaton
referred to this model as the Abelian sandpile model. The model is a cellular automaton. In its original formulation, each site on a finite grid has an associated
Abelian_sandpile_model
Kind of evolutionary algorithm
Cellular automaton Dual-phase evolution Enrique Alba Evolutionary algorithm Metaheuristic Parallel metaheuristic E. Alba, B. Dorronsoro, Cellular Genetic
Cellular evolutionary algorithm
Cellular_evolutionary_algorithm
Cellular automaton neighborhood consisting of eight adjacent cells
dimensions, for example forming a 26-cell cubic neighborhood for a cellular automaton in three dimensions, as used by 3D Life. In dimension d, where 0 ≤
Moore_neighborhood
Topics referred to by the same term
Critter may refer to: Critter (chess), a Slovak chess engine Critters (cellular automaton) Critters (comics), an anthology comic book published by Fantagraphics
Critter
Cellular automaton
in concept to Langton's loop. It is a two-dimensional, 5-neighbor cellular automaton with 7 states per cell, and was developed in 1989 by John Byl, from
Byl's_loop
Computer science problem
problem is a problem in computer science and cellular automata in which the goal is to design a cellular automaton that, starting with a single active cell
Firing squad synchronization problem
Firing_squad_synchronization_problem
Type of computer architecture prominent in parallel computing
fine-grained optimization but makes software development more complex. Cellular automaton "Cell Designer talks about PS3 and IBM Cell Processors". Archived
Cellular_architecture
Book by Konrad Zuse
Zuse proposed that the universe is being computed by some sort of cellular automaton or other discrete computing machinery, challenging the long-held view
Calculating_Space
lattice-gas cellular automaton (BIO-LGCA) is a discrete model for moving and interacting biological agents, a type of cellular automaton. The BIO-LGCA
BIO-LGCA
Study of abstract machines and automata
of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows). As the automaton sees
Automata_theory
Algorithm for speeding up cellular automaton simulations
cellular automata, much more quickly than would be possible using alternative algorithms that simulate each time step of each cell of the automaton.
Hashlife
Topics referred to by the same term
the Thunderbirds and Captain Scarlett puppet series 0X, a living cellular automaton from the Of Man and Manta novels Zero X, an electric motorcycle model
0X
Italian-American professor of electrical and computer engineering (born 1943)
computer Block cellular automaton CAM-6 Computronium Critters (cellular automaton) Programmable matter Reversible cellular automaton Toffoli, Tommaso
Tommaso_Toffoli
Turing machine on a two-dimensional grid
absolute turmites are of course simply known as Turing machines.) Cellular automaton – Discrete model of computation Langton's ant – Two-dimensional Turing
Turmite
Topics referred to by the same term
by Mathematica Wolfram code, a naming system for one-dimensional cellular automaton rules introduced by Stephen Wolfram Wolfram syndrome, a genetic disorder
Wolfram
1994 science fiction novel by Greg Egan
reality. The Autoverse is an artificial life simulator based on a cellular automaton complex enough to represent the substratum of an artificial chemistry
Permutation_City
Class of theories in quantum mechanics
2022 by Donadi and Hossenfelder. Gerard 't Hooft has referred to his cellular automaton model of quantum mechanics as superdeterministic though it has remained
Superdeterminism
Cellular automaton model for spiking neural networks
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
CoDi
logic-based automaton, not requiring a physical body but based on the changing states of the cells in an infinite grid – the first cellular automaton. It was
History_of_artificial_life
Abstract machines which have a continuum of locations with finite states
spatial automaton is a type of computer model studied in automata theory, a subfield of computer science. It is similar to a cellular automaton, in that
Continuous_spatial_automaton
Type of conservative logic circuit
computers on several types of reversible cellular automaton, including block cellular automata and second-order cellular automata. In these simulations, the
Billiard-ball_computer
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
Wa-Tor
Topics referred to by the same term
refer more specifically to a Turing machine, finite-state machine, or cellular automaton a stochastic kernel In statistics and probability theory, the conditional
Transition_function
Geometric fractal-like pattern
T-square fractal, or the arrangement of cells in the Ulam–Warburton cellular automaton. All of the bounded regions surrounded by toothpicks in the pattern
Toothpick_sequence
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