Difference between revisions of "Cellular automaton"
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An initial state (time t = 0) is selected by assigning a state for each cell. | An initial state (time t = 0) is selected by assigning a state for each cell. | ||
| − | A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. | + | A new generation is created (advancing t by 1), according to some fixed rule (generally, a [[Function (mathematics)|mathematical function]]) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. |
| − | Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton. | + | Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the [[stochastic cellular automaton]] and [[asynchronous cellular automaton]]. |
== See also == | == See also == | ||
| + | * [[Automata theory]] | ||
| + | * [[Bidirectional traffic]] | ||
| + | * [[Cantor space]] | ||
| + | * [[Cellular automata in popular culture]] | ||
* [[Computability theory]] | * [[Computability theory]] | ||
* [[Conway's Game of Life]] | * [[Conway's Game of Life]] | ||
| + | * [[Cyclic cellular automaton]] | ||
* [[Discrete mathematics]] | * [[Discrete mathematics]] | ||
| + | * [[Elementary cellular automaton]] | ||
| + | * [[Excitable medium]] | ||
| + | * [[Mirek's Cellebration]] | ||
| + | * [[Movable cellular automaton]] | ||
* [[Procedural generation]] | * [[Procedural generation]] | ||
| + | * [[Quantum cellular automata]] | ||
| + | * [[Reversible cellular automaton]] | ||
| + | * [[Second-order cellular automaton]] | ||
| + | * [[Spatial decision support system]] | ||
| + | * [[Turmites]] | ||
=== Specific rules === | === Specific rules === | ||
| Line 56: | Line 70: | ||
=== Software === | === Software === | ||
| + | |||
* [https://github.com/gollygang/ready Ready] - "Ready is a program for exploring continuous and discrete cellular automata, including reaction-diffusion systems, on grids and arbitrary meshes." | * [https://github.com/gollygang/ready Ready] - "Ready is a program for exploring continuous and discrete cellular automata, including reaction-diffusion systems, on grids and arbitrary meshes." | ||
Latest revision as of 09:05, 4 April 2017
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling.
Contents
Description
Cellular automata are also called:
- Cellular spaces
- Tessellation automata
- Homogeneous structures
- Cellular structures
- Tessellation structures
- Iterative arrays
A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice).
The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell.
An initial state (time t = 0) is selected by assigning a state for each cell.
A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood.
Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton.
See also
- Automata theory
- Bidirectional traffic
- Cantor space
- Cellular automata in popular culture
- Computability theory
- Conway's Game of Life
- Cyclic cellular automaton
- Discrete mathematics
- Elementary cellular automaton
- Excitable medium
- Mirek's Cellebration
- Movable cellular automaton
- Procedural generation
- Quantum cellular automata
- Reversible cellular automaton
- Second-order cellular automaton
- Spatial decision support system
- Turmites
Specific rules
- Brian's Brain
- Langton's ant
- Wireworld
- Rule 30
- Rule 90
- Rule 184
- von Neumann cellular automata
- Nobili cellular automata
- Codd's cellular automaton
- Langton's loops
- CoDi
Problems solved
Problems that can be solved with cellular automata include:
External links
- Cellular automaton @ Wikipedia
- Elementary cellular automata @ mathworld.wolfram.com
Software
- Ready - "Ready is a program for exploring continuous and discrete cellular automata, including reaction-diffusion systems, on grids and arbitrary meshes."
