Cellular automaton

related topics
{math, number, function}
{acid, form, water}
{math, energy, light}
{system, computer, user}
{@card@, make, design}
{theory, work, human}
{area, community, home}
{work, book, publish}
{disease, patient, cell}
{specie, animal, plant}
{area, part, region}
{ship, engine, design}
{black, white, people}
{style, bgcolor, rowspan}

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. It 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 (usually including the cell itself) is defined relative to the specified cell. For example, the neighborhood of a cell might be defined as the set of cells a distance of 2 or less from the 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. For example, the rule might be that the cell is "On" in the next generation if exactly two of the cells in the neighborhood are "On" in the current generation, otherwise the cell is "Off" in the next generation. 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.

Contents

Full article ▸

related documents
Wiener process
Plane (geometry)
Euclidean space
Gradient
Dihedral group
Euler characteristic
Shor's algorithm
Probability density function
Goldbach's conjecture
Homology (mathematics)
Breadth-first search
Chaitin's constant
Linear independence
Type theory
Factorization
Glossary of topology
Euclidean algorithm
Heine–Borel theorem
Axiom schema of replacement
Pushdown automaton
Presentation of a group
MATLAB
Natural number
Preprocessor
Binary relation
Fourier analysis
Abstract interpretation
Random variable
E (mathematical constant)
Algebraic structure