Moore neighborhood

E169176

The Moore neighborhood is a pattern in cellular automata where each cell interacts with all surrounding cells in a square grid, including diagonals, commonly used in Conway’s Game of Life.

All labels observed (1)

Label Occurrences
Moore neighborhood canonical 2

How this entity was disambiguated

Statements (43)

Predicate Object
instanceOf cellular automaton neighborhood
alternativeName 8-neighborhood (for radius 1 in 2D)
cardinalityGrowth quadratic in radius r in 2D
cellInteractionType local interaction
centerIncludedCountFormula (2r + 1)^2 (in 2D, including center)
commonlyAssumedBoundary periodic boundary conditions (in finite grids)
componentOf definition of Conway's Game of Life rule B3/S23
connectivity 8-way connectivity in 2D
contrastedWith von Neumann neighborhood
definedOn square grid
dimension two-dimensional (standard form)
distanceMetric Chebyshev distance (L-infinity metric)
fieldOfStudy cellular automata theory
discrete mathematics
Theoretical Computer Science
surface form: theoretical computer science
generalization can be defined for higher radii r > 1
gridType orthogonal lattice
includes diagonally adjacent cells
orthogonally adjacent cells
includesCenterCell true (when counting total neighborhood size)
introducedInContextOf early cellular automata research
latticeRequirement regular square tiling
namedAfter Edward F. Moore
neighborCountFormula (2r + 1)^2 - 1 (in 2D, excluding center)
neighborhoodRadius 1 (for the standard Moore neighborhood)
numberOfNeighbors 8 (for radius 1 in 2D)
relationToMetric corresponds to Chebyshev distance ≤ r in 2D
relationToVonNeumann superset of von Neumann neighborhood in 2D
shape square (in 2D grids)
spaceType discrete space
symmetry reflection symmetry across grid axes
rotational symmetry of order 4 in 2D
topologyType 8-connected neighborhood
totalCellsWithCenter 9 (for radius 1 in 2D)
updateDependency state of all surrounding cells in the 3x3 block
updateRuleScope local but isotropic on the square grid
usedFor defining local update rules in cellular automata
image processing operations
modeling diffusion processes
usedIn Game of Life
surface form: Conway's Game of Life

agent-based models on grids
cellular automata
lattice-based simulations

How these facts were elicited

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Game of Life neighborhoodType Moore neighborhood
R-pentomino neighborhood Moore neighborhood