Neighbourhood

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Further information: Cellular automaton#Common dimensions and neighborhoods
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A neighbourhood is the set of nearby cells that are considered by a given rule when determining a cell's next state.

Conway's Game of Life utilizes the Moore neighbourhood, which consists of the eight cells that are either orthogonally or diagonally adjacent to the center cell. Other cellular automata on a square grid use the von Neumann neighbourhood, which consists only of orthogonal neighbours. Larger than Life and higher-range outer totalistic rules feature neighbourhoods with higher ranges - i.e. they include cells located further away from the center. Finally, alternative grid tilings, such as hexagonal and triangular, feature their own neighbourhoods which may or may not correspond to equivalent square grid neighbourhoods.

Representation of the hexagonal neighbourhood on the square tessellation.

Identical cases

For the systematic neighbourhoods implemented in Golly and LifeViewer, the following cases are identical:

  • Range 1 cross, von Neumann, Euclidean and checkerboard
  • Range 1 Moore, circular, hash and star
  • Range 2 von Neumann and Euclidean
  • Range 1 hexagonal and asterisk

See also

External links