Cellular Automata/Neighborhood
1D neighborhood
editSince in 1D there are no shapes, the definition of the neighborhood is usually very simple.
Radial neighborhood
editUsually the neighborhood in 1D is described by its radius , meaning the number of cell left and right from the central cell that are used for the neighborhood. The output cell is positioned at the center.
- Formal definition
Formally the radial neighborhood is the set of neighbors
or simply the neighborhood size with the output cell at the center .
- Symmetries
- reflection symmetry
Stephen Wolfram's notation
editIn Wolframs's texts and many others the number of available cell states and the radius are combined into a pair
- See also
- Stephen Wolfram, Statistical Mechanics of Cellular Automata (1983)
Brickwall neighborhood
editAn unaligned neighborhood, usually the smallest possible . The output cell is positioned at between the two cells of the neighborhood. It is usually processed by alternatively shifting the output cell between and .
2D neighborhood
editvon Neumann neighborhood
editIt is the smallest symmetric 2D aligned neighborhood usually described by directions on the compass sometimes the central cell is omitted.
- Formal definition
Formally the von Neumann neighborhood is the set of neighbors
or a subset of the rectangular neighborhood size with the output cell at the center .
- Symmetries
- reflection symmetry
- rotation symmetry 4-fold
- See also
Moore neighborhood
editIs a simple square (usually 3×3 cells) with the output cell in the center. Usually cells in the neighborhood are described by directions on the compass sometimes the central cell is omitted.
- Formal definition
Formally the Moore neighborhood is the set of neighbors
or simply a square size with the output cell at the center .
- Symmetries
- reflection symmetry
- rotation symmetry 4-fold
- See also
- [mathworld] - [Moore Neighborhood]
Margolus neighborhood
editreversible
see also [1]
Unaligned rectangular neighborhood
editAn unaligned (brickwall) rectangular neighborhood, usually the smallest possible . The output cell is positioned at between the four cells of the neighborhood. It is usually processed by alternatively shifting the output cell to and .
Hexagonal neighborhood
editHexagonal neighborhood
edit- Symmetries
- reflection symmetry
- rotation symmetry 6-fold
Small unaligned hexagonal neighborhood
edit- Formal definition
Formally the small (3-cell) unaligned hexagonal neighborhood represented on a rectangular lattice is the set of neighbors
- Symmetries
- reflection symmetry
- rotation symmetry 3-fold
References
edit- [mathworld] - [Neighborhood]