Square tiling: Difference between revisions
No edit summary |
|||
| Line 5: | Line 5: | ||
== Neighbourhoods on the square grid == | == Neighbourhoods on the square grid == | ||
=== Range-1 cases === | |||
Most of the cellular automata which are investigated are isotropic and use neighbourhoods of range 1. These constraints permit two neighbourhoods of interest; the 4-cell ''[[von Neumann neighbourhood]]'', consisting of the four cells orthogonally adjacent to a central cell, and the 8-cell ''[[Moore neighbourhood]]'', consisting of the four cells orthogonally adjacent to a central cell as well as the four cells diagonally adjacent to said center cell. (A third neighbourhood, referred to on this wiki as the "saltire" neighbourhood, which consists only of the four cells diagonally adjacent to the central cell, functionally duplicates the von Neumann neighbourhood and is disregarded in this section for the sake of brevity.) | Most of the cellular automata which are investigated are isotropic and use neighbourhoods of range 1. These constraints permit two neighbourhoods of interest; the 4-cell ''[[von Neumann neighbourhood]]'', consisting of the four cells orthogonally adjacent to a central cell, and the 8-cell ''[[Moore neighbourhood]]'', consisting of the four cells orthogonally adjacent to a central cell as well as the four cells diagonally adjacent to said center cell. (A third neighbourhood, referred to on this wiki as the "saltire" neighbourhood, which consists only of the four cells diagonally adjacent to the central cell, functionally duplicates the von Neumann neighbourhood and is disregarded in this section for the sake of brevity.) | ||
{| style="margin: | {| class="wikitable" style="margin-left: auto; margin-right: auto; text-align: center;" | ||
| [[File:von Neumann neighbourhood (range 1).png]] | |||
| [[File:von Neumann neighbourhood (range 1).png | | [[File:Moore neighbourhood (range 1).png]] | ||
| [[File:Moore neighbourhood (range 1).png| | | [[File:Saltire neighbourhood (range 1).png]] | ||
|- | |||
! von<br>Neumann | |||
! Moore | |||
! saltire<br>''(trivial)'' | |||
|} | |} | ||
== Symmetries == | == Symmetries == | ||
Revision as of 13:44, 11 January 2022
The square grid, square tiling or square tessellation is one of the three possible proper Euclidean tilings of 2D space, in which four squares are placed at each vertex.
The square grid is the most familiar of all 2D tilings, with cell positions being easily and uniquely defined via Cartesian coordinates, and is the grid on which cellular automata are simulated most frequently.
Neighbourhoods on the square grid
Range-1 cases
Most of the cellular automata which are investigated are isotropic and use neighbourhoods of range 1. These constraints permit two neighbourhoods of interest; the 4-cell von Neumann neighbourhood, consisting of the four cells orthogonally adjacent to a central cell, and the 8-cell Moore neighbourhood, consisting of the four cells orthogonally adjacent to a central cell as well as the four cells diagonally adjacent to said center cell. (A third neighbourhood, referred to on this wiki as the "saltire" neighbourhood, which consists only of the four cells diagonally adjacent to the central cell, functionally duplicates the von Neumann neighbourhood and is disregarded in this section for the sake of brevity.)
.png)
|
.png)
|
.png)
|
| von Neumann |
Moore | saltire (trivial) |
|---|