Difference between revisions of "Triangular neighbourhood"

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The triangular neigbourhood can either refer to:
The triangular neigbourhood can either refer to:
* The 12-cell triangular neighbourhood (sometimes referred to as the Triangular Moore neighbourhood)
* The 12-cell triangular neighbourhood (sometimes referred to as the Triangular Moore neighbourhood)
[[File:Triangular12.png|150px]]
* The 9-cell triangular vertices neighbourhood
* The 9-cell triangular vertices neighbourhood
[[File:Triangular9.png|150px]]
* The 3-cell triangular edges neighbourhood (sometimes referred to as the Triangular von Neumann neighbourhood.
* The 3-cell triangular edges neighbourhood (sometimes referred to as the Triangular von Neumann neighbourhood.
[[File:Triangular3.png|150px]]


The triangular tiling shares its symmetries with that of the hexagonal tiling.
The triangular tiling shares its symmetries with that of the hexagonal tiling.

Revision as of 11:48, 5 April 2019

The triangular neighbourhood is the set of all cells that are adjacent to the region of interest in a grid tiled with triangles (the region of interest itself may or may not be considered part of the triangular neighbourhood, depending on context).

The triangular neigbourhood can either refer to:

  • The 12-cell triangular neighbourhood (sometimes referred to as the Triangular Moore neighbourhood)

File:Triangular12.png

  • The 9-cell triangular vertices neighbourhood

File:Triangular9.png

  • The 3-cell triangular edges neighbourhood (sometimes referred to as the Triangular von Neumann neighbourhood.

File:Triangular3.png

The triangular tiling shares its symmetries with that of the hexagonal tiling.

Software support

These triangular neighbourhoods are currently in testing for LifeViewer as of build 318. Triangular tiling is dealt with using 2 states and the following neighbourhood on a square tiling:

File:Triangular neighbourhood (radius 1).png

Generations is also supported.

TriLife.zip is available on Golly's online pattern archive, and simulates 2-state triangular outer-totalistic rule's using 4 states, dividing each square cell into two triangles.

Symmetries

Main article: Symmetry

The triangular neighbourhood relies on a different grid than the Moore and von Neumann neighborhoods and thus features a different set of inherent symmetries when dealing with isotropic rules:

  • Asymmetric (C1, 8x32, 4x64, 2x128, 1x256)
  • C2_1
  • C2_4
  • C3_1
  • C3_3
  • C6
  • D2_xo
  • D2_x
  • D4_x1
  • D4_x4
  • D6_1
  • D6_1o
  • D6_3
  • D12

See also

External links